#include <SnowDrift.h>

Public Member Functions
	SnowDriftA3D (const mio::DEMObject &dem, const mio::Config &cfg)

virtual	~SnowDriftA3D ()

virtual void	setSnowSurfaceData (const mio::Grid2DObject &cH_in, const mio::Grid2DObject &sp_in, const mio::Grid2DObject &rg_in, const mio::Grid2DObject &N3_in, const mio::Grid2DObject &rb_in)

void	setSnowPack (SnowpackInterface &mysnowpack)

void	setEnergyBalance (EnergyBalance &myeb)

virtual void	Compute (const mio::Date &calcDate)
	Main: Calls the essential routines. More...

bool	isNewWindField (const unsigned int current_step)

void	setMeteo (const unsigned int &steps, const mio::Grid2DObject &new_psum, const mio::Grid2DObject &new_psum_ph, const mio::Grid2DObject &new_p, const mio::Grid2DObject &new_vw, const mio::Grid2DObject &new_rh, const mio::Grid2DObject &new_ta, const mio::Grid2DObject &new_ilwr, const mio::Date &calcDate, const std::vector< mio::MeteoData > &vecMeteo)
	Sets the required meteo fields. More...

void	GetTResults (double outtime_v[15], double outtime_tau[15], double outtime_salt[15], double outtime_diff[15])

double	getTiming () const

void	Destroy ()

std::string	getGridsRequirements () const

Protected Member Functions
void	Initialize ()
	Initialize for snowdrift Allocate saltation variable, snow height and new snow mass per bottom element. More...

void	ConstructElements ()

void	InitializeNodes (const mio::Grid3DObject &z_readMatr)
	Initialize nodes Each (3D) node receives its (x,y,z), slope, aspect, normals. More...

void	CompleteNodes ()
	Initialize concentration according to the rain rate (uniform) Now calculate the missing parameters Slope in direction of the wind. More...

virtual void	compSaltation (bool setbound)
	Calculate Saltation Fluxes for all Bottom Elements. More...

virtual void	SnowMassChange (bool setbound, const mio::Date &calcDate)

virtual void	Suspension ()

virtual void	Diffusion (double deltaT, double &diff_max, double t)

virtual void	Sublimation ()
	Sublimation Calculates drifting snow sublimation at every node of the concentration field. More...

double	terminalFallVelocity (const double Radius, const double Temperature, const double RH, const double altitude)
	Terminal fall velocity NB assumed to be 0.5. More...

double	calcS (const double concentration, const double sublradius, const double dmdt)
	Calculate sublimation The mass change of a single particle is now extended to all particles. More...

double	calcSubldM (const double Radius, const double AirTemperature, const double RH, const double WindSpeed, const double altitude)
	Calculate sublimation mass change This function calculates the mass change of a single ice particle for the given conditions. More...

double	reynoldsNumberforFallingParticles (const double Radius, const double Windspeed, const double AirTemperature, const double RH, const double altitude)
	Reynolds number Calculate the Reynolds number for a falling particle. More...

double	ventilationVelocity (const double Radius, const double Windspeed, const double AirTemperature, const double RH, const double altitude)
	Ventilation velocity. More...

double	waterVaporDensity (const double Temperature, const double VaporPressure)

double	RH_from_q (const double AirTemp, const double q, const double altitude)
	Relative humidity Gives the relative humidity for a given air temperature and specific humidity. More...

void	initializeTRH ()
	Initialize RH, T and q Initialize fields of humidity and temperature, necessary for sublimation calculations. More...

virtual void	Jacobian (double DETERMINANTJ, double J[][3], const int element, const double P, int k, const int ix, const int iy, const int iz)
	Compute Jacobian This function calculates the Jacobian at the given point P and and stores the value of its determinant at point P in the global variable DETERMINANTJ[k] the input value is the respective element, the position where to store the DETERMINANTJ[k], and the function is of type void, the Jacobian matrix J and the integration point P and the DETERMINANTJ array. More...

virtual void	J0fun (double J0[3][3], const double J[3][3])
	J0 function computes the matrix of cofactors of the input matrix J and stores it in J0. More...

virtual double	GQIntB (double *DETERMINANTJ, const int i, const int j)
	GQIntB returns the integral of the product of basis functions i and j over a hexahedral element using gaussian quadrature, DETERMINANTK[0],...DETERMINANTK[7] contains the determinant of the jacobian of the mapping onto the unit cube evaluated at the corners. More...

virtual double	GQIntC (double *DETERMINANTJ, const double J0M[3][3][8], const int i, const int j, const double b[3], const double K[3][3])
	GQIntC returns the integral of the product of the gradients of basis functions i and j over a hexahedral element using gaussian quadrature, DETERMINANTK[0],...DETERMINANTK[7] contains the determinant of the jacobian of the mapping onto the unit cube evaluated at the corners. More...

virtual double	GQIntApdx (double DETERMINANTJ[], const double J0M[3][3][8], const int i, const int j, double b[], const double deltak)
	GQIntApdx returns the integral of the product of a basis function i and the gradient of basis function j over a hexahedral element using gaussian quadrature, DETERMINANTK[0],...DETERMINANTK[7] contains the determinant of the jacobian of the mapping onto the unit cube evaluated at the corners. More...

virtual double	GQIntAdxdx (double DETERMINANTJ, double J0M[3][3][8], const int i, const int j, double b, const double deltak)
	GQIntAdxdx ... More...

virtual void	TTfun (double TT[3][8], const double P[])
	TT function TTfun is a function calculating the values of the partial derivative of phi at the point P and putting them in a (3,8) array. More...

virtual void	phi (double PHI, double P)
	Phi - shape functions Calculates the value of the 8 shape functions at point P. More...

virtual void	setQuadraturePoints ()

virtual void	matmult (CDoubleArray &res, const CDoubleArray &x, double sm, int ijm)
	matmult computes a matrix vector product for a sparse matrix More...

virtual void	matmult (CDoubleArray &res, const CDoubleArray &x, const CDoubleArray &sA, const CIntArray &colA, CIntArray &rowA)
	matmult computes a matrix vector product for a sparse matrix of CSR format More...

virtual void	transmult (CDoubleArray &res, const CDoubleArray &x, double sm, int ijm)
	transmult this is the transmult function that multiplies the vector x by the transpose of the matrix M in its sparse form sm, ijm More...

virtual void	SolveEquation (int timeStep, int maxTimeStep, const param_type param)
	Solve the advection diffusion equation. More...

virtual void	bicgStab (CDoubleArray &result, CDoubleArray &rhs, const CDoubleArray &sA, const CIntArray &colA, CIntArray &rowA, const int nmax, const double tol, double &testres)
	bicgStab iterative equation solver iterative equation solver Tests : Tested by the followin procedure: given a sparse matrix A (CRS-format) characterized by colA and rowA and an arbitrary, or rather: a few nontrivial examples of a vector x. For each x matmult(y,x,sA,rowA,colA) and bicgStab(result,y,sA,colA,rowA,...) have been computed and then verified that result=x More...

