Functions
double	step_position (const double &time)
	Position of step (x-axis intercept) More...

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, double &flux)
	Flux required by the exact solution on a boundary on which y is fixed. More...

Variables
double	Alpha
	Parameter for steepness of step. More...

double	Beta
	Parameter for amplitude of step translation. More...

double	Gamma
	Parameter for timescale of step translation. More...

double	TanPhi
	Parameter for angle of step. More...

Detailed Description

//////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////// ///////////////////////////////////////////////////////////////////// Namespace for exact solution of unsteady heat equation with sharp step

Function Documentation

◆ get_exact_u() [1/2]

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

Exact solution as a scalar.

  {
   double X=x[0];
   double Y=x[1];
   u=tanh(0.1E1-Alpha*(TanPhi*(X-Beta*tanh(Gamma*cos(0.2E1*
          MathematicalConstants::Pi*time)))-Y));
  }

References Alpha, Beta, cos(), Gamma, BiharmonicTestFunctions2::Pi, Eigen::bfloat16_impl::tanh(), TanPhi, plotDoE::x, X, and Y.

◆ get_exact_u() [2/2]

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

Exact solution as a Vector.

  {
   double X=x[0];
   double Y=x[1];
   u[0]=tanh(0.1E1-Alpha*(TanPhi*(X-Beta*tanh(Gamma*cos(0.2E1*
        MathematicalConstants::Pi*time)))-Y));
  }

References Alpha, Beta, cos(), Gamma, BiharmonicTestFunctions2::Pi, Eigen::bfloat16_impl::tanh(), TanPhi, plotDoE::x, X, and Y.

Referenced by RefineableUnsteadyHeatProblem< ELEMENT >::doc_solution().

◆ get_source()

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

Source function to make it an exact solution.

  {
   double X=x[0];
   double Y=x[1];
   source =  -2.0*tanh(0.1E1-Alpha*(TanPhi*(X-Beta*tanh(Gamma*cos(0.2E1*
 MathematicalConstants::Pi*time)))-Y))*(1.0-pow(tanh(0.1E1-Alpha*(TanPhi*(X-
 Beta*tanh(Gamma*cos(0.2E1*MathematicalConstants::Pi*time)))-Y)),2.0))*Alpha*
 Alpha*TanPhi*TanPhi-2.0*tanh(0.1E1-Alpha*(TanPhi*(X-Beta*tanh(Gamma*cos(0.2E1*
 MathematicalConstants::Pi*time)))-Y))*(1.0-pow(tanh(0.1E1-Alpha*(TanPhi*(X-
 Beta*tanh(Gamma*cos(0.2E1*MathematicalConstants::Pi*time)))-Y)),2.0))*Alpha*
 Alpha+0.2E1*(1.0-pow(tanh(0.1E1-Alpha*(TanPhi*(X-Beta*tanh(Gamma*cos(0.2E1*
 MathematicalConstants::Pi*time)))-Y)),2.0))*Alpha*TanPhi*Beta*(1.0-pow(tanh(
 Gamma*cos(0.2E1*MathematicalConstants::Pi*time)),2.0))*Gamma*sin(0.2E1*
 MathematicalConstants::Pi*time)*MathematicalConstants::Pi;
  }

References Alpha, Beta, cos(), Gamma, BiharmonicTestFunctions2::Pi, Eigen::bfloat16_impl::pow(), sin(), TestProblem::source(), Eigen::bfloat16_impl::tanh(), TanPhi, plotDoE::x, X, and Y.

Referenced by main(), and run_it().

◆ prescribed_flux_on_fixed_y_boundary()

void TanhSolnForUnsteadyHeat::prescribed_flux_on_fixed_y_boundary	(	const double &	time,
		const Vector< double > &	x,
		double &	flux
	)

Flux required by the exact solution on a boundary on which y is fixed.

  {
   double X=x[0];
   double Y=x[1];
  
   //The outer unit normal to the boundary is (0,-1)
   double NX =  0.0;
   double NY = -1.0;
  
   //The flux in terms of the normal is
   flux =  -(1.0-pow(tanh(0.1E1-Alpha*(TanPhi*(X-Beta*tanh(Gamma*cos(0.2E1*
 MathematicalConstants::Pi*time)))-Y)),2.0))*Alpha*TanPhi*NX+(1.0-pow(tanh(
 0.1E1-Alpha*(TanPhi*(X-Beta*tanh(Gamma*cos(0.2E1*MathematicalConstants::Pi*
 time)))-Y)),2.0))*Alpha*NY;
  }

References Alpha, Beta, cos(), ProblemParameters::flux(), Gamma, BiharmonicTestFunctions2::Pi, Eigen::bfloat16_impl::pow(), Eigen::bfloat16_impl::tanh(), TanPhi, plotDoE::x, X, and Y.

Referenced by RefineableUnsteadyHeatProblem< ELEMENT >::RefineableUnsteadyHeatProblem().

◆ step_position()

double TanhSolnForUnsteadyHeat::step_position ( const double & time )

Position of step (x-axis intercept)

  {
   return Beta*tanh(Gamma*cos(0.2E1*MathematicalConstants::Pi*time));
  }

References Beta, cos(), Gamma, BiharmonicTestFunctions2::Pi, and Eigen::bfloat16_impl::tanh().

Referenced by RefineableUnsteadyHeatProblem< ELEMENT >::doc_solution().

Variable Documentation

◆ Alpha

double TanhSolnForUnsteadyHeat::Alpha

Parameter for steepness of step.

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

◆ Beta

double TanhSolnForUnsteadyHeat::Beta

Parameter for amplitude of step translation.

Referenced by get_exact_u(), get_source(), prescribed_flux_on_fixed_y_boundary(), RefineableUnsteadyHeatProblem< ELEMENT >::RefineableUnsteadyHeatProblem(), and step_position().

◆ Gamma

double TanhSolnForUnsteadyHeat::Gamma

Parameter for timescale of step translation.