#include <source/euler/riemann_solver.h>

Public Member Functions
Compute wavespeed estimates
	RiemannSolver (const HyperbolicSystem &hyperbolic_system, const Parameters &parameters, const PrecomputedVector &precomputed_values)

Number	compute (const primitive_type &riemann_data_i, const primitive_type &riemann_data_j) const

Number	compute (const state_type &U_i, const state_type &U_j, const unsigned int i, const unsigned int *js, const dealii::Tensor< 1, dim, Number > &n_ij) const

Typedefs and constexpr constants
using	View = HyperbolicSystemView< dim, Number >

using	ScalarNumber = typename View::ScalarNumber

using	state_type = typename View::state_type

using	primitive_type = std::array< Number, riemann_data_size >

using	precomputed_type = typename View::precomputed_type

using	PrecomputedVector = typename View::PrecomputedVector

using	Parameters = RiemannSolverParameters< ScalarNumber >

static constexpr auto	problem_dimension = View::problem_dimension

static constexpr unsigned int	riemann_data_size = 4

Internal functions used in the Riemann solver
Number	f (const primitive_type &riemann_data, const Number p_star) const

Number	df (const primitive_type &riemann_data, const Number &p_star) const

Number	phi (const primitive_type &riemann_data_i, const primitive_type &riemann_data_j, const Number p_in) const

Number	dphi (const primitive_type &riemann_data_i, const primitive_type &riemann_data_j, const Number &p) const

Number	phi_of_p_max (const primitive_type &riemann_data_i, const primitive_type &riemann_data_j) const

Number	lambda1_minus (const primitive_type &riemann_data, const Number p_star) const

Number	lambda3_plus (const primitive_type &primitive_state, const Number p_star) const

std::array< Number, 2 >	compute_gap (const primitive_type &riemann_data_i, const primitive_type &riemann_data_j, const Number p_1, const Number p_2) const

Number	compute_lambda (const primitive_type &riemann_data_i, const primitive_type &riemann_data_j, const Number p_star) const

Number	p_star_two_rarefaction (const primitive_type &riemann_data_i, const primitive_type &riemann_data_j) const

Number	p_star_failsafe (const primitive_type &riemann_data_i, const primitive_type &riemann_data_j) const

primitive_type	riemann_data_from_state (const state_type &U, const dealii::Tensor< 1, dim, Number > &n_ij) const

Detailed Description

template<int dim, typename Number = double>
class ryujin::Euler::RiemannSolver< dim, Number >

A fast approximative solver for the 1D Riemann problem. The solver ensures that the estimate \(\lambda_{\text{max}}\) that is returned for the maximal wavespeed is a strict upper bound.

The solver is based on [5].

Definition at line 60 of file riemann_solver.h.

Member Typedef Documentation

◆ View

template<int dim, typename Number = double>

using ryujin::Euler::RiemannSolver< dim, Number >::View = HyperbolicSystemView<dim, Number>

Definition at line 68 of file riemann_solver.h.

◆ ScalarNumber

template<int dim, typename Number = double>

using ryujin::Euler::RiemannSolver< dim, Number >::ScalarNumber = typename View::ScalarNumber

Definition at line 70 of file riemann_solver.h.

◆ state_type

template<int dim, typename Number = double>

using ryujin::Euler::RiemannSolver< dim, Number >::state_type = typename View::state_type

Definition at line 74 of file riemann_solver.h.

◆ primitive_type

template<int dim, typename Number = double>

using ryujin::Euler::RiemannSolver< dim, Number >::primitive_type = std::array<Number, riemann_data_size>

The array type to store the expanded primitive state for the Riemann solver \([\rho, v, p, a]\)

Definition at line 86 of file riemann_solver.h.

◆ precomputed_type

template<int dim, typename Number = double>

using ryujin::Euler::RiemannSolver< dim, Number >::precomputed_type = typename View::precomputed_type

Definition at line 88 of file riemann_solver.h.

◆ PrecomputedVector

template<int dim, typename Number = double>

using ryujin::Euler::RiemannSolver< dim, Number >::PrecomputedVector = typename View::PrecomputedVector

Definition at line 90 of file riemann_solver.h.

◆ Parameters

template<int dim, typename Number = double>

using ryujin::Euler::RiemannSolver< dim, Number >::Parameters = RiemannSolverParameters<ScalarNumber>

Definition at line 92 of file riemann_solver.h.

Constructor & Destructor Documentation

◆ RiemannSolver()

template<int dim, typename Number = double>

ryujin::Euler::RiemannSolver< dim, Number >::RiemannSolver	(	const HyperbolicSystem &	hyperbolic_system,
		const Parameters &	parameters,
		const PrecomputedVector &	precomputed_values
	)

inline

Constructor taking a HyperbolicSystem instance as argument

Definition at line 103 of file riemann_solver.h.

