Functions
Exact solution as a Vector void	get_exact_u (const Vector< double > &x, Vector< double > &u)

Exact solution as a scalar void	get_exact_u (const Vector< double > &x, double &u)

Source function required to make the solution above an exact solution void	source_function (const Vector< double > &x_vect, double &source)

Beta required by the exact solution on a boundary on which r is fixed void	prescribed_beta_on_fixed_r_boundary (const Vector< double > &x_vect, double &beta)

Alfa required by the exact solution on a boundary on which r is fixed void	prescribed_alpha_on_fixed_r_boundary (const Vector< double > &x_vect, double &alpha)

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

Variables
double	Peclet = 0.0
	Peclet number. More...

double	TanPhi = 0.5
	Parameter for angle of step. More...

double	Omega = 0.5
	Parameter for switch z-dependence. More...

double	Epsilon = 0.1
	Amplitude of boundary deflection (Epsilon<R!!!) More...

double	K_Alpha = 1.0
	Relation between alfa and beta (. More...

Detailed Description

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

Function Documentation

◆ get_exact_u() [1/2]

Exact solution as a scalar void TanhSolnForSteadyAxisymAdvectionDiffusion::get_exact_u	(	const Vector< double > &	x,
		double &	u
	)

  {
   double f_rz = 1.0-(TanPhi*pow(x[0],2.0)-Omega*x[1]); 
   u = tanh(f_rz);
  
  }

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

◆ get_exact_u() [2/2]

Exact solution as a Vector void TanhSolnForSteadyAxisymAdvectionDiffusion::get_exact_u	(	const Vector< double > &	x,
		Vector< double > &	u
	)

  {
   double f_rz = 1.0-(TanPhi*pow(x[0],2.0)-Omega*x[1]); 
   u[0] = tanh(f_rz);
  }

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

Referenced by TwoMeshFluxSteadyAxisymAdvectionDiffusionProblem< ELEMENT >::doc_solution(), and for().

◆ prescribed_alpha_on_fixed_r_boundary()

Alfa required by the exact solution on a boundary on which r is fixed void TanhSolnForSteadyAxisymAdvectionDiffusion::prescribed_alpha_on_fixed_r_boundary	(	const Vector< double > &	x_vect,
		double &	alpha
	)

  {
   double r = x_vect[0];
   double z = x_vect[1];
  
   double f_rz = 1.0-(TanPhi*pow(r,2.0)-Omega*z);
  
   alpha = -K_Alpha*( 1.0/( sqrt(1.0 + pow(Epsilon*cos(z),2.0) ) ) )*
                    ( 1.0/( 1.0 -  K_Alpha*tanh(f_rz) ) )*
                    ( 1.0 - pow(tanh(f_rz),2.0))*
                    (-2.0*TanPhi*r + Epsilon*cos(z)*Omega);
  
  }

References alpha, cos(), Epsilon, K_Alpha, Omega, Eigen::bfloat16_impl::pow(), UniformPSDSelfTest::r, sqrt(), Eigen::bfloat16_impl::tanh(), and TanPhi.

Referenced by Wind_fct_pt().

◆ prescribed_beta_on_fixed_r_boundary()

Beta required by the exact solution on a boundary on which r is fixed void TanhSolnForSteadyAxisymAdvectionDiffusion::prescribed_beta_on_fixed_r_boundary	(	const Vector< double > &	x_vect,
		double &	beta
	)

  {
   double r = x_vect[0];
   double z = x_vect[1];
  
   double f_rz = 1.0-(TanPhi*pow(r,2.0)-Omega*z);
  
   //The beta is (for the problem with bound1 = F(z) = R + epsilon*sin(z) with 0<z<H=2*Pi)
  
   beta = -1.0*( 1.0/( sqrt(1.0 + pow(Epsilon*cos(z),2.0) ) ) )*
               ( 1.0/( 1.0 -  K_Alpha*tanh(f_rz) ) )*
               ( 1.0 - pow(tanh(f_rz),2.0))*
               (-2.0*TanPhi*r + Epsilon*cos(z)*Omega);
  
  }

References beta, cos(), Epsilon, K_Alpha, Omega, Eigen::bfloat16_impl::pow(), UniformPSDSelfTest::r, sqrt(), Eigen::bfloat16_impl::tanh(), and TanPhi.

Referenced by Wind_fct_pt().

◆ source_function()

Source function required to make the solution above an exact solution void TanhSolnForSteadyAxisymAdvectionDiffusion::source_function	(	const Vector< double > &	x_vect,
		double &	source
	)

  {
   double r = x_vect[0];
   double z = x_vect[1];
  
   double f_rz = 1.0-(TanPhi*pow(r,2.0)-Omega*z); 
  
    source =  
     (1.0-pow(tanh(f_rz),2.0))*
     ( Peclet*(-2*r*TanPhi*sin(6.0*z) + Omega*cos(6.0*r)) + 
       2.0*tanh(f_rz)*( pow(Omega,2.0) + 4.0*pow(r*TanPhi,2.0) ) +
       4.0*TanPhi); 
  }

References cos(), Omega, Peclet, Eigen::bfloat16_impl::pow(), UniformPSDSelfTest::r, sin(), TestProblem::source(), Eigen::bfloat16_impl::tanh(), and TanPhi.

Referenced by main().

◆ wind_function()

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

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

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

Referenced by main().

Variable Documentation

◆ Epsilon

double TanhSolnForSteadyAxisymAdvectionDiffusion::Epsilon = 0.1

Amplitude of boundary deflection (Epsilon<R!!!)

Referenced by prescribed_alpha_on_fixed_r_boundary(), prescribed_beta_on_fixed_r_boundary(), and Wind_fct_pt().

◆ K_Alpha

double TanhSolnForSteadyAxisymAdvectionDiffusion::K_Alpha = 1.0

Relation between alfa and beta (.

Referenced by prescribed_alpha_on_fixed_r_boundary(), and prescribed_beta_on_fixed_r_boundary().

◆ Omega

double TanhSolnForSteadyAxisymAdvectionDiffusion::Omega = 0.5

Parameter for switch z-dependence.

Referenced by get_exact_u(), prescribed_alpha_on_fixed_r_boundary(), prescribed_beta_on_fixed_r_boundary(), and source_function().

◆ Peclet

double TanhSolnForSteadyAxisymAdvectionDiffusion::Peclet = 0.0

Peclet number.

Referenced by source_function(), and Wind_fct_pt().

◆ TanPhi

double TanhSolnForSteadyAxisymAdvectionDiffusion::TanPhi = 0.5

Parameter for angle of step.