ryujin::Euler::Indicator< ScalarNumber > Class Template Reference

#include <source/euler/indicator.h>

Inheritance diagram for ryujin::Euler::Indicator< ScalarNumber >:

Collaboration diagram for ryujin::Euler::Indicator< ScalarNumber >:

Classes
struct	Parameters

Public Types
Typedefs and constexpr constants
template<int dim, typename Number = double, typename MemorySpace = dealii::MemorySpace::Host>
using	View = IndicatorView< dim, Number, MemorySpace >

Public Member Functions
Constructor and setup
	Indicator (const HyperbolicSystem &hyperbolic_system, const std::string &subsection="/Indicator")
template<int dim, typename Number , typename MemorySpace = dealii::MemorySpace::Host>
auto	view () const

Internal data
template<int , typename , typename >
class	IndicatorView

Detailed Description

template<typename ScalarNumber = double>
class ryujin::Euler::Indicator< ScalarNumber >

An indicator strategy used to form the preliminary high-order update.

The indicator is an entropy-viscosity commutator as described in [7] and [9]. For a given entropy \(\eta\) (either the mathematical entropy, or a Harten entropy, see the documentation of HyperbolicSystem) we let \(\eta'\) denote its derivative with respect to the state variables. We then compute a normalized entropy viscosity ratio \(\alpha_i^n\) for the state \(\boldsymbol U_i^n\) as follows:

\begin{align} \alpha_i^n\;=\;\frac{N_i^n}{D_i^n}, \quad N_i^n\;:=\;\left|a_i^n- \eta'(\boldsymbol U^n_i)\cdot\boldsymbol b_i^n +\frac{\eta(\boldsymbol U^n_i)}{\rho_i^n}\big(\boldsymbol b_i^n\big)_1\right|, \quad D_i^n\;:=\;\left|a_i^n\right| + \sum_{k=1}^{d+1}\left|\big(\eta'(\boldsymbol U^n_i)\big)_k- \delta_{1k}\frac{\eta(\boldsymbol U^n_i)}{\rho_i^n}\right| \,\left|\big(\boldsymbol b_i^n\big)_k\right|, \end{align}

where where \(\big(\,.\,\big)_k\) denotes the \(k\)-th component of a vector, \(\delta_{ij}\) is Kronecker's delta, and where we have set

\begin{align} a_i^n \;:=\; \sum_{j\in\mathcal{I}_i}\left(\frac{\eta(\boldsymbol U_j^n)}{\rho_j^n} -\frac{\eta(\boldsymbol U_i^n)}{\rho_i^n}\right)\, \boldsymbol m_j^n\cdot\boldsymbol c_{ij}, \qquad \boldsymbol b_i^n \;:=\; \sum_{j\in\mathcal{I}_i}\left(\mathbf{f}(\boldsymbol U_j^n)- \mathbf{f}(\boldsymbol U_i^n)\right)\cdot\boldsymbol c_{ij}, \end{align}

Definition at line 69 of file indicator.h.

Member Typedef Documentation

View

template<typename ScalarNumber = double>

template<int dim, typename Number = double, typename MemorySpace = dealii::MemorySpace::Host>

using ryujin::Euler::Indicator< ScalarNumber >::View = IndicatorView<dim, Number, MemorySpace>

Alias for the view on the indicator for a given dimension dim, choice of number type Number, and memory space MemorySpace.

Definition at line 91 of file indicator.h.

Constructor & Destructor Documentation

Indicator()

template<typename ScalarNumber = double>

ryujin::Euler::Indicator< ScalarNumber >::Indicator ( const HyperbolicSystem &  hyperbolic_system, const std::string &  subsection = "/Indicator< ScalarNumber >"  )

inline

Constructor.

Definition at line 102 of file indicator.h.

Member Function Documentation

view()

template<typename ScalarNumber = double>

template<int dim, typename Number , typename MemorySpace = dealii::MemorySpace::Host>

auto ryujin::Euler::Indicator< ScalarNumber >::view ( ) const

inline

Return a view on the Indicator for a given dimension dim and choice of number type Number (which can be a scalar float, or double, as well as a VectorizedArray holding packed scalars). The optional MemorySpace template parameter selects whether the view is intended for the host or device memory space.

Definition at line 144 of file indicator.h.

Friends And Related Symbol Documentation

IndicatorView

template<typename ScalarNumber = double>

template<int , typename , typename >

friend class IndicatorView

friend

Definition at line 171 of file indicator.h.

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

• source/euler/indicator.h