Member Function Documentation

◆ compute() [1/2]

template<int dim, typename Number >

Number ryujin::Euler::RiemannSolver< dim, Number >::compute	(	const primitive_type &	riemann_data_i,
		const primitive_type &	riemann_data_j
	)		const

For two given 1D primitive states riemann_data_i and riemann_data_j, compute an estimation of an upper bound for the maximum wavespeed lambda.

Definition at line 407 of file riemann_solver.template.h.

References ryujin::quadratic_newton_step().

◆ compute() [2/2]

template<int dim, typename Number >

DEAL_II_ALWAYS_INLINE Number ryujin::Euler::RiemannSolver< dim, Number >::compute	(	const state_type &	U_i,
		const state_type &	U_j,
		const unsigned int	i,
		const unsigned int *	js,
		const dealii::Tensor< 1, dim, Number > &	n_ij
	)		const

inline

For two given states U_i a U_j and a (normalized) "direction" n_ij compute an estimation of an upper bound for lambda.

Returns a tuple consisting of lambda max and the number of Newton iterations used in the solver to find it.

Definition at line 586 of file riemann_solver.template.h.

◆ f()

template<int dim, typename Number >

DEAL_II_ALWAYS_INLINE Number ryujin::EulerAEOS::RiemannSolver< dim, Number >::f	(	const primitive_type &	riemann_data,
		const Number	p_star
	)		const

inlineprotected

See [5], page 912, (3.4).

Cost: 1x pow, 1x division, 2x sqrt

Definition at line 23 of file riemann_solver.template.h.

References ryujin::pow().

◆ df()

template<int dim, typename Number >

DEAL_II_ALWAYS_INLINE Number ryujin::Euler::RiemannSolver< dim, Number >::df	(	const primitive_type &	riemann_data,
		const Number &	p_star
	)		const

inlineprotected

See [5], page 912, (3.4).

Cost: 1x pow, 3x division, 1x sqrt

Definition at line 51 of file riemann_solver.template.h.

References ryujin::pow().

◆ phi()

template<int dim, typename Number >

DEAL_II_ALWAYS_INLINE Number ryujin::EulerAEOS::RiemannSolver< dim, Number >::phi	(	const primitive_type &	riemann_data_i,
		const primitive_type &	riemann_data_j,
		const Number	p_in
	)		const

inlineprotected

See [5], page 912, (3.3).

Cost: 2x pow, 6x division, 2x sqrt

Definition at line 89 of file riemann_solver.template.h.

◆ dphi()

template<int dim, typename Number >

DEAL_II_ALWAYS_INLINE Number ryujin::Euler::RiemannSolver< dim, Number >::dphi	(	const primitive_type &	riemann_data_i,
		const primitive_type &	riemann_data_j,
		const Number &	p
	)		const

inlineprotected

See [5], page 912, (3.3).

Cost: 2x pow, 6x division, 2x sqrt

Definition at line 102 of file riemann_solver.template.h.

◆ phi_of_p_max()

template<int dim, typename Number >

DEAL_II_ALWAYS_INLINE Number ryujin::Euler::RiemannSolver< dim, Number >::phi_of_p_max	(	const primitive_type &	riemann_data_i,
		const primitive_type &	riemann_data_j
	)		const

inlineprotected

See [5], page 912, (3.3).

The approximate Riemann solver is based on a function phi(p) that is montone increasing in p, concave down and whose (weak) third derivative is non-negative and locally bounded [1, p. 912]. Because we actually do not perform any iteration for computing our wavespeed estimate we can get away by only implementing a specialized variant of the phi function that computes phi(p_max). It inlines the implementation of the "f" function and eliminates all unnecessary branches in "f".

Cost: 0x pow, 2x division, 2x sqrt

Definition at line 124 of file riemann_solver.template.h.

◆ lambda1_minus()

template<int dim, typename Number >

DEAL_II_ALWAYS_INLINE Number ryujin::Euler::RiemannSolver< dim, Number >::lambda1_minus	(	const primitive_type &	riemann_data,
		const Number	p_star
	)		const

inlineprotected

see [5], page 912, (3.7)

Cost: 0x pow, 1x division, 1x sqrt

Definition at line 166 of file riemann_solver.template.h.

References ryujin::positive_part().

◆ lambda3_plus()

template<int dim, typename Number >

DEAL_II_ALWAYS_INLINE Number ryujin::Euler::RiemannSolver< dim, Number >::lambda3_plus	(	const primitive_type &	primitive_state,
		const Number	p_star
	)		const

inlineprotected

see [5], page 912, (3.8)

Cost: 0x pow, 1x division, 1x sqrt

Definition at line 191 of file riemann_solver.template.h.

References ryujin::positive_part().

