ScalarAdvection::Solutions::Krivodonova Class Reference

Initial data for the 1D scalar advection problem adopted from [121] and its analytic solution. More...

#include <Krivodonova.hpp>

Public Types
using	options = implementation defined

Public Member Functions
	Krivodonova (const Krivodonova &)=default
Krivodonova &	operator= (const Krivodonova &)=default
	Krivodonova (Krivodonova &&)=default
Krivodonova &	operator= (Krivodonova &&)=default
auto	get_clone () const -> std::unique_ptr< evolution::initial_data::InitialData > override
template<typename DataType >
tuples::TaggedTuple< ScalarAdvection::Tags::U >	variables (const tnsr::I< DataType, 1 > &x, double t, tmpl::list< ScalarAdvection::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

Detailed Description

Initial data for the 1D scalar advection problem adopted from [121] and its analytic solution.

The initial profile consists of a combination of Gaussians, a square pulse, a sharp triangle, and a combination of half-ellipses.

$$\begin{array}{r}u(x,t=0)=\left\{\begin{array}{lcl}(G(x,\beta ,z-\delta )+G(x,\beta ,z+\delta )+4G(x,\beta ,z))/6& \text{if}& -0.8\le x\le -0.6\\ 1& \text{if}& -0.4\le x\le -0.2\\ 1-|10(x-0.1)|& \text{if}& 0\le x\le 0.2\\ (F(x,\alpha ,a-\delta )+F(x,\alpha ,a+\delta )+4F(x,\alpha ,a))/6& \text{if}& 0.4\le x\le 0.6\\ 0& \text{otherwise}& \end{array}\right\},\end{array}$$

where

$$\begin{array}{rl}G(x,\beta ,z)& =e^{-\beta (x-z{)}^2}\\ F(x,\alpha ,a)& =\sqrt{max(1-{\alpha }^2(x-a{)}^2,0)}\end{array}$$

with $a=0.5,z=-0.7,\delta =0.005,\alpha =10,\text{and }\beta =\log 2/(36{\delta }^2)$.

The system is evolved over the 1D domain $[-1,1]$ with the constant advection velocity field $v(x)=1.0$ and with the periodic boundary condition. The initial profile is simply advected (translated) to +x direction, going over cycles in the domain every 2.0 time unit.

Member Function Documentation

get_clone()

auto ScalarAdvection::Solutions::Krivodonova::get_clone ( ) const -> std::unique_ptr< evolution::initial_data::InitialData >

overridevirtual

Implements evolution::initial_data::InitialData.

Member Data Documentation

help

constexpr Options::String ScalarAdvection::Solutions::Krivodonova::help

staticconstexpr

Initial value:

{
      "An advecting 1D profile adopted from Krivodonova2007 paper, periodic "
      "over the interval [-1, 1]"}

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

• src/PointwiseFunctions/AnalyticSolutions/ScalarAdvection/Krivodonova.hpp