virtual void	assembleSystem (CIntArray &colA, CIntArray &rowA, CDoubleArray &sA, CDoubleArray &sB, CDoubleArray &Psi, CDoubleArray &f, const double dt)
	Assemble System loop over all elements, updates the system matrices A, B and the 'bare' right hand side (rhs) of the system, in other words: prepares the system prior to the inclusion of dirichlet boundary conditions. More...

virtual void	applyBoundaryValues (CDoubleArray &c00, CDoubleArray &Psi)
	applyBoundaryValues Apply boundary values to all elements Author: Marc Ryser More...

virtual void	prepareSolve ()
	prepareSolve Some preparations to solve a 3D-field. More...

virtual void	computeDiffusionTensor (double K[3][3], const unsigned int ix, const unsigned int iy, const unsigned int iz)
	Compute diffusion tensor Computes the diffusion tensor of an element, accesses the nodes array and the nodeMap array. More...

virtual void	computeDriftVector (double b[3], const unsigned int ix, const unsigned int iy, const unsigned int iz)
	Compute the drift vector of an element. More...

virtual void	computeElementParameters (const int &element, double DETERMINANTJ[8], double J0M[3][3][8], double J0[3][3], double J[3][3], double b[3], double K[3][3], double &deltak, double &qualla, const int ix, const int iy, const int iz)
	Compute parameters of the SUPG method Compute the parameters of the SUPG method for each element. More...

virtual void	computeElementSystem (int &element, int &nDofNodes, int *dofNode, double Ael[9][9], double Del[9][9], bool stationary, double DETERMINANTJ[8], double J0M[3][3][8], double b[3], double K[3][3], double &deltak, const double &dt, CDoubleArray &f, CDoubleArray &Psi)
	compute element system .... More...

virtual void	computeDirichletBoundaryValues (int element, double DETERMINANTJ[8], double J0M[3][3][8], double J0[3][3], double b[3], double K[3][3], double deltak, int spec[8], int length_spec, int length_complSpec, CDoubleArray &c00, CDoubleArray &Psi)

virtual void	addElementMatrix (CDoubleArray &sA, const CIntArray &colInd, const CIntArray &rowPtr, const double Bel[9][9], const int element, const int *spec, const int length_spec)
	Add element matrix given a sparse matrix A in CSR format ( specified by sA, colInd, rowPtr) and the element matrix Bel, this function adds the element contributions to the global ones ; the first length_spec entries of the vector spec contains the indices of the matrix which are inserted Comments : Beware of the enumeration of the matrix sA (size is one bigger than required, zero index is unused => dangerous accesses nodeMap, nodeMap. More...

virtual void	computeDepositionFlux (const CDoubleArray &c, const double theta)
	compute deposition flux Authors : Marc Ryser Description : calculates the deposition flux i.e. (b c + K grad c) at the artificial layer of nodes and write it to the flux_x,y,z variable Comments : Beware of the enumeration of elements and nodes, Must be consistent with SnowDriftA3D::SnowMassChange(...) Note: this solution has temporary character since flux_x has size (nx-1)*(ny-1) and therefore only internal fluxes are written More...

virtual void	computeDepositionFluxSublimation (const CDoubleArray &c, const double theta)
	compute deposition flux Authors : Marc Ryser Description : calculates the deposition flux i.e. (b c + K grad c) at the artificial layer of nodes and write it to the flux_x,y,z variable Comments : Beware of the enumeration of elements and nodes, Must be consistent with SnowDriftA3D::SnowMassChange(...) Note: this solution has temporary character since flux_x has size (nx-1)*(ny-1) and therefore only internal fluxes are written More...

void	setBC_BottomLayer (CDoubleArray &var00, const param_type param)
	Set Bottom Boundary Condition Set the boundary condition of bottom layer +intialize concentration in rest of domain. More...

void	values_nodes_to_elements (const mio::Grid3DObject &nodesGrid, CDoubleArray &elementsArray)
	nodes_to_elements More...

void	values_elements_to_nodes (mio::Grid3DObject &nodesGrid, const CDoubleArray &elementsArray)
	elements_to_nodes Extract a 3D-grid of nodes from an array of elements More...

void	setRobinBoundaryCondition (const aspect_type aspect, const double gamma_val, const int ix, const int iy, const int iz, CDoubleArray &var00, const param_type param)
	Set Robin Boundary Condition. More...

virtual void	InitializeFEData ()
	Initializes system size and all data members which are required for the finite element solution. More...

virtual void	prepareSparseMatrix (CIntArray &colA, CIntArray &rowA, CDoubleArray &adjA)
	prepare sparse matrix Description : generates the auxiliary arrays (i.e. the arrays row-pointer and column-index) for a sparse matrix of CSR format. The sparsity pattern is assumed to be given by a finite element problem on a nodal mesh which is topologically equivalent to a simple cubic lattice with N=nxnynz number of nodes. For these hexahedral elements each node belongs to 8 elements. Hence, the support of the basis function of that given node overlaps with the support of 27 nodes' basis functions (including its own) which implies 27 nonzero entries per node in the interior of the domain. On the surface one has 18, 12 and 8 nonzero entries depending on the location (interior, edge, corner) From that the total number of nonzero elements can be computed. Usually, the dimensions of colA and rowA are nNZ and nDOF + 1,respectively where the last entry of rowA holds the number of nonzeros. Note: Here the sizes are nNZ + 1 for colA nDOF + 2 for rowA. This stems from the fact that originally Numerical recipes routines are used for the sparse matrix arrays in numerical recipes start with index one. In order to adopt them an the size was simply enlarged by one and the zero-index entry is unused. => fragile More...

virtual void	initializeSystem (CIntArray &colA, CIntArray &rowA, CDoubleArray &sA, CDoubleArray &sB, CDoubleArray &rhs, CDoubleArray &f, CDoubleArray &Psi, CDoubleArray &var, CDoubleArray &var00, const param_type param)
	Initialize system initializes vectors for the algorithm required for each time step. More...

virtual void	resetArray (CDoubleArray &sA)

virtual void	resetArray (CIntArray &sA)

virtual void	classifySubdomain ()
	Description... this functions sets summation limits for the loops over boundary elements (faces,bars,corners), presently the assemble routines depend on these limits => fragile the values of the limits is also affected by the enumeration of the elements presently the the first element has the number 1 (instead of 0) => even more fragile. More...

virtual int	numberOfNonzeros ()
	Number of nonzero elements of the finite element system matrix Description : computes the number of nonzero elements of the finite element system matrix, assumes a rectangular domain with simple cubic connectivity of size nx ny nz and linear elements. Then the support of the basis function at each of the (nx-2)(ny-2)(nz-2) degrees of freedom overlaps with the support of the basis functions of a certain number of nodes. The number of these nodes depends on the location of the degree of freedom. This defines four classes of dofs: interior (= adjacent to 0 boundary nodes) face (= adjacent to one boundary node) bar (= adjacent to two boundary nodes) and corner (= adjacent to three boundary nodes) where here adjacency refers to the simple cubic lattice graph. More...

void	iterativeSublimationCalculation (int timeStep, int maxTimeStep)
	Calculate the steady state sublimation in several steps. Single feedbacks can be switched on or off in SnowDrift.h. More...

void	zeroRow (int node)

void	buildWindFieldsTable (const std::string &wind_field_string)

void	debugOutputs (const mio::Date &calcDate, const std::string &fname, const DRIFT_OUTPUT &filetype)

void	writeOutput (const std::string &fname)
	Write output Writes the values of several nodes-fields. More...

