DiFfRG::FV::KurganovTadmor::MaxEigenvalueWaveSpeed Struct Reference

Default wave-speed strategy. More...

#include <max_eigenvalue_wave_speed.hh>

Static Public Member Functions
template<typename NumberType , int dim, size_t n_components>
static std::array< NumberType, dim >	compute_speeds (const std::array< internal::JacobianMatrix< NumberType, n_components >, dim > &J_plus, const std::array< internal::JacobianMatrix< NumberType, n_components >, dim > &J_minus)
template<typename NumberType , int dim, size_t n_components>
static std::array< WaveSpeedBranch, dim >	select_speed_branches (const std::array< internal::JacobianMatrix< NumberType, n_components >, dim > &J_plus, const std::array< internal::JacobianMatrix< NumberType, n_components >, dim > &J_minus)
template<typename NumberType , int dim, size_t n_components>
static std::pair< std::array< std::array< NumberType, n_components >, dim >, std::array< std::array< NumberType, n_components >, dim > >	compute_speed_derivatives (const std::array< internal::JacobianMatrix< NumberType, n_components >, dim > &J_plus, const std::array< internal::JacobianMatrix< NumberType, n_components >, dim > &J_minus, const internal::HessianTensor< NumberType, dim, n_components > &H_plus, const internal::HessianTensor< NumberType, dim, n_components > &H_minus)
	Compute da[d]/du_c analytically from J and H: a[d] = spectral_radius(J[d]) da[d]/du_c = d(spectral_radius)/dJ[d] : H[d][:][:][ c].
template<typename NumberType , int dim, size_t n_components>
static std::pair< std::array< std::array< NumberType, n_components >, dim >, std::array< std::array< NumberType, n_components >, dim > >	compute_selected_speed_derivatives (const std::array< internal::JacobianMatrix< NumberType, n_components >, dim > &J_plus, const std::array< internal::JacobianMatrix< NumberType, n_components >, dim > &J_minus, const internal::HessianTensor< NumberType, dim, n_components > &H_plus, const internal::HessianTensor< NumberType, dim, n_components > &H_minus)

Static Private Member Functions
template<typename NumberType , int dim, size_t n_components>
static std::pair< std::array< NumberType, dim >, std::array< NumberType, dim > >	compute_spectral_radii (const std::array< internal::JacobianMatrix< NumberType, n_components >, dim > &J_plus, const std::array< internal::JacobianMatrix< NumberType, n_components >, dim > &J_minus)

Detailed Description

Default wave-speed strategy.

compute_speeds: a[d] = max(spectral_radius(J_plus[d]), spectral_radius(J_minus[d])) compute_speed_derivatives: analytical derivative via eigenvector perturbation theory compute_selected_speed_derivatives: derivative for the branch selected by compute_speeds

Member Function Documentation

compute_selected_speed_derivatives()

template<typename NumberType , int dim, size_t n_components>

static std::pair< std::array< std::array< NumberType, n_components >, dim >, std::array< std::array< NumberType, n_components >, dim > > DiFfRG::FV::KurganovTadmor::MaxEigenvalueWaveSpeed::compute_selected_speed_derivatives ( const std::array< internal::JacobianMatrix< NumberType, n_components >, dim > & J_plus, const std::array< internal::JacobianMatrix< NumberType, n_components >, dim > & J_minus, const internal::HessianTensor< NumberType, dim, n_components > & H_plus, const internal::HessianTensor< NumberType, dim, n_components > & H_minus )

inlinestatic

compute_spectral_radii()

template<typename NumberType , int dim, size_t n_components>

static std::pair< std::array< NumberType, dim >, std::array< NumberType, dim > > DiFfRG::FV::KurganovTadmor::MaxEigenvalueWaveSpeed::compute_spectral_radii ( const std::array< internal::JacobianMatrix< NumberType, n_components >, dim > & J_plus, const std::array< internal::JacobianMatrix< NumberType, n_components >, dim > & J_minus )

inlinestaticprivate

compute_speed_derivatives()

template<typename NumberType , int dim, size_t n_components>

static std::pair< std::array< std::array< NumberType, n_components >, dim >, std::array< std::array< NumberType, n_components >, dim > > DiFfRG::FV::KurganovTadmor::MaxEigenvalueWaveSpeed::compute_speed_derivatives ( const std::array< internal::JacobianMatrix< NumberType, n_components >, dim > & J_plus, const std::array< internal::JacobianMatrix< NumberType, n_components >, dim > & J_minus, const internal::HessianTensor< NumberType, dim, n_components > & H_plus, const internal::HessianTensor< NumberType, dim, n_components > & H_minus )

inlinestatic

Compute da[d]/du_c analytically from J and H: a[d] = spectral_radius(J[d]) da[d]/du_c = d(spectral_radius)/dJ[d] : H[d][:][:][ c].

For n_components == 1: a[d] = |J[d][0][0]|, da/du_c = sign(J[d][0][0]) * H[d][0][0][c]

For n_components > 1: Find the dominant eigenvalue lambda* and its right/left eigenvectors v, w (Eigen EigenSolver). Then by first-order eigenvalue perturbation theory: da[d]/du_c = sign(Re(lambda*)) * sum_{i,j} Re(w[i]) * Re(v[j]) * H[d][i][j][c] / Re(w . v)

Returns

{da_plus, da_minus}

compute_speeds()

template<typename NumberType , int dim, size_t n_components>

static std::array< NumberType, dim > DiFfRG::FV::KurganovTadmor::MaxEigenvalueWaveSpeed::compute_speeds ( const std::array< internal::JacobianMatrix< NumberType, n_components >, dim > & J_plus, const std::array< internal::JacobianMatrix< NumberType, n_components >, dim > & J_minus )

inlinestatic

select_speed_branches()

template<typename NumberType , int dim, size_t n_components>

static std::array< WaveSpeedBranch, dim > DiFfRG::FV::KurganovTadmor::MaxEigenvalueWaveSpeed::select_speed_branches ( const std::array< internal::JacobianMatrix< NumberType, n_components >, dim > & J_plus, const std::array< internal::JacobianMatrix< NumberType, n_components >, dim > & J_minus )

inlinestatic

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

• /home/runner/work/DiFfRG_current/DiFfRG_current/DiFfRG/include/DiFfRG/discretization/FV/wave_speed/max_eigenvalue_wave_speed.hh