Burgers::Solutions::Step Class Reference

A propagating shock between two constant states. More...

#include <Step.hpp>

Classes
struct	InitialPosition
struct	LeftValue
struct	RightValue

Public Types
using	options = tmpl::list< LeftValue, RightValue, InitialPosition >

Public Member Functions
	Step (double left_value, double right_value, double initial_shock_position, const Options::Context &context={})
	Step (const Step &)=default
Step &	operator= (const Step &)=default
	Step (Step &&)=default
Step &	operator= (Step &&)=default
auto	get_clone () const -> std::unique_ptr< evolution::initial_data::InitialData > override
template<typename T >
Scalar< T >	u (const tnsr::I< T, 1 > &x, double t) const
template<typename T >
Scalar< T >	du_dt (const tnsr::I< T, 1 > &x, double t) const
tuples::TaggedTuple< Tags::U >	variables (const tnsr::I< DataVector, 1 > &x, double t, tmpl::list< Tags::U >) const
tuples::TaggedTuple<::Tags::dt< Tags::U > >	variables (const tnsr::I< DataVector, 1 > &x, double t, tmpl::list<::Tags::dt< Tags::U > >) const
void	pup (PUP::er &p) override
virtual auto	get_clone () const -> std::unique_ptr< InitialData >=0

Static Public Attributes
static constexpr Options::String	help {"A propagating shock solution"}

Detailed Description

A propagating shock between two constant states.

The shock propagates left-to-right, with profile \(U(x, t) = U_R + (U_L - U_R) H(-(x - x_0 - v t))\). Here \(U_L\) and \(U_R\) are the left and right constant states, satisfying \(U_L > U_R\); \(H\) is the Heaviside function; \(x_0\) is the initial (i.e., \(t=0\)) position of the shock; and \(v = 0.5 (U_L + U_R)\) is the speed of the shock.

Note

At the shock, where \(x = x_0 + vt\), we have \(U(x, t) = U_L\). (This is inherited from the Heaviside implementation step_function.) Additionally, the time derivative \(\partial_t u0\) is zero, rather than the correct delta function.

Member Function Documentation

get_clone()

auto Burgers::Solutions::Step::get_clone ( ) const -> std::unique_ptr< evolution::initial_data::InitialData >

overridevirtual

Implements evolution::initial_data::InitialData.

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

• src/PointwiseFunctions/AnalyticSolutions/Burgers/Step.hpp