Protected Attributes
Saltation	saltation_obj

double	time_v [15]

double	time_tau [15]

double	time_salt [15]

double	time_diff [15]

int	DOITERATION

double	auxLayerHeight

double	station_altitude

mio::IOManager	io

SnowpackInterface *	snowpack

EnergyBalance *	eb

mio::Timer	timer

mio::Grid2DObject	cH

mio::Grid2DObject	sp

mio::Grid2DObject	rg

mio::Grid2DObject	N3

mio::Grid2DObject	rb

unsigned int	nx

unsigned int	ny

unsigned int	nz

unsigned int	nDOF

unsigned int	nNodes

unsigned int	nElements

unsigned int	nNZ

CDoubleArray	sA

CDoubleArray	sB

CIntArray	colA

CIntArray	rowA

CDoubleArray	Psi

CDoubleArray	c

CDoubleArray	q

CDoubleArray	T

CDoubleArray	rhs

CDoubleArray	f

CDoubleArray	c00

CDoubleArray	q00

CDoubleArray	T00

CDoubleArray	precond

CDoubleArray	gNeumann

CDoubleArray	gDirichlet

CDoubleArray	gamma

CIntArray	nnzA

CDoubleArray	adjA

double	qualla

double	theta

mio::Array2D< int >	nz_face

mio::Array2D< int >	ny_face

mio::Array2D< int >	nx_face

mio::Array2D< int >	nz_bar

mio::Array2D< int >	ny_bar

mio::Array2D< int >	nx_bar

mio::Array2D< int >	nz_interior

mio::Array2D< int >	ny_interior

mio::Array2D< int >	nx_interior

CIntArray	n_corner

mio::Array2D< double >	qPoint

CElementArray	nodeMap

CElementArray	dofMap

CDoubleArray	flux_x

CDoubleArray	flux_y

CDoubleArray	flux_z

CDoubleArray	flux_x_subl

CDoubleArray	flux_y_subl

CDoubleArray	flux_z_subl

bool	new_wind_status

CElementArray	elems

mio::Array2D< double >	saltation

mio::Array2D< double >	c_salt

mio::Array2D< double >	mns_subl

mio::Array2D< double >	mns_nosubl

mio::Array2D< double >	dif_mns_subl

mio::Grid2DObject	mns

mio::Grid2DObject	vw

mio::Grid2DObject	rh

mio::Grid2DObject	ta

mio::Grid2DObject	p

mio::Grid2DObject	psum

mio::Grid2DObject	psum_ph

double	ta_1D

mio::Date	skip_date

mio::Grid3DObject	nodes_x

mio::Grid3DObject	nodes_y

mio::Grid3DObject	nodes_z

mio::Grid3DObject	nodes_sy

mio::Grid3DObject	nodes_sx

mio::Grid3DObject	nodes_slope

mio::Grid3DObject	nodes_wstar

mio::Grid3DObject	nodes_u

mio::Grid3DObject	nodes_v

mio::Grid3DObject	nodes_w

mio::Grid3DObject	nodes_K

mio::Grid3DObject	nodes_e

mio::Grid3DObject	nodes_c

mio::Grid3DObject	nodes_Tair

mio::Grid3DObject	nodes_Tair_ini

mio::Grid3DObject	nodes_q

mio::Grid3DObject	nodes_q_ini

mio::Grid3DObject	nodes_RH

mio::Grid3DObject	nodes_Subl

mio::Grid3DObject	nodes_Subl_ini

mio::Grid3DObject	nodes_WindVel

mio::Grid3DObject	nodes_tmp_c

bool	STATIONARY

std::vector< struct WIND_FIELD >	wind_fields

int	wind_field_index

Static Protected Attributes
static const double	kinematicViscosityAir = 1.3E-5

static const double	USTAR =0.87

static const double	molecularWeightofWater = 18.015E-3

static const double	thermalConductivityofAtm = 0.024

static const double	c_red = 1.0

static const double	grain_size = 0.000680

static const double	tau_thresh = 0.094

static const double	z0 = 0.01

static const bool	thresh_snow = true

Constructor & Destructor Documentation

◆ SnowDriftA3D()

SnowDriftA3D::SnowDriftA3D	(	const mio::DEMObject &	dem,
		const mio::Config &	cfg
	)

◆ ~SnowDriftA3D()

SnowDriftA3D::~SnowDriftA3D ( )

virtual

Member Function Documentation

◆ addElementMatrix()

void SnowDriftA3D::addElementMatrix	(	CDoubleArray &	sA_loc,
		const CIntArray &	colInd,
		const CIntArray &	rowPtr,
		const double	Bel[9][9],
		const int	element,
		const int *	spec,
		const int	length_spec
	)

protectedvirtual

Add element matrix given a sparse matrix A in CSR format ( specified by sA, colInd, rowPtr) and the element matrix Bel, this function adds the element contributions to the global ones ; the first length_spec entries of the vector spec contains the indices of the matrix which are inserted Comments : Beware of the enumeration of the matrix sA (size is one bigger than required, zero index is unused => dangerous accesses nodeMap, nodeMap.

Parameters

sA
colInd
rowPtr
Bel
element
spec
length_spec

◆ applyBoundaryValues()

void SnowDriftA3D::applyBoundaryValues	(	CDoubleArray &	var00,
		CDoubleArray &	Psi_loc
	)

protectedvirtual

applyBoundaryValues Apply boundary values to all elements Author: Marc Ryser

Parameters

var00	initial variable
Psi	vector for incorporating inhomogeneous Dirichlet BC

◆ assembleSystem()

void SnowDriftA3D::assembleSystem	(	CIntArray &	colA_loc,
		CIntArray &	rowA_loc,
		CDoubleArray &	sA_loc,
		CDoubleArray &	sB_loc,
		CDoubleArray &	Psi_loc,
		CDoubleArray &	f_loc,
		const double	dt
	)

protectedvirtual

Assemble System loop over all elements, updates the system matrices A, B and the 'bare' right hand side (rhs) of the system, in other words: prepares the system prior to the inclusion of dirichlet boundary conditions.

