TestCaseStefanPME Class Reference

The TestCaseStefanPME class provides definition of test cases (exact solution, diffusion) for the Stefan and PME problems. More...

#include <TestCaseStefanPME.hpp>

Public Member Functions
	TestCaseStefanPME (const std::vector< int > iTCS)
	Initialise data.
double	sol (const double x, const double y)
	Returns the exact solution at the points x, y.
Eigen::Vector2d	grad_sol (const double x, const double y, const Cell *cell)
	Returns the gradient of the exact solution at the points x, y.
Eigen::Matrix2d	hess_sol (const double x, const double y, const Cell *cell)
	Returns the Hessian of the exact solution at the points x, y.
Eigen::Matrix2d	diff (const double x, const double y, const Cell *cell)
	Returns the diffusion matrix at the points x, y.
Eigen::Vector2d	div_diff (const double x, const double y, const Cell *cell)
	Returns the divergence by row of the diffusion matrix at the points x, y.
double	source (const double x, const double y, const Cell *cell)
	Returns the source term at the points x, y.
double	get_lambda ()
	Returns the value of the parameter lambda.
void	validate ()
	Check if the provided test cases are valid (within range, and combination of solution/diffusion valid)
size_t	get_deg_diff ()
	Returns the degree of the diffusion tensor (useful to set up quadrature rules of proper degree)
Eigen::Vector2d	translate (double x, double y) const
double	radial (const double x, const double y) const

Detailed Description

The TestCaseStefanPME class provides definition of test cases (exact solution, diffusion) for the Stefan and PME problems.

Constructor & Destructor Documentation

TestCaseStefanPME()

TestCaseStefanPME::TestCaseStefanPME

(

const std::vector< int >

iTCS

)

Initialise data.

Parameters

iTCS	The vector id of the test case: (id of solution, id of diffusion). For positive id of solutions, we take the solutions from TestCase.cpp. Otherwise, it's specific solutions for Stefan or PME.

Member Function Documentation

diff()

Eigen::Matrix2d TestCaseStefanPME::diff	(	const double	x,
		const double	y,
		const Cell *	cell
	)

Returns the diffusion matrix at the points x, y.

iTCS[1]=1: Diff = Id

iTCS[1]=2: Diff = \(\left[\begin{array}{cc}y^2+1 & -xy\\ -xy & x^2+1\end{array}\right]\)

iTCS[1]=3: Diff= \(\left[\begin{array}{cc}\lambda & 0\\ 0 & 1\end{array}\right]\) if \(y<1/2\), Diff=Id if \(y\ge 1/2\). Only valid with iTCS[0]=2 ( \(\partial_x u\) must vanish along \(y=1/2\)).

iTCS[1]=4: rotating diffusion. Diff= \(\left[\begin{array}{cc}\epsilon \bar{x}^2 + \bar{y}^2 & (\epsilon-1)\bar{x}\bar{y}\\ (\epsilon-1)\bar{x}\bar{y} & \bar{x}^2+\epsilon \bar{y}^2\end{array}\right]\), where \(\bar{x}=x+0.1\) and \(\bar{y}=y+0.1\).

iTCS[1]=5: Diff= \(\left[\begin{array}{cc}\lambda & 0\\ 0 & 1\end{array}\right]\).

Parameters

cell	In case of discontinuity, we need to know the cell we're in to select the correct formula

div_diff()

Eigen::Vector2d TestCaseStefanPME::div_diff	(	const double	x,
		const double	y,
		const Cell *	cell
	)

Returns the divergence by row of the diffusion matrix at the points x, y.

Parameters

cell	In case of discontinuity, we need to know the cell we're in to select the correct formula

get_deg_diff()

size_t TestCaseStefanPME::get_deg_diff ( )

inline

Returns the degree of the diffusion tensor (useful to set up quadrature rules of proper degree)

get_lambda()

double TestCaseStefanPME::get_lambda ( )

inline

Returns the value of the parameter lambda.

grad_sol()

Eigen::Vector2d TestCaseStefanPME::grad_sol	(	const double	x,
		const double	y,
		const Cell *	cell
	)

Returns the gradient of the exact solution at the points x, y.

Parameters

cell	In case of discontinuity, we need to know the cell we're in to select the correct formula

hess_sol()

Eigen::Matrix2d TestCaseStefanPME::hess_sol	(	const double	x,
		const double	y,
		const Cell *	cell
	)

Returns the Hessian of the exact solution at the points x, y.

Parameters

cell	In case of discontinuity, we need to know the cell we're in to select the correct formula

radial()

double TestCaseStefanPME::radial ( const double  x, const double  y  ) const

inline

sol()

double TestCaseStefanPME::sol	(	const double	x,
		const double	y
	)

Returns the exact solution at the points x, y.

iTCS[0]=-1, \(u=\cosh(\frac{x+y}{\sqrt{2}}-\gamma\) if \(\frac{x+y}{\sqrt{2}}>\gamma\).

iTCS[0]=-2, \(u=(\frac{x+y}{\sqrt{2}}-\frac12)^3\).

iTCS[0]=-3, \(u=max(\rho - r^2, 0)\) where \(r^2=(x-.5)^2+(y-.5)^2\).

source()

double TestCaseStefanPME::source	(	const double	x,
		const double	y,
		const Cell *	cell
	)

Returns the source term at the points x, y.

Parameters

cell	In case of discontinuity, we need to know the cell we're in to select the correct formula

translate()

Eigen::Vector2d TestCaseStefanPME::translate ( double  x, double  y  ) const

inline

validate()

void TestCaseStefanPME::validate

(

)

Check if the provided test cases are valid (within range, and combination of solution/diffusion valid)

---

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

• Schemes/TestCase/TestCaseStefanPME.hpp
• Schemes/TestCase/TestCaseStefanPME.cpp