◆ compute_gap()

template<int dim, typename Number = double>

DEAL_II_ALWAYS_INLINE std::array< Number, 2 > ryujin::Euler::RiemannSolver< dim, Number >::compute_gap	(	const primitive_type &	riemann_data_i,
		const primitive_type &	riemann_data_j,
		const Number	p_1,
		const Number	p_2
	)		const

inlineprotected

For two given primitive states riemann_data_i and riemann_data_j, and two guesses p_1 <= p* <= p_2, compute the gap in lambda between both guesses.

See [5], page 914, (4.4a), (4.4b), (4.5), and (4.6)

Cost: 0x pow, 4x division, 4x sqrt

For two given primitive states riemann_data_i and riemann_data_j, and two guesses p_1 <= p* <= p_2, compute the gap in lambda between both guesses.

See [1], page 914, (4.4a), (4.4b), (4.5), and (4.6)

Cost: 0x pow, 4x division, 4x sqrt

Definition at line 219 of file riemann_solver.template.h.

References ryujin::negative_part(), and ryujin::positive_part().

◆ compute_lambda()

template<int dim, typename Number >

DEAL_II_ALWAYS_INLINE Number ryujin::Euler::RiemannSolver< dim, Number >::compute_lambda	(	const primitive_type &	riemann_data_i,
		const primitive_type &	riemann_data_j,
		const Number	p_star
	)		const

inlineprotected

see [5], page 912, (3.9)

For two given primitive states riemann_data_i and riemann_data_j, and a guess p_2, compute an upper bound for lambda.

Cost: 0x pow, 2x division, 2x sqrt (inclusive)

Definition at line 254 of file riemann_solver.template.h.

References ryujin::negative_part(), and ryujin::positive_part().

◆ p_star_two_rarefaction()

template<int dim, typename Number >

DEAL_II_ALWAYS_INLINE Number ryujin::Euler::RiemannSolver< dim, Number >::p_star_two_rarefaction	(	const primitive_type &	riemann_data_i,
		const primitive_type &	riemann_data_j
	)		const

inlineprotected

Two-rarefaction approximation to p_star computed for two primitive states riemann_data_i and riemann_data_j.

See [5], page 914, (4.3)

Cost: 2x pow, 2x division, 0x sqrt

Definition at line 276 of file riemann_solver.template.h.

References ryujin::positive_part(), and ryujin::pow().

◆ p_star_failsafe()

template<int dim, typename Number >

DEAL_II_ALWAYS_INLINE Number ryujin::Euler::RiemannSolver< dim, Number >::p_star_failsafe	(	const primitive_type &	riemann_data_i,
		const primitive_type &	riemann_data_j
	)		const

inlineprotected

Failsafe approximation to p_star computed for two primitive states riemann_data_i and riemann_data_j.

See [2], (5.11):

Cost: 0x pow, 3x division, 3x sqrt

Definition at line 332 of file riemann_solver.template.h.

◆ riemann_data_from_state()

template<int dim, typename Number >

DEAL_II_ALWAYS_INLINE auto ryujin::Euler::RiemannSolver< dim, Number >::riemann_data_from_state	(	const state_type &	U,
		const dealii::Tensor< 1, dim, Number > &	n_ij
	)		const

inlineprotected

For a given (2+dim dimensional) state vector U, and a (normalized) "direction" n_ij, first compute the corresponding projected state in the corresponding 1D Riemann problem, and then compute and return the Riemann data [rho, u, p, a] (used in the approximative Riemann solver).

Definition at line 379 of file riemann_solver.template.h.

Member Data Documentation

◆ problem_dimension

template<int dim, typename Number = double>

constexpr auto ryujin::Euler::RiemannSolver< dim, Number >::problem_dimension = View::problem_dimension

staticconstexpr

Definition at line 72 of file riemann_solver.h.

◆ riemann_data_size

template<int dim, typename Number = double>

constexpr unsigned int ryujin::Euler::RiemannSolver< dim, Number >::riemann_data_size = 4

staticconstexpr

Number of components in a primitive state, we store \([\rho, v, p, a]\), thus, 4.

Definition at line 80 of file riemann_solver.h.

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

source/euler/riemann_solver.h
source/euler/riemann_solver.template.h
source/euler_aeos/riemann_solver.template.h

Public Member Functions

Typedefs and constexpr constants

Internal functions used in the Riemann solver

Detailed Description

Member Typedef Documentation

◆ View

◆ ScalarNumber

◆ state_type

◆ primitive_type

◆ precomputed_type

◆ PrecomputedVector

◆ Parameters

Constructor & Destructor Documentation

◆ RiemannSolver()

Member Function Documentation

◆ compute() [1/2]

◆ compute() [2/2]

◆ f()

◆ df()

◆ phi()

◆ dphi()

◆ phi_of_p_max()

◆ lambda1_minus()

◆ lambda3_plus()

◆ compute_gap()

◆ compute_lambda()

◆