Parameters

colA	column index to locate within sparse matrix
rowA	row index
sA	"system matrix"
sB	"system matrix"
Psi	vector for incorporating inhomogeneous Dirichlet BC
f	source in diffusion equation
dt

◆ bicgStab()

void SnowDriftA3D::bicgStab	(	CDoubleArray &	result,
		CDoubleArray &	rhs_loc,
		const CDoubleArray &	sA_loc,
		const CIntArray &	colA_loc,
		CIntArray &	rowA_loc,
		const int	nmax,
		const double	tol,
		double &	testres
	)

protectedvirtual

bicgStab iterative equation solver iterative equation solver Tests : Tested by the followin procedure: given a sparse matrix A (CRS-format) characterized by colA and rowA and an arbitrary, or rather: a few nontrivial examples of a vector x. For each x matmult(y,x,sA,rowA,colA) and bicgStab(result,y,sA,colA,rowA,...) have been computed and then verified that result=x

Parameters

res	result
rhs
sA
colA
rowA
nmax	max number of iterations
tol	tolerance

◆ buildWindFieldsTable()

void SnowDriftA3D::buildWindFieldsTable ( const std::string & wind_field_string )

protected

◆ calcS()

double SnowDriftA3D::calcS	(	const double	concentration,
		const double	sublradius,
		const double	dmdt
	)

protected

Calculate sublimation The mass change of a single particle is now extended to all particles.

Parameters

concentration	snow concentration
sublradius	radius of a single particle
dmdt	mass change of a single particle due to sublimation

◆ calcSubldM()

double SnowDriftA3D::calcSubldM	(	const double	Radius,
		const double	AirTemperature,
		const double	RH,
		const double	WindSpeed,
		const double	altitude
	)

protected

Calculate sublimation mass change This function calculates the mass change of a single ice particle for the given conditions.

Parameters

Radius	radius of the ice particle
AirTemperature
RH	relative humidity
WindSpeed	magnitude of the wind

◆ classifySubdomain()

void SnowDriftA3D::classifySubdomain ( void )

protectedvirtual

Description... this functions sets summation limits for the loops over boundary elements (faces,bars,corners), presently the assemble routines depend on these limits => fragile the values of the limits is also affected by the enumeration of the elements presently the the first element has the number 1 (instead of 0) => even more fragile.

This setting will become important for the domain decomposition, since then an element on the domain boundary is not necessarily an element of the physical boundary, and these array account for that. Note: these summation limits are related to the number of nodes, the number of elements, the number of dofs and accordingly the number of nonzero matrix elemens in the system matrix. It would be better to have one class which holds all these information consistently.

◆ CompleteNodes()

void SnowDriftA3D::CompleteNodes ( )

protected

Initialize concentration according to the rain rate (uniform) Now calculate the missing parameters Slope in direction of the wind.

CompleteNodes

◆ compSaltation()

void SnowDriftA3D::compSaltation ( bool setbound )

protectedvirtual

Calculate Saltation Fluxes for all Bottom Elements.

Parameters

setbound bool

◆ Compute()

void SnowDriftA3D::Compute ( const mio::Date & calcDate )

virtual

Main: Calls the essential routines.

Parameters

calcDate date of current time step

◆ computeDepositionFlux()

void SnowDriftA3D::computeDepositionFlux	(	const CDoubleArray &	concentration,
		const double	theta_l
	)

protectedvirtual

compute deposition flux Authors : Marc Ryser Description : calculates the deposition flux i.e. (b c + K grad c) at the artificial layer of nodes and write it to the flux_x,y,z variable Comments : Beware of the enumeration of elements and nodes, Must be consistent with SnowDriftA3D::SnowMassChange(...) Note: this solution has temporary character since flux_x has size (nx-1)*(ny-1) and therefore only internal fluxes are written

Parameters

CDoubleArray&c	Concentration of snow
theta	height above bottom of element

◆ computeDepositionFluxSublimation()

void SnowDriftA3D::computeDepositionFluxSublimation	(	const CDoubleArray &	concentration,
		const double	theta_l
	)

protectedvirtual

compute deposition flux Authors : Marc Ryser Description : calculates the deposition flux i.e. (b c + K grad c) at the artificial layer of nodes and write it to the flux_x,y,z variable Comments : Beware of the enumeration of elements and nodes, Must be consistent with SnowDriftA3D::SnowMassChange(...) Note: this solution has temporary character since flux_x has size (nx-1)*(ny-1) and therefore only internal fluxes are written

Parameters

CDoubleArray&c	Concentration of snow
theta	height above bottom of element

◆ computeDiffusionTensor()

void SnowDriftA3D::computeDiffusionTensor	(	double	K[3][3],
		const unsigned int	ix,
		const unsigned int	iy,
		const unsigned int	iz
	)

protectedvirtual

Compute diffusion tensor Computes the diffusion tensor of an element, accesses the nodes array and the nodeMap array.

Parameters

element	element number
K	diffusion coefficient
layer	layer of the element

◆ computeDirichletBoundaryValues()

void SnowDriftA3D::computeDirichletBoundaryValues	(	int	element,
		double	DETERMINANTJ[8],
		double	J0M[3][3][8],
		double	J0[3][3],
		double	b[3],
		double	K[3][3],
		double	deltak,
		int	spec[8],
		int	length_spec,
		int	length_complSpec,
		CDoubleArray &	c00,
		CDoubleArray &	Psi
	)

protectedvirtual

◆ computeDriftVector()

void SnowDriftA3D::computeDriftVector	(	double	b[3],
		const unsigned int	ix,
		const unsigned int	iy,
		const unsigned int	iz
	)

protectedvirtual

Compute the drift vector of an element.

Parameters

element	element number
b	drift vector

◆ computeElementParameters()

void SnowDriftA3D::computeElementParameters	(	const int &	element,
		double	DETERMINANTJ[8],
		double	J0M[3][3][8],
		double	J0[3][3],
		double	J[3][3],
		double	b[3],
		double	K[3][3],
		double &	deltak,
		double &	qualla_loc,
		const int	ix,
		const int	iy,
		const int	iz
	)

protectedvirtual

Compute parameters of the SUPG method Compute the parameters of the SUPG method for each element.

Parameters

element	Element number
DETERMINANTJ	Determinant of Jacobian matrix
J0M
J0	JO matrix
J	Jacobian matrix
b	drift vector
K	Diffusion tensor
&deltak	parameter SUPG method
&qualla	parameter SUPG method (to vary delta_k)

◆ computeElementSystem()

void SnowDriftA3D::computeElementSystem	(	int &	element,
		int &	nDofNodes,
		int *	dofNode,
		double	Ael[9][9],
		double	Del[9][9],
		bool	stationary,
		double	DETERMINANTJ[8],
		double	J0M[3][3][8],
		double	b[3],
		double	K[3][3],
		double &	deltak,
		const double &	dt,
		CDoubleArray &	f_loc,
		CDoubleArray &	Psi_loc
	)

protectedvirtual

compute element system ....

