Numerical Methods

Collaboration diagram for Numerical Methods:

Classes
class	asl::DataCoarser
	Algorithm for generation of coarsed dataset. More...
class	asl::DataClipper
	Algorithm for generation of coarsed dataset. More...
class	asl::DFOptimizer
	Numerical method which makes changes in the input map and produces map suitbale and optimal for use in BC. More...
class	asl::FDAdvectionDiffusion
	Numerical method which computes multicomponent transport processes. More...
class	asl::FDAdvectionDiffusion2
	Numerical method which computes multicomponent transport processes; \(O^2(dt)\). More...
class	asl::FDElasticityIncompressibleStatic
	Numerical method which computes homogenious isotropic elasticity equation. More...
class	asl::FDElasticityRelaxation
	Numerical method which computes homogenious isotropic elasticity equation. More...
class	asl::FDElasticity2
	Numerical method which computes homogenious isotropic elasticity equation. More...
class	asl::FDBVKinetics
	Numerical method which computes electrode reactions. More...
class	asl::FDMultiPhase
	Numerical method which computes multiphase transport processes. More...
class	asl::FDPoroElasticity
	Numerical method which computes homogenious isotropic poro-elasticity equation. More...
class	asl::FDStefanMaxwell
	Numerical method which computes multicomponent transport processes. More...
class	asl::InterfaceTrackingAlg1
	Numerical method which computes evolution of an interface. More...
class	asl::LBGK
	Numerical method for fluid flow. More...
class	asl::LevelSet
	Numerical method which computes evolution of an interface. More...
class	asl::LevelSetLinear
	Numerical method which computes evolution of an interface. More...
class	asl::LSFacetedGrowth
	Numerical method which computes evolution of an interface with a crystalographic kinetics. More...
class	asl::LSNormalGrowth
	Numerical method which computes evolution of an interface. More...
class	asl::TimeContinuations
	Numerical method that generates temporal extrapolation of the data, Abstract class. More...
class	asl::TimeContinPLagrange
	Numerical method that generates temporal extrapolation of the data with Lagrangian polynoms. More...
class	asl::TimeContinPLagrangeFraction
	Numerical method that generates temporal extrapolation of the data with Lagrangian polynoms of fractional argument. More...

Functions
SPFDAdvectionDiffusion	asl::generateFDAdvectionDiffusion (SPDataWithGhostNodesACLData c, double diffustionCoeff, SPAbstractDataWithGhostNodes v, const VectorTemplate *vt, bool compressibilityCorrection=false)
SPFDAdvectionDiffusion	asl::generateFDAdvectionDiffusion (SPDataWithGhostNodesACLData c, double diffustionCoeff, const VectorTemplate *vt)
SPFDMultiPhase	asl::generateFDMultiPhase (SPDataWithGhostNodesACLData c, SPAbstractDataWithGhostNodes v, const VectorTemplate *vt, bool compressibilityCorrection=false)
SPFDStefanMaxwell	asl::generateFDStefanMaxwell (SPDataWithGhostNodesACLData c1, SPDataWithGhostNodesACLData c2, double diffustionCoeff, SPAbstractDataWithGhostNodes v, const VectorTemplate *vt)
SPFDStefanMaxwell	asl::generateFDStefanMaxwell (SPDataWithGhostNodesACLData c1, SPDataWithGhostNodesACLData c2, double diffustionCoeff, const VectorTemplate *vt)

Detailed Description

Function Documentation

generateFDAdvectionDiffusion() [1/2]

SPFDMultiPhase asl::generateFDAdvectionDiffusion	(	SPDataWithGhostNodesACLData	c,
		double	diffustionCoeff,
		const VectorTemplate *	vt )

\[ \partial_t c_i= D_i \Delta c_i \]

where

Parameters

cData	corresponds to \( c_i \)
diffusionCoefficient	corresponds to \( D_i \)

\[ \partial_t c_i= D_i \Delta c_i \]

where

Parameters

cData

corresponds to \( c_i \)

\( D_i is diffusionCoefficient \), \(a\) is repulsion constant

generateFDAdvectionDiffusion() [2/2]

SPFDAdvectionDiffusion asl::generateFDAdvectionDiffusion	(	SPDataWithGhostNodesACLData	c,
		double	diffustionCoeff,
		SPAbstractDataWithGhostNodes	v,
		const VectorTemplate *	vt,
		bool	compressibilityCorrection = false )

\[ \partial_t c_i= D_i \Delta c_i - \nabla (\vec v c_i)\]

where

Parameters

cData	corresponds to \(c_i\)
diffusionCoefficient	corresponds to \(D_i\)
velocity	corresponds to \(\vec v\)

Examples

flowKDPGrowth.cc, and multicomponent_flow.cc.

generateFDMultiPhase()

SPFDMultiPhase asl::generateFDMultiPhase	(	SPDataWithGhostNodesACLData	c,
		SPAbstractDataWithGhostNodes	v,
		const VectorTemplate *	vt,
		bool	compressibilityCorrection = false )

\[ \partial_t c_i= D \Delta c_i - \nabla (\vec v c_i) - \nabla\left( a c_i \sum_{j\neq i}\nabla c_j\]

where

Parameters

cData	corresponds to \(c_i\)
diffusionCoefficient	corresponds to \(D_i\)
velocity	corresponds to \(\vec v\)

Examples

multiphase_flow.cc.

generateFDStefanMaxwell() [1/2]

SPFDStefanMaxwell asl::generateFDStefanMaxwell	(	SPDataWithGhostNodesACLData	c1,
		SPDataWithGhostNodesACLData	c2,
		double	diffustionCoeff,
		const VectorTemplate *	vt )

\[ \partial_t c_i= - \vec \nabla \cdot \vec J\]

\[ -\nabla c_i = \sum_{j, i\neq j} \frac{c_j\vec J_i-c_i\vec J_j}{c_tD_{ij}} + \frac{\vec J_i}{D_{i,D}}\]

where \(c_i\) is a molar concentration, \( v \) is the flow velocity, \(J_i\) is the molar flux, \(D_{i,D}\) is the component-dust diffusion coefficient, \(D_{ij}\) is the pair diffusion coefficient.

Parameters

c1	\(c_1\)
c2	\(c_2\)
diffusionCoeff	corresponds to \(D_{12}\)
vt	used VectorTemplate

generateFDStefanMaxwell() [2/2]

SPFDStefanMaxwell asl::generateFDStefanMaxwell	(	SPDataWithGhostNodesACLData	c1,
		SPDataWithGhostNodesACLData	c2,
		double	diffustionCoeff,
		SPAbstractDataWithGhostNodes	v,
		const VectorTemplate *	vt )

\[ \partial_t c_i= - \vec \nabla \cdot \vec J - \vec \nabla \cdot (\vec v c_i) \]

\[ -\nabla c_i = \sum_{j, i\neq j} \frac{c_j\vec J_i-c_i\vec J_j}{c_tD_{ij}} + \frac{\vec J_i}{D_{i,D}}\]

where \(c_i\) is a molar concentration, \( v \) is the flow velocity, \(J_i\) is the molar flux, \(D_{i,D}\) is the component-dust diffusion coefficient, \(D_{ij}\) is the pair diffusion coefficient.

parameters are related to the quation ones as follows

Parameters

c1	\(c_1\)
c2	\(c_2\)
diffusionCoeff	corresponds to \(D_{12}\)
v	velocity field
vt	used VectorTemplate