TanhSolnForAdvectionDiffusion Namespace Reference

Functions
void	get_exact_u (const Vector< double > &x, Vector< double > &u)
	Exact solution as a Vector. More...
void	get_exact_u (const Vector< double > &x, double &u)
	Exact solution as a scalar. More...
void	source_function (const Vector< double > &x_vect, double &source)
	Source function required to make the solution above an exact solution. More...
void	wind_function (const Vector< double > &x, Vector< double > &wind)
	Wind. More...
void	tanh_profile (const Vector< double > &x, Vector< double > &u)
	Tanh profile for assignment of boundary conditons as a Vector. More...
void	tanh_profile (const Vector< double > &x, double &u)
	Tanh profile for assignment of boundary conditons as a Vector. More...
void	prescribed_flux_on_fixed_x_boundary (const Vector< double > &x, double &flux)
	Flux required by the exact solution on a boundary on which x is fixed. More...

Variables
double	Peclet =200.0
	Peclet number. More...
double	Alpha =10.0
	Parameter for steepness of step. More...
double	TanPhi =1.0
	Parameter for angle of step. More...

Detailed Description

Namespace for exact solution for AdvectionDiffusion equation with "sharp" step

Namespace for physical parameters and boundary conditions "sharp" step

Function Documentation

get_exact_u() [1/2]

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

Exact solution as a scalar.

 {
  u=tanh(1.0-Alpha*(TanPhi*x[0]-x[1]));
 }

References Alpha, Eigen::bfloat16_impl::tanh(), TanPhi, and plotDoE::x.

get_exact_u() [2/2]

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

Exact solution as a Vector.

 {
  u[0]=tanh(1.0-Alpha*(TanPhi*x[0]-x[1]));
 }

References Alpha, Eigen::bfloat16_impl::tanh(), TanPhi, and plotDoE::x.

Referenced by RefineableAdvectionDiffusionProblem< ELEMENT >::actions_before_newton_solve(), TwoMeshFluxAdvectionDiffusionProblem< ELEMENT >::actions_before_newton_solve(), RefineableAdvectionDiffusionProblem< ELEMENT >::doc_solution(), and TwoMeshFluxAdvectionDiffusionProblem< ELEMENT >::doc_solution().

prescribed_flux_on_fixed_x_boundary()

void TanhSolnForAdvectionDiffusion::prescribed_flux_on_fixed_x_boundary	(	const Vector< double > &	x,
		double &	flux
	)

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

 {
  //The outer unit normal to the boundary is (1,0)
  double N[2] = {1.0, 0.0};
  //The flux in terms of the normal is
  flux = 
   -(1.0-pow(tanh(-1.0+Alpha*(TanPhi*x[0]-x[1])),2.0))*Alpha*TanPhi*N[0]+(
   1.0-pow(tanh(-1.0+Alpha*(TanPhi*x[0]-x[1])),2.0))*Alpha*N[1];
//  Use this one for the funky unforced solution
//  flux=-1.0; 
 }

References Alpha, ProblemParameters::flux(), N, Eigen::bfloat16_impl::pow(), Eigen::bfloat16_impl::tanh(), TanPhi, and plotDoE::x.

Referenced by TwoMeshFluxAdvectionDiffusionProblem< ELEMENT >::actions_after_adapt(), and TwoMeshFluxAdvectionDiffusionProblem< ELEMENT >::TwoMeshFluxAdvectionDiffusionProblem().

source_function()

void TanhSolnForAdvectionDiffusion::source_function	(	const Vector< double > &	x_vect,
		double &	source
	)

Source function required to make the solution above an exact solution.

Zero source function.

 {
  double x=x_vect[0];
  double y=x_vect[1];
  source = 
2.0*tanh(-0.1E1+Alpha*(TanPhi*x-y))*(1.0-pow(tanh(-0.1E1+Alpha*(
TanPhi*x-y)),2.0))*Alpha*Alpha*TanPhi*TanPhi+2.0*tanh(-0.1E1+Alpha*(TanPhi*x-y)
)*(1.0-pow(tanh(-0.1E1+Alpha*(TanPhi*x-y)),2.0))*Alpha*Alpha-Peclet*(-sin(6.0*y
)*(1.0-pow(tanh(-0.1E1+Alpha*(TanPhi*x-y)),2.0))*Alpha*TanPhi+cos(6.0*x)*(1.0-
pow(tanh(-0.1E1+Alpha*(TanPhi*x-y)),2.0))*Alpha);
 }

References Alpha, cos(), Peclet, Eigen::bfloat16_impl::pow(), sin(), TestProblem::source(), Eigen::bfloat16_impl::tanh(), TanPhi, plotDoE::x, and y.