Parameters

element	element number
nDofNodes	degrees of freedom of element
Ael
Del
stationary
DETERMINANTJ
J0M
b	wind field
K	diffusion tensor
deltak	parameter
dt
f	source
Psi

◆ ConstructElements()

void SnowDriftA3D::ConstructElements ( )

protected

◆ debugOutputs()

void SnowDriftA3D::debugOutputs	(	const mio::Date &	calcDate,
		const std::string &	fname,
		const DRIFT_OUTPUT &	filetype
	)

protected

◆ Destroy()

void SnowDriftA3D::Destroy ( )

◆ Diffusion()

void SnowDriftA3D::Diffusion	(	double	deltaT,
		double &	diff_max,
		double	t
	)

protectedvirtual

◆ getGridsRequirements()

std::string SnowDriftA3D::getGridsRequirements ( ) const

◆ getTiming()

double SnowDriftA3D::getTiming ( ) const

◆ GetTResults()

void SnowDriftA3D::GetTResults	(	double	outtime_v[15],
		double	outtime_tau[15],
		double	outtime_salt[15],
		double	outtime_diff[15]
	)

◆ GQIntAdxdx()

double SnowDriftA3D::GQIntAdxdx	(	double *	DETERMINANTJ,
		double	J0M[3][3][8],
		const int	i,
		const int	j,
		double *	b,
		const double	deltak
	)

protectedvirtual

GQIntAdxdx ...

Parameters

DETERMINANTJ	determinant of Jacobian
J0M
i	pointer
j	pointer
*b	drift vector
deltak	parameter SUPG method

◆ GQIntApdx()

double SnowDriftA3D::GQIntApdx	(	double	DETERMINANTJ[],
		const double	J0M[3][3][8],
		const int	i,
		const int	j,
		double	b[],
		const double	deltak
	)

protectedvirtual

GQIntApdx returns the integral of the product of a basis function i and the gradient of basis function j over a hexahedral element using gaussian quadrature, DETERMINANTK[0],...DETERMINANTK[7] contains the determinant of the jacobian of the mapping onto the unit cube evaluated at the corners.

Parameters

DETERMINANTJ	determinant of Jacobian
J0M
i	nr basis function
j	nr basis function
b	drift vector
deltak	parameter SUPG method

◆ GQIntB()

double SnowDriftA3D::GQIntB	(	double *	DETERMINANTJ,
		const int	i,
		const int	j
	)

protectedvirtual

GQIntB returns the integral of the product of basis functions i and j over a hexahedral element using gaussian quadrature, DETERMINANTK[0],...DETERMINANTK[7] contains the determinant of the jacobian of the mapping onto the unit cube evaluated at the corners.

Parameters

DETERMINANTJ	determinant of Jacobian
i	nr shape function
j	nr shape function

◆ GQIntC()

double SnowDriftA3D::GQIntC	(	double *	DETERMINANTJ,
		const double	J0M[3][3][8],
		const int	i,
		const int	j,
		const double	b[3],
		const double	K[3][3]
	)

protectedvirtual

GQIntC returns the integral of the product of the gradients of basis functions i and j over a hexahedral element using gaussian quadrature, DETERMINANTK[0],...DETERMINANTK[7] contains the determinant of the jacobian of the mapping onto the unit cube evaluated at the corners.

Parameters

DETERMINANTJ	determinant of Jacobian
J0M
i	pointer/index
j	pointer/index
b	drift vector
K	Diffusion tensor

◆ Initialize()

void SnowDriftA3D::Initialize ( )

protected

Initialize for snowdrift Allocate saltation variable, snow height and new snow mass per bottom element.

◆ InitializeFEData()

void SnowDriftA3D::InitializeFEData ( void )

protectedvirtual

Initializes system size and all data members which are required for the finite element solution.

◆ InitializeNodes()

void SnowDriftA3D::InitializeNodes ( const mio::Grid3DObject & z_readMatr )

protected

Initialize nodes Each (3D) node receives its (x,y,z), slope, aspect, normals.

◆ initializeSystem()

void SnowDriftA3D::initializeSystem	(	CIntArray &	colA_loc,
		CIntArray &	rowA_loc,
		CDoubleArray &	sA_loc,
		CDoubleArray &	sB_loc,
		CDoubleArray &	rhs_loc,
		CDoubleArray &	f_loc,
		CDoubleArray &	Psi_loc,
		CDoubleArray &	var,
		CDoubleArray &	var00,
		const param_type	param
	)

protectedvirtual

Initialize system initializes vectors for the algorithm required for each time step.

Parameters

colA	array determining the sparsity pattern
rowA	array determining the sparsity pattern
sA	system matrix in compressed sparse row (CSR) storage format
sB	system matrix in compressed sparse row (CSR) storage format
rhs	vector which contains the right hand side of the linear system
f	source term in the advection/diffusion equation (sublimation amount)
Psi	auxiliary vector for incorporating inhomogeneous Dirichlet boundary conditions
var	variable for which equation has to be solved (Humidity, Concentration or Temperature)
var00	boundary condition at bottom + initial condition interior domain of variable var

◆ initializeTRH()

void SnowDriftA3D::initializeTRH ( )

protected

Initialize RH, T and q Initialize fields of humidity and temperature, necessary for sublimation calculations.

◆ isNewWindField()

bool SnowDriftA3D::isNewWindField ( const unsigned int current_step )

◆ iterativeSublimationCalculation()

void SnowDriftA3D::iterativeSublimationCalculation	(	int	timeStep,
		int	maxTimeStep
	)

protected

Calculate the steady state sublimation in several steps. Single feedbacks can be switched on or off in SnowDrift.h.

◆ J0fun()

void SnowDriftA3D::J0fun	(	double	J0[3][3],
		const double	J[3][3]
	)

protectedvirtual

J0 function computes the matrix of cofactors of the input matrix J and stores it in J0.

Parameters

J0	matrix of cofactors (transpose of the adjoint of J)
J	Jacobian matrix

◆ Jacobian()

void SnowDriftA3D::Jacobian	(	double *	DETERMINANTJ,
		double	J[][3],
		const int	element,
		const double *	P,
		int	k,
		const int	ix,
		const int	iy,
		const int	iz
	)

protectedvirtual

Compute Jacobian This function calculates the Jacobian at the given point P and and stores the value of its determinant at point P in the global variable DETERMINANTJ[k] the input value is the respective element, the position where to store the DETERMINANTJ[k], and the function is of type void, the Jacobian matrix J and the integration point P and the DETERMINANTJ array.

Parameters

DETERMINANTJ	Determinant of Jacobian matrix
J	Jacobian matrix
element	element number
P	point where Jacobian has to be calculated
k	for storing Jacobian at DETERMINANTJ(k)

◆ matmult() [1/2]

void SnowDriftA3D::matmult	(	CDoubleArray &	res,
		const CDoubleArray &	x_loc,
		double *	sm,
		int *	ijm
	)

protectedvirtual

matmult computes a matrix vector product for a sparse matrix

Parameters

res	result (matrix vector product)
x
sm	sparse matrix
ijm

◆ matmult() [2/2]

void SnowDriftA3D::matmult	(	CDoubleArray &	y_loc,
		const CDoubleArray &	x_loc,
		const CDoubleArray &	sA_loc,
		const CIntArray &	colInd,
		CIntArray &	rowPtr
	)

protectedvirtual

matmult computes a matrix vector product for a sparse matrix of CSR format

Parameters

y	result (matrix vector product)
x
sA
colind	column index
rowPtr	row index

◆ numberOfNonzeros()

int SnowDriftA3D::numberOfNonzeros ( )

protectedvirtual

Number of nonzero elements of the finite element system matrix Description : computes the number of nonzero elements of the finite element system matrix, assumes a rectangular domain with simple cubic connectivity of size nx ny nz and linear elements. Then the support of the basis function at each of the (nx-2)*(ny-2)*(nz-2) degrees of freedom overlaps with the support of the basis functions of a certain number of nodes. The number of these nodes depends on the location of the degree of freedom. This defines four classes of dofs: interior (= adjacent to 0 boundary nodes) face (= adjacent to one boundary node) bar (= adjacent to two boundary nodes) and corner (= adjacent to three boundary nodes) where here adjacency refers to the simple cubic lattice graph.

accesses the SnowDrift variable nNZ Comments : For parallelization issues this must be in accordance with the summation limits set in SnowDriftA3D::classifySubdomain()

◆ phi()

void SnowDriftA3D::phi	(	double *	PHI,
		double *	P
	)

protectedvirtual

Phi - shape functions Calculates the value of the 8 shape functions at point P.

