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

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

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

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

Variables
double	U_shift =8.0

Detailed Description

Namespace for forced exact solution for UnsteadyHeat equation.

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Function Documentation

◆ get_exact_u() [1/2]

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

Exact solution as a scalar.

   {
     // Cache the value of pi
     double pi=MathematicalConstants::Pi;
  
     // The full solution
     u=sin(pi*x[0])*sin(pi*x[1])*cos(2.0*pi*t)+U_shift;
   } // End of get_exact_u

References cos(), constants::pi, oomph::MathematicalConstants::Pi, sin(), plotPSD::t, U_shift, and plotDoE::x.

◆ get_exact_u() [2/2]

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

Exact solution as a vector.

   {
     // Cache the value of pi
     double pi=MathematicalConstants::Pi;
  
     // The full solution
     u[0]=sin(pi*x[0])*sin(pi*x[1])*cos(2.0*pi*t)+U_shift;
   } // End of get_exact_u

References cos(), constants::pi, oomph::MathematicalConstants::Pi, sin(), plotPSD::t, U_shift, and plotDoE::x.

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

◆ get_source()

void SinSolution::get_source	(	const double &	t,
		const Vector< double > &	x,
		double &	source
	)

Source function to make it an exact solution.

   {
     // Cache the value of pi
     double pi=MathematicalConstants::Pi;
  
     // The temporal derivative of the solution
     double du_dt=-2.0*pi*sin(pi*x[0])*sin(pi*x[1])*sin(2.0*pi*t);
  
     // Second derivative of spatial contribution w.r.t. x
     double d2u_dx2=-pow(pi,2)*sin(pi*x[0])*sin(pi*x[1])*cos(2.0*pi*t);
  
     // Second derivative of spatial contribution w.r.t. y
     double d2u_dy2=-pow(pi,2)*sin(pi*x[0])*sin(pi*x[1])*cos(2.0*pi*t);
  
     // Assign the source function value
     source=-GlobalParameters::Alpha*du_dt+
            GlobalParameters::Beta*(d2u_dx2+d2u_dy2);
   } // End of get_source

References GlobalParameters::Alpha, GlobalParameters::Beta, cos(), constants::pi, oomph::MathematicalConstants::Pi, Eigen::bfloat16_impl::pow(), sin(), TestProblem::source(), plotPSD::t, and plotDoE::x.

Referenced by main().

Variable Documentation

◆ U_shift

double SinSolution::U_shift =8.0

Referenced by get_exact_u().

Functions