hexed::Elem_nonsmooth Class Reference

compute the elementwise nonsmoothness indicator of the provided function More...

#include <Element_func.hpp>

Inheritance diagram for hexed::Elem_nonsmooth:

Public Member Functions
	Elem_nonsmooth (const Qpoint_func &func)
	Elem_nonsmooth (Qpoint_func &&)=delete
int	n_var (int n_dim) const override
	number of output variables when called on n_dim-dimensional input
std::string	variable_name (int n_dim, int i_var) const override
	name of i_varth variable (for plotting) when called on n_dim-dimensional input
std::vector< double >	operator() (Element &elem, const Basis &, double time) const override
Public Member Functions inherited from hexed::Element_func
std::vector< double >	operator() (Element &, const Basis &, int i_qpoint, double time) const override

Detailed Description

compute the elementwise nonsmoothness indicator of the provided function

The elementwise nonsmoothness indicator (different from the nonsmoothness indicator in Solver::set_art_visc_smoothness) is essentially a measure of how much of the flow state resides in the highest-order polynomial components. If you want the nonsmoothness of the variable \(u\), it is given by

\[ \sqrt{\frac{1}{n_{dim}} \sum_{0 \le i_{dim} < n_{dim}} \| \langle u(\vec{x}), P_{r - 1}(x_{i_{dim}}) \rangle P_{r - 1}(x_{i_{dim}}) \|^2} \]

where \(P_j\) is the \(j\)th Legendre polynomial and \(r\) is the row size of the basis. In other words, you project the solution onto the highest-order univariate Legendre polynomial along each dimension, take the \(L_2\) norm of this in the other dimensions, and then take the RMS of that whole expression over all dimensions.

Constructor & Destructor Documentation

Elem_nonsmooth()

hexed::Elem_nonsmooth::Elem_nonsmooth

(

const Qpoint_func &

func

)

Parameters

func	the function you want to compute the nonsmoothness of ( \(u\) in the explanation above).

Member Function Documentation

n_var()

int hexed::Elem_nonsmooth::n_var ( int n_dim ) const

inlineoverridevirtual

number of output variables when called on n_dim-dimensional input

Implements hexed::Output_data.

operator()()

std::vector< double > hexed::Elem_nonsmooth::operator() ( Element & elem, const Basis & , double time ) const

overridevirtual

–

Implements hexed::Element_func.

variable_name()

std::string hexed::Elem_nonsmooth::variable_name ( int n_dim, int i_var ) const

inlineoverridevirtual

name of i_varth variable (for plotting) when called on n_dim-dimensional input

Reimplemented from hexed::Output_data.

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

• /home/micaiah/Desktop/hexed/include/Element_func.hpp
• /home/micaiah/Desktop/hexed/libhexed/Element_func.cpp