Parameters

*PHI	...................shape functions
*P	pointer

◆ prepareSolve()

void SnowDriftA3D::prepareSolve ( )

protectedvirtual

prepareSolve Some preparations to solve a 3D-field.

◆ prepareSparseMatrix()

void SnowDriftA3D::prepareSparseMatrix	(	CIntArray &	colA,
		CIntArray &	rowA,
		CDoubleArray &	adjA
	)

protectedvirtual

prepare sparse matrix Description : generates the auxiliary arrays (i.e. the arrays row-pointer and column-index) for a sparse matrix of CSR format. The sparsity pattern is assumed to be given by a finite element problem on a nodal mesh which is topologically equivalent to a simple cubic lattice with N=nx*ny*nz number of nodes. For these hexahedral elements each node belongs to 8 elements. Hence, the support of the basis function of that given node overlaps with the support of 27 nodes' basis functions (including its own) which implies 27 nonzero entries per node in the interior of the domain. On the surface one has 18, 12 and 8 nonzero entries depending on the location (interior, edge, corner) From that the total number of nonzero elements can be computed. Usually, the dimensions of colA and rowA are nNZ and nDOF + 1,respectively where the last entry of rowA holds the number of nonzeros. Note: Here the sizes are nNZ + 1 for colA nDOF + 2 for rowA. This stems from the fact that originally Numerical recipes routines are used for the sparse matrix arrays in numerical recipes start with index one. In order to adopt them an the size was simply enlarged by one and the zero-index entry is unused. => fragile

◆ resetArray() [1/2]

void SnowDriftA3D::resetArray ( CDoubleArray & sA )

protectedvirtual

◆ resetArray() [2/2]

void SnowDriftA3D::resetArray ( CIntArray & sA )

protectedvirtual

◆ reynoldsNumberforFallingParticles()

double SnowDriftA3D::reynoldsNumberforFallingParticles	(	const double	Radius,
		const double	Windspeed,
		const double	AirTemperature,
		const double	RH,
		const double	altitude
	)

protected

Reynolds number Calculate the Reynolds number for a falling particle.

Parameters

Radius	radius of the particle
Windspeed	magnitude of the wind
AirTemperature
RH	relative humidity of the air

◆ RH_from_q()

double SnowDriftA3D::RH_from_q	(	const double	AirTemp,
		const double	qi,
		const double	altitude
	)

protected

Relative humidity Gives the relative humidity for a given air temperature and specific humidity.

Parameters

AirTemp	Air temperature
qi	specific humidity
altitude	Altitude above sea level

◆ setBC_BottomLayer()

void SnowDriftA3D::setBC_BottomLayer	(	CDoubleArray &	var00,
		const param_type	param
	)

protected

Set Bottom Boundary Condition Set the boundary condition of bottom layer +intialize concentration in rest of domain.

Parameters

c00	initial concentration/humidity at bottom

◆ setEnergyBalance()

void SnowDriftA3D::setEnergyBalance ( EnergyBalance & myeb )

◆ setMeteo()

void SnowDriftA3D::setMeteo	(	const unsigned int &	steps,
		const mio::Grid2DObject &	new_psum,
		const mio::Grid2DObject &	new_psum_ph,
		const mio::Grid2DObject &	new_p,
		const mio::Grid2DObject &	new_vw,
		const mio::Grid2DObject &	new_rh,
		const mio::Grid2DObject &	new_ta,
		const mio::Grid2DObject &	new_ilwr,
		const mio::Date &	calcDate,
		const std::vector< mio::MeteoData > &	vecMeteo
	)

Sets the required meteo fields.

◆ setQuadraturePoints()

void SnowDriftA3D::setQuadraturePoints ( void )

protectedvirtual

◆ setRobinBoundaryCondition()

void SnowDriftA3D::setRobinBoundaryCondition	(	const aspect_type	aspect,
		const double	gamma_val,
		const int	ix,
		const int	iy,
		const int	iz,
		CDoubleArray &	var00,
		const param_type	param
	)

protected

Set Robin Boundary Condition.

Parameters

aspect	Location of boundary (NSWE or top/bottom)
gamma_val	(double) constant to approach Dirichlet or Neumann condition
ix,iy,iz	location
var00	Initial 3D field (T, q or c) that needs to be set
param	Type of field (T, q or c)

◆ setSnowPack()

void SnowDriftA3D::setSnowPack ( SnowpackInterface & mysnowpack )

◆ setSnowSurfaceData()

void SnowDriftA3D::setSnowSurfaceData	(	const mio::Grid2DObject &	cH_in,
		const mio::Grid2DObject &	sp_in,
		const mio::Grid2DObject &	rg_in,
		const mio::Grid2DObject &	N3_in,
		const mio::Grid2DObject &	rb_in
	)

virtual

◆ SnowMassChange()

void SnowDriftA3D::SnowMassChange	(	bool	setbound,
		const mio::Date &	calcDate
	)

protectedvirtual

◆ SolveEquation()

void SnowDriftA3D::SolveEquation	(	int	timeStep,
		int	maxTimeStep,
		const param_type	param
	)

protectedvirtual

Solve the advection diffusion equation.

Parameters

timeStep	(parameter only for non stationary)
maxTimeStep	(parameter only for non stationary)
param	variable that should be solved

◆ Sublimation()

void SnowDriftA3D::Sublimation ( )

protectedvirtual

Sublimation Calculates drifting snow sublimation at every node of the concentration field.

◆ Suspension()

void SnowDriftA3D::Suspension ( )

protectedvirtual

◆ terminalFallVelocity()

double SnowDriftA3D::terminalFallVelocity	(	const double	Radius,
		const double	Temperature,
		const double	RH,
		const double	altitude
	)

protected

Terminal fall velocity NB assumed to be 0.5.

Parameters

Radius	radius of the particle
Temperature	air temperature (K)
RH	relative humidity of the air (between 0 and 1)
altitude	Altitude above sea level

◆ transmult()

void SnowDriftA3D::transmult	(	CDoubleArray &	res,
		const CDoubleArray &	x_loc,
		double *	sm,
		int *	ijm
	)

protectedvirtual

transmult this is the transmult function that multiplies the vector x by the transpose of the matrix M in its sparse form sm, ijm

Parameters

res	result
x
sm
ijm	index

◆ TTfun()

void SnowDriftA3D::TTfun	(	double	TT[3][8],
		const double	P[]
	)

protectedvirtual

TT function TTfun is a function calculating the values of the partial derivative of phi at the point P and putting them in a (3,8) array.

