Implementation of the explicit Richardson scheme (CTCS). More...

#include <richardson.hpp>

Inheritance diagram for Richardson:

Collaboration diagram for Richardson:

Public Member Functions
bool	uses_previous_step () const noexcept override
	Indicate that this is a three-level scheme.
std::string	name () const override
	Get human-readable name of the scheme.
void	step (const Grid &g, double D, double dt, const std::vector< double > &Tprev, const std::vector< double > &Tcurr, std::vector< double > &Tnext) const override
	Advance one time step using the Richardson explicit scheme.
Public Member Functions inherited from Method
virtual	~Method ()=default

Detailed Description

Implementation of the explicit Richardson scheme (CTCS).

The scheme reads:

$\‍[ T_i^{n+1} = T_i^{n-1} + 2 r \left( T_{i+1}^n - 2 T_i^n + T_{i-1}^n \right), \quad r = \frac{D \, \Delta t}{\Delta x^2} \‍]$

It is a three-level scheme, therefore it requires both $T^{n-1}$ and $T^n$ to produce $T^{n+1}$ . Boundary conditions are not enforced here, but left to the solver.

Definition at line 26 of file richardson.hpp.

Member Function Documentation

◆ name()

std::string Richardson::name ( ) const

inlineoverridevirtual

Get human-readable name of the scheme.

Returns: "Richardson"

Implements Method.

Definition at line 42 of file richardson.hpp.

◆ step()

void Richardson::step	(	const Grid &	g,
		double	D,
		double	dt,
		const std::vector< double > &	Tprev,
		const std::vector< double > &	Tcurr,
		std::vector< double > &	Tnext ) const

overridevirtual

Advance one time step using the Richardson explicit scheme.

This computes $T^{n+1}$ from $T^{n}$ and $T^{n-1}$ . Interior nodes $i = 1, \dots, N-2$ are updated, while boundary nodes are left untouched (the solver will impose Dirichlet BCs).

Parameters

g	Grid metadata (spacing and number of nodes)
D	Diffusivity [cm^2/h]
dt	Time step [h]
Tprev	Temperature field at previous time layer $T^{n-1}$
Tcurr	Temperature field at current time layer $T^{n}$
Tnext	Output temperature field to be filled with $T^{n+1}$

Implements Method.

Definition at line 10 of file richardson.cpp.

◆ uses_previous_step()

bool Richardson::uses_previous_step ( ) const

inlineoverridevirtualnoexcept

Indicate that this is a three-level scheme.

Returns: true always, since Richardson needs $T^{n-1}$ .

Implements Method.

Definition at line 33 of file richardson.hpp.

The documentation for this class was generated from the following files:

include/methods/richardson.hpp
src/methods/richardson.cpp

Public Member Functions

Detailed Description

Member Function Documentation

◆ name()

◆ step()

◆ uses_previous_step()