Referenced by main(), and run_it().

tanh_profile() [1/2]

void TanhSolnForAdvectionDiffusion::tanh_profile	(	const Vector< double > &	x,
		double &	u
	)

Tanh profile for assignment of boundary conditons as a Vector.

 {
  u=tanh(1.0-Alpha*(TanPhi*x[0]-x[1]));
 }

References Alpha, Eigen::bfloat16_impl::tanh(), TanPhi, and plotDoE::x.

tanh_profile() [2/2]

void TanhSolnForAdvectionDiffusion::tanh_profile	(	const Vector< double > &	x,
		Vector< double > &	u
	)

Tanh profile for assignment of boundary conditons as a Vector.

 {
  u[0]=tanh(1.0-Alpha*(TanPhi*x[0]-x[1]));
 }

References Alpha, Eigen::bfloat16_impl::tanh(), TanPhi, and plotDoE::x.

wind_function()

void TanhSolnForAdvectionDiffusion::wind_function	(	const Vector< double > &	x,
		Vector< double > &	wind
	)

Wind.

Wind: Recirculating cells.

 {
  wind[0]=sin(6.0*x[1]);
  wind[1]=cos(6.0*x[0]);
 }

References cos(), sin(), and plotDoE::x.

Referenced by main(), and run_it().

Variable Documentation

Alpha

double TanhSolnForAdvectionDiffusion::Alpha =10.0

Parameter for steepness of step.

Parameter for steepness of step in tanh profile.

Referenced by EntryFlowProblem< ELEMENT >::actions_before_newton_solve(), CombCanSpineMesh< ELEMENT, INTERFACE_ELEMENT >::build_single_layer_mesh(), CombTipSpineMesh< ELEMENT, INTERFACE_ELEMENT >::build_single_layer_mesh(), STSpineMesh< ELEMENT, INTERFACE_ELEMENT >::build_single_layer_mesh(), QThermalPVDElement< DIM >::Default_Physical_Constant_Value(), oomph::PolarStreamfunctionTractionElement< ELEMENT >::fill_in_generic_residual_contribution(), oomph::PolarNavierStokesTractionElement< ELEMENT >::fill_in_generic_residual_contribution(), oomph::PolarNavierStokesEquations::fill_in_generic_residual_contribution(), oomph::RefineablePolarNavierStokesEquations::fill_in_generic_residual_contribution(), oomph::RefineablePolarStreamfunctionEquations::fill_in_generic_residual_contribution(), oomph::PolarStreamfunctionEquations::fill_in_generic_residual_contribution(), TanhSolnForLinearWave::get_exact_gradient(), TanhSolnForPoisson::get_exact_gradient(), ArcTanSolnForPoisson::get_exact_gradient(), get_exact_u(), GlobalParameters::get_source(), PolarNSProblem< ELEMENT >::header(), oomph::PolarStreamfunctionEquations::interpolated_vorticity(), main(), oomph::PolarNavierStokesEquations::output(), prescribed_flux_on_fixed_x_boundary(), TanhSolnForPoisson::prescribed_flux_on_fixed_x_boundary(), Global_Parameters::pressure_load(), FlowAroundCylinderProblem< ELEMENT >::set_boundary_conditions(), InclinedPlaneProblem< ELEMENT, INTERFACE_ELEMENT >::solve_steady(), TanhSolnForPoisson::source_function(), source_function(), oomph::PolarNavierStokesEquations::strain_rate(), oomph::PolarNavierStokesEquations::strain_rate_by_r(), and tanh_profile().

Peclet

double TanhSolnForAdvectionDiffusion::Peclet =200.0

Peclet number.

Referenced by RefineableBuoyantQCrouzeixRaviartElement< DIM >::Default_Physical_Constant_Value(), QCrouzeixRaviartElementWithTwoExternalElement< DIM >::Default_Physical_Constant_Value(), main(), RefineableAdvectionDiffusionProblem< ELEMENT >::RefineableAdvectionDiffusionProblem(), source_function(), and TwoMeshFluxAdvectionDiffusionProblem< ELEMENT >::TwoMeshFluxAdvectionDiffusionProblem().

TanPhi

double TanhSolnForAdvectionDiffusion::TanPhi =1.0

Parameter for angle of step.

Parameter for angle of step in tanh profile.

Referenced by TanhSolnForPoisson::get_exact_gradient(), get_exact_u(), GlobalParameters::get_source(), main(), prescribed_flux_on_fixed_x_boundary(), TanhSolnForPoisson::prescribed_flux_on_fixed_x_boundary(), source_function(), and tanh_profile().