Parameters

TT	partial derivative of phi at point P (result of this function)
P	pointer

◆ values_elements_to_nodes()

void SnowDriftA3D::values_elements_to_nodes	(	mio::Grid3DObject &	nodesGrid,
		const CDoubleArray &	elementsArray
	)

protected

elements_to_nodes Extract a 3D-grid of nodes from an array of elements

Parameters

nodesGrid	grid of nodes that should be filled
elementsArray	array with elements

◆ values_nodes_to_elements()

void SnowDriftA3D::values_nodes_to_elements	(	const mio::Grid3DObject &	nodesGrid,
		CDoubleArray &	elementsArray
	)

protected

nodes_to_elements

Parameters

nodesGrid	3Dgrid of nodes
elementsArray	array with elements

◆ ventilationVelocity()

double SnowDriftA3D::ventilationVelocity	(	const double	Radius,
		const double	Windspeed,
		const double	AirTemperature,
		const double	RH,
		const double	altitude
	)

protected

Ventilation velocity.

Parameters

Radius	radius of the particle
Windspeed	magnitude of the wind
AirTemperature
RH	relative humidity of the air
altitude	Altitude above sea level

◆ waterVaporDensity()

double SnowDriftA3D::waterVaporDensity	(	const double	Temperature,
		const double	VaporPressure
	)

protected

◆ writeOutput()

void SnowDriftA3D::writeOutput ( const std::string & fname )

protected

Write output Writes the values of several nodes-fields.

◆ zeroRow()

void SnowDriftA3D::zeroRow ( int node )

