ScalarAdvection::Solutions::Kuzmin Class Reference

Initial data for the 2D scalar advection problem adopted from [123] and its analytic solution. More...

#include <Kuzmin.hpp>

Public Types
using	options = implementation defined

Public Member Functions
	Kuzmin (const Kuzmin &)=default
Kuzmin &	operator= (const Kuzmin &)=default
	Kuzmin (Kuzmin &&)=default
Kuzmin &	operator= (Kuzmin &&)=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, 2 > &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 2D scalar advection problem adopted from [123] and its analytic solution.

Let $r(x,y)=\sqrt{(x-x_0{)}^2+(y-y_0{)}^2}/r_0$ be the normalized distance from a point $(x_0,y_0)$ within a circle with the radius $r_0=0.15$. The initial profile consists of three bodies:

• a slotted cylinder centered at $(0.5,0.75)$

  $$\begin{array}{r}u(x,y)=\left\{\begin{array}{ll}1& \text{if }|x-x_0|\ge 0.025\text{ or }y\ge 0.85\\ 0& \text{otherwise}\end{array}\right\},\end{array}$$

• a cone centered at $(0.5,0.25)$

  $$\begin{array}{r}u(x,y)=1-r(x,y),\end{array}$$

• and a hump centered at $(0.25,0.5)$

  $$\begin{array}{r}u(x,y)=\frac{1+\cos (\pi r(x,y))}{4}.\end{array}$$

The system is evolved over the domain $[0,1]\times [0,1]$ with the advection velocity field $v(x,y)=(0.5-y,-0.5+x)$, which causes a solid rotation about $(x,y)=(0.5,0.5)$ with angular velocity being 1.0. We use the periodic boundary condition for evolving this problem.

Member Function Documentation

get_clone()

auto ScalarAdvection::Solutions::Kuzmin::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::Kuzmin::help

staticconstexpr

Initial value:

{
      "A rotating 2D scalar advecting problem adopted from Kuzmin2014 paper"}

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

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