Functions
double	exact_u (const double &time, const Vector< double > &x)
	Exact solution. More...

double	exact_dudt (const double &time, const Vector< double > &x)
	1st time-deriv of exact solution More...

double	exact_d2udt2 (const double &time, const Vector< double > &x)
	2nd time-deriv of exact solution More...

void	get_exact_u (const double &time, const Vector< double > &x, Vector< double > &u)
	Exact solution as a vector. More...

void	get_source (const double &time, const Vector< double > &x, double &source)
	Source function to make it an exact solution. More...

void	get_exact_gradient (const double &time, const Vector< double > &x, Vector< double > &dudx)
	Gradient of exact solution. More...

void	prescribed_flux_on_fixed_y_boundary (const double &time, const Vector< double > &x, double &flux)
	Prescribed flux on a fixed y max boundary. More...

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

double	Phi
	Orientation of step wave. More...

Detailed Description

Namespace for exact solution for LinearWave equation with sharp step

Namespace for travelling wave solution for LinearWave equation with sharp step

Function Documentation

◆ exact_d2udt2()

double TanhSolnForLinearWave::exact_d2udt2	(	const double &	time,
		const Vector< double > &	x
	)

2nd time-deriv of exact solution

  {
   double zeta=cos(Phi)*x[0]+sin(Phi)*x[1];
   return -2.0*Alpha*Alpha*tanh(1.0-Alpha*(zeta-time))/
    (cosh(1.0-Alpha*(zeta-time))*cosh(1.0-Alpha*(zeta-time)));
  }

References Alpha, cos(), Eigen::bfloat16_impl::cosh(), Phi, sin(), Eigen::bfloat16_impl::tanh(), plotDoE::x, and Eigen::zeta().

Referenced by LinearWaveProblem< ELEMENT, TIMESTEPPER >::actions_before_implicit_timestep(), get_exact_u(), and LinearWaveProblem< ELEMENT, TIMESTEPPER >::set_initial_condition().

◆ exact_dudt()

double TanhSolnForLinearWave::exact_dudt	(	const double &	time,
		const Vector< double > &	x
	)

1st time-deriv of exact solution

  {
   double zeta=cos(Phi)*x[0]+sin(Phi)*x[1];
   return Alpha/(cosh(1.0-Alpha*(zeta-time))*
               cosh(1.0-Alpha*(zeta-time)));
  }

References Alpha, cos(), Eigen::bfloat16_impl::cosh(), Phi, sin(), plotDoE::x, and Eigen::zeta().

Referenced by LinearWaveProblem< ELEMENT, TIMESTEPPER >::actions_before_implicit_timestep(), get_exact_u(), and LinearWaveProblem< ELEMENT, TIMESTEPPER >::set_initial_condition().

◆ exact_u()

double TanhSolnForLinearWave::exact_u	(	const double &	time,
		const Vector< double > &	x
	)

Exact solution.

  {
   double zeta=cos(Phi)*x[0]+sin(Phi)*x[1];
   return tanh(1.0-Alpha*(zeta-time));
  }

References Alpha, cos(), Phi, sin(), Eigen::bfloat16_impl::tanh(), plotDoE::x, and Eigen::zeta().

Referenced by LinearWaveProblem< ELEMENT, TIMESTEPPER >::actions_before_implicit_timestep(), PolarNSProblem< ELEMENT >::actions_before_solve(), oomph::EulerEquations< DIM >::compute_error(), oomph::ScalarAdvectionEquations< DIM >::compute_error(), get_exact_u(), and LinearWaveProblem< ELEMENT, TIMESTEPPER >::set_initial_condition().

◆ get_exact_gradient()

void TanhSolnForLinearWave::get_exact_gradient	(	const double &	time,
		const Vector< double > &	x,
		Vector< double > &	dudx
	)

Gradient of exact solution.

  {
   double zeta=cos(Phi)*x[0]+sin(Phi)*x[1];
   dudx[0] = -Alpha*cos(Phi)/(cosh(1.0-Alpha*(zeta-time))
                              *cosh(1.0-Alpha*(zeta-time)));
   dudx[1] = -Alpha*sin(Phi)/(cosh(1.0-Alpha*(zeta-time))
                              *cosh(1.0-Alpha*(zeta-time)));
  }

References TanhSolnForAdvectionDiffusion::Alpha, cos(), Eigen::bfloat16_impl::cosh(), ExactSolnForUnsteadyHeat::Phi, sin(), plotDoE::x, and Eigen::zeta().

Referenced by prescribed_flux_on_fixed_y_boundary().

◆ get_exact_u()

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

Exact solution as a vector.

  {
   u[0]=exact_u(time,x);
   u[1]=exact_dudt(time,x);
   u[2]=exact_d2udt2(time,x);
  }

References exact_d2udt2(), exact_dudt(), exact_u(), and plotDoE::x.

Referenced by LinearWaveProblem< ELEMENT, TIMESTEPPER >::doc_solution().

◆ get_source()

void TanhSolnForLinearWave::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().

◆ prescribed_flux_on_fixed_y_boundary()

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

Prescribed flux on a fixed y max boundary.

  {
   // Set up normal
   Vector<double> dudx(2), n(2);
   n[0]=1.0;
   n[1]=0.0;
  
   // Get gradient
   get_exact_gradient(time,x,dudx);
  
   // Flux
   flux = dudx[0]*n[0] + dudx[1]*n[1];
  }