protected

Member Data Documentation

◆ adjA

CDoubleArray SnowDriftA3D::adjA

protected

◆ auxLayerHeight

double SnowDriftA3D::auxLayerHeight

protected

◆ c

CDoubleArray SnowDriftA3D::c

protected

◆ c00

CDoubleArray SnowDriftA3D::c00

protected

◆ c_red

const double SnowDriftA3D::c_red = 1.0

staticprotected

◆ c_salt

mio::Array2D<double> SnowDriftA3D::c_salt

protected

◆ cH

mio::Grid2DObject SnowDriftA3D::cH

protected

◆ colA

CIntArray SnowDriftA3D::colA

protected

◆ dif_mns_subl

mio::Array2D<double> SnowDriftA3D::dif_mns_subl

protected

◆ dofMap

CElementArray SnowDriftA3D::dofMap

protected

◆ DOITERATION

int SnowDriftA3D::DOITERATION

protected

◆ eb

EnergyBalance* SnowDriftA3D::eb

protected

◆ elems

CElementArray SnowDriftA3D::elems

protected

◆ f

CDoubleArray SnowDriftA3D::f

protected

◆ flux_x

CDoubleArray SnowDriftA3D::flux_x

protected

◆ flux_x_subl

CDoubleArray SnowDriftA3D::flux_x_subl

protected

◆ flux_y

CDoubleArray SnowDriftA3D::flux_y

protected

◆ flux_y_subl

CDoubleArray SnowDriftA3D::flux_y_subl

protected

◆ flux_z

CDoubleArray SnowDriftA3D::flux_z

protected

◆ flux_z_subl

CDoubleArray SnowDriftA3D::flux_z_subl

protected

◆ gamma

CDoubleArray SnowDriftA3D::gamma

protected

◆ gDirichlet

CDoubleArray SnowDriftA3D::gDirichlet

protected

◆ gNeumann

CDoubleArray SnowDriftA3D::gNeumann

protected

◆ grain_size

const double SnowDriftA3D::grain_size = 0.000680

staticprotected

◆ io

mio::IOManager SnowDriftA3D::io

protected

◆ kinematicViscosityAir

const double SnowDriftA3D::kinematicViscosityAir = 1.3E-5

staticprotected

◆ mns

mio::Grid2DObject SnowDriftA3D::mns

protected

◆ mns_nosubl

mio::Array2D<double> SnowDriftA3D::mns_nosubl

protected

◆ mns_subl

mio::Array2D<double> SnowDriftA3D::mns_subl

protected

◆ molecularWeightofWater

const double SnowDriftA3D::molecularWeightofWater = 18.015E-3

staticprotected

◆ N3

mio::Grid2DObject SnowDriftA3D::N3

protected

◆ n_corner

CIntArray SnowDriftA3D::n_corner

protected

◆ nDOF

unsigned int SnowDriftA3D::nDOF

protected

◆ nElements

unsigned int SnowDriftA3D::nElements

protected

◆ new_wind_status

bool SnowDriftA3D::new_wind_status

protected

◆ nNodes

unsigned int SnowDriftA3D::nNodes

protected

◆ nNZ

unsigned int SnowDriftA3D::nNZ

protected

◆ nnzA

CIntArray SnowDriftA3D::nnzA

protected

◆ nodeMap

CElementArray SnowDriftA3D::nodeMap

protected

◆ nodes_c

mio::Grid3DObject SnowDriftA3D::nodes_c

protected

◆ nodes_e

mio::Grid3DObject SnowDriftA3D::nodes_e

protected

◆ nodes_K

mio::Grid3DObject SnowDriftA3D::nodes_K

protected

◆ nodes_q

mio::Grid3DObject SnowDriftA3D::nodes_q

protected

◆ nodes_q_ini

mio::Grid3DObject SnowDriftA3D::nodes_q_ini

protected

◆ nodes_RH

mio::Grid3DObject SnowDriftA3D::nodes_RH

protected

◆ nodes_slope

mio::Grid3DObject SnowDriftA3D::nodes_slope

protected

◆ nodes_Subl

mio::Grid3DObject SnowDriftA3D::nodes_Subl

protected

◆ nodes_Subl_ini

mio::Grid3DObject SnowDriftA3D::nodes_Subl_ini

protected

◆ nodes_sx

mio::Grid3DObject SnowDriftA3D::nodes_sx

protected

◆ nodes_sy

mio::Grid3DObject SnowDriftA3D::nodes_sy

protected

◆ nodes_Tair

mio::Grid3DObject SnowDriftA3D::nodes_Tair

protected

◆ nodes_Tair_ini

mio::Grid3DObject SnowDriftA3D::nodes_Tair_ini

protected

◆ nodes_tmp_c

mio::Grid3DObject SnowDriftA3D::nodes_tmp_c

protected

◆ nodes_u

mio::Grid3DObject SnowDriftA3D::nodes_u

protected

◆ nodes_v

mio::Grid3DObject SnowDriftA3D::nodes_v

protected

◆ nodes_w

mio::Grid3DObject SnowDriftA3D::nodes_w

protected

◆ nodes_WindVel

mio::Grid3DObject SnowDriftA3D::nodes_WindVel

protected

◆ nodes_wstar

mio::Grid3DObject SnowDriftA3D::nodes_wstar

protected

◆ nodes_x

mio::Grid3DObject SnowDriftA3D::nodes_x

protected

◆ nodes_y

mio::Grid3DObject SnowDriftA3D::nodes_y

protected

◆ nodes_z

mio::Grid3DObject SnowDriftA3D::nodes_z

protected

◆ nx

unsigned int SnowDriftA3D::nx

protected

◆ nx_bar

mio::Array2D<int> SnowDriftA3D::nx_bar

protected

◆ nx_face

mio::Array2D<int> SnowDriftA3D::nx_face

protected

◆ nx_interior

mio::Array2D<int> SnowDriftA3D::nx_interior

protected

◆ ny

unsigned int SnowDriftA3D::ny

protected

◆ ny_bar

mio::Array2D<int> SnowDriftA3D::ny_bar

protected

◆ ny_face

mio::Array2D<int> SnowDriftA3D::ny_face

protected

◆ ny_interior

mio::Array2D<int> SnowDriftA3D::ny_interior

protected

◆ nz

unsigned int SnowDriftA3D::nz

protected

◆ nz_bar

mio::Array2D<int> SnowDriftA3D::nz_bar

protected

◆ nz_face

mio::Array2D<int> SnowDriftA3D::nz_face

protected

◆ nz_interior

mio::Array2D<int> SnowDriftA3D::nz_interior

protected

◆ p

mio::Grid2DObject SnowDriftA3D::p

protected

◆ precond

CDoubleArray SnowDriftA3D::precond

protected

◆ Psi

CDoubleArray SnowDriftA3D::Psi

protected

◆ psum

mio::Grid2DObject SnowDriftA3D::psum

protected

◆ psum_ph

mio::Grid2DObject SnowDriftA3D::psum_ph

protected

◆ q

CDoubleArray SnowDriftA3D::q

protected

◆ q00

CDoubleArray SnowDriftA3D::q00

protected

◆ qPoint

mio::Array2D<double> SnowDriftA3D::qPoint

protected

◆ qualla

double SnowDriftA3D::qualla

protected

◆ rb

mio::Grid2DObject SnowDriftA3D::rb

protected

◆ rg

mio::Grid2DObject SnowDriftA3D::rg

protected

◆ rh

mio::Grid2DObject SnowDriftA3D::rh

protected

◆ rhs

CDoubleArray SnowDriftA3D::rhs

protected

◆ rowA

CIntArray SnowDriftA3D::rowA

protected

◆ sA

CDoubleArray SnowDriftA3D::sA

protected

◆ saltation

mio::Array2D<double> SnowDriftA3D::saltation

protected

◆ saltation_obj

Saltation SnowDriftA3D::saltation_obj

protected

◆ sB

CDoubleArray SnowDriftA3D::sB

protected

◆ skip_date

mio::Date SnowDriftA3D::skip_date

protected

◆ snowpack

SnowpackInterface* SnowDriftA3D::snowpack

protected

◆ sp

mio::Grid2DObject SnowDriftA3D::sp

protected

◆ station_altitude

double SnowDriftA3D::station_altitude

protected

◆ STATIONARY

bool SnowDriftA3D::STATIONARY

protected

◆ T

CDoubleArray SnowDriftA3D::T

protected

◆ T00

CDoubleArray SnowDriftA3D::T00

protected

◆ ta

mio::Grid2DObject SnowDriftA3D::ta

protected

◆ ta_1D

double SnowDriftA3D::ta_1D

protected

◆ tau_thresh

const double SnowDriftA3D::tau_thresh = 0.094

staticprotected

◆ thermalConductivityofAtm

const double SnowDriftA3D::thermalConductivityofAtm = 0.024

staticprotected

◆ theta

double SnowDriftA3D::theta

protected

◆ thresh_snow

const bool SnowDriftA3D::thresh_snow = true

staticprotected

◆ time_diff

double SnowDriftA3D::time_diff[15]

protected

◆ time_salt

double SnowDriftA3D::time_salt[15]

protected

◆ time_tau

double SnowDriftA3D::time_tau[15]

protected

◆ time_v

double SnowDriftA3D::time_v[15]

protected

◆ timer

mio::Timer SnowDriftA3D::timer

protected

◆ USTAR

const double SnowDriftA3D::USTAR =0.87

staticprotected

◆ vw

mio::Grid2DObject SnowDriftA3D::vw

protected

◆ wind_field_index

int SnowDriftA3D::wind_field_index

protected

◆ wind_fields

std::vector<struct WIND_FIELD> SnowDriftA3D::wind_fields

protected

◆ z0

const double SnowDriftA3D::z0 = 0.01

staticprotected

The documentation for this class was generated from the following files:

Public Member Functions

Protected Member Functions

Protected Attributes

Static Protected Attributes

Constructor & Destructor Documentation

◆ SnowDriftA3D()

◆ ~SnowDriftA3D()

Member Function Documentation

◆ addElementMatrix()

◆ applyBoundaryValues()

◆ assembleSystem()

◆ bicgStab()

◆ buildWindFieldsTable()

◆ calcS()

◆ calcSubldM()

◆ classifySubdomain()

◆ CompleteNodes()

◆ compSaltation()

◆ Compute()

◆ computeDepositionFlux()

◆ computeDepositionFluxSublimation()

◆ computeDiffusionTensor()

◆ computeDirichletBoundaryValues()

◆ computeDriftVector()

◆ computeElementParameters()

◆ computeElementSystem()

◆ ConstructElements()

◆ debugOutputs()

◆ Destroy()

◆ Diffusion()

◆ getGridsRequirements()

◆ getTiming()

◆ GetTResults()

◆ GQIntAdxdx()

◆ GQIntApdx()

◆ GQIntB()

◆ GQIntC()

◆ Initialize()

◆ InitializeFEData()

◆ InitializeNodes()

◆ initializeSystem()

◆ initializeTRH()

◆ isNewWindField()

◆ iterativeSublimationCalculation()

◆ J0fun()

◆ Jacobian()

◆ matmult() [1/2]

◆ matmult() [2/2]

◆ numberOfNonzeros()

◆ phi()

◆ prepareSolve()

◆ prepareSparseMatrix()

◆ resetArray() [1/2]

◆ resetArray() [2/2]

◆ reynoldsNumberforFallingParticles()

◆ RH_from_q()

◆ setBC_BottomLayer()

◆ setEnergyBalance()

◆ setMeteo()

◆ setQuadraturePoints()

◆ setRobinBoundaryCondition()

◆ setSnowPack()

◆ setSnowSurfaceData()

◆ SnowMassChange()

◆ SolveEquation()

◆ Sublimation()

◆ Suspension()

◆ terminalFallVelocity()

◆ transmult()

◆ TTfun()

◆ values_elements_to_nodes()

◆ values_nodes_to_elements()

◆ ventilationVelocity()

◆ waterVaporDensity()

◆ writeOutput()

◆ zeroRow()

Member Data Documentation

◆ adjA

◆ auxLayerHeight

◆ c