ExactSolnForUnsteadyHeat Namespace Reference

Namespace for unforced exact solution for UnsteadyHeat equation. More...

Functions
void	get_exact_u (const double &time, const Vector< double > &x, Vector< double > &u)
	Exact solution as a Vector. More...
void	get_exact_u (const double &time, const Vector< double > &x, double &u)
	Exact solution as a scalar. More...
void	get_source (const double &time, const Vector< double > &x, double &source)
	Source function to make it an exact solution. More...
void	prescribed_flux_on_fixed_y_boundary (const double &time, const Vector< double > &x, const Vector< double > &n, const double &u, double &flux)
	Flux required by the exact solution. More...

Variables
double	K =10
	Decay factor. More...
double	Phi =1.0
	Angle of bump. More...
double	Gamma =10.0
	Factor controlling the rate of change. More...

Detailed Description

Namespace for unforced exact solution for UnsteadyHeat equation.

Namespace for forced exact solution for UnsteadyHeat equation.

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Function Documentation

get_exact_u() [1/2]

void ExactSolnForUnsteadyHeat::get_exact_u	(	const double &	time,
		const Vector< double > &	x,
		double &	u
	)

Exact solution as a scalar.

 {
  double zeta=cos(Phi)*x[0]+sin(Phi)*x[1];
  u=exp(-K*time)*sin(zeta*sqrt(K));
 }

References cos(), Eigen::bfloat16_impl::exp(), K, Phi, sin(), sqrt(), plotDoE::x, and Eigen::zeta().

get_exact_u() [2/2]

void ExactSolnForUnsteadyHeat::get_exact_u	(	const double &	time,
		const Vector< double > &	x,
		Vector< double > &	u
	)

Exact solution as a Vector.

 {
  double zeta=cos(Phi)*x[0]+sin(Phi)*x[1];
  u[0]=exp(-K*time)*sin(zeta*sqrt(K));
 }

References cos(), Eigen::bfloat16_impl::exp(), K, Phi, sin(), sqrt(), plotDoE::x, and Eigen::zeta().

Referenced by UnsteadyHeatProblem< ELEMENT >::actions_before_implicit_timestep(), UnsteadyHeatProblem< ELEMENT >::doc_solution(), and UnsteadyHeatProblem< ELEMENT >::set_initial_condition().

get_source()

void ExactSolnForUnsteadyHeat::get_source	(	const double &	time,
		const Vector< double > &	x,
		double &	source
	)

Source function to make it an exact solution.

 {
  source = 0.0;
 }

References TestProblem::source().

Referenced by main(), and run_it().

prescribed_flux_on_fixed_y_boundary()

void ExactSolnForUnsteadyHeat::prescribed_flux_on_fixed_y_boundary	(	const double &	time,
		const Vector< double > &	x,
		const Vector< double > &	n,
		const double &	u,
		double &	flux
	)

Flux required by the exact solution.

 {  
  double NX = n[0];
  double NY = n[1];
  
  //The flux in terms of the normal is
  double zeta=cos(Phi)*x[0]+sin(Phi)*x[1];
  flux=exp(-K*time)*sqrt(K)*cos(zeta*sqrt(K))*(cos(Phi)*NX+sin(Phi)*NY);
 }

References cos(), Eigen::bfloat16_impl::exp(), ProblemParameters::flux(), K, n, Phi, sin(), sqrt(), plotDoE::x, and Eigen::zeta().

Variable Documentation

Gamma

double ExactSolnForUnsteadyHeat::Gamma =10.0

Factor controlling the rate of change.

K

double ExactSolnForUnsteadyHeat::K =10

Decay factor.

Wavenumber.

Referenced by get_exact_u(), prescribed_flux_on_fixed_y_boundary(), and UnsteadyHeatProblem< ELEMENT >::UnsteadyHeatProblem().

Phi

double ExactSolnForUnsteadyHeat::Phi =1.0

Angle of bump.

Referenced by TanhSolnForLinearWave::get_exact_gradient(), get_exact_u(), and prescribed_flux_on_fixed_y_boundary().