ScalarAdvection::Solutions::Krivodonova Class Reference

Initial data for the 1D scalar advection problem adopted from [129] 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
Public Member Functions inherited from evolution::initial_data::InitialData
virtual const InitialData &	unwrap () const
	Unwrap wrapper types (e.g. WithNoise, which wraps analytic initial data and adds random noise) to reach the underlying analytic solution or data.

Static Public Attributes
static constexpr Options::String	help

Detailed Description

Initial data for the 1D scalar advection problem adopted from [129] 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

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