Numerical Methods
Numerics
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, multicomponent_flow.cc, surfaceFlux.cc, and testSMPhiBV.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

Examples
  testSMDiff.cc, testSMDiff3C.cc, testSMPhi.cc, and testSMPhiBV.cc.