ScalarAdvection::Solutions::Krivodonova Class Reference

Initial data for the 1D scalar advection problem adopted from [113] and its analytic solution. More...

#include <Krivodonova.hpp>

Public Types
using	options = tmpl::list<>

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 [113] 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{align*} 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 \leq x \leq -0.6 \\ 1 & \text{if} & -0.4 \leq x \leq -0.2 \\ 1 - |10(x-0.1)| & \text{if} & 0 \leq x \leq 0.2 \\ (F(x,\alpha,a-\delta) + F(x,\alpha,a+\delta) + 4F(x,\alpha,a))/6 & \text{if} & 0.4 \leq x \leq 0.6 \\ 0 & \text{otherwise} & \\ \end{array}\right\}, \end{align*}

where

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

with \(a=0.5, z=-0.7, \delta=0.005, \alpha=10, \text{and }\beta = \log2/(36\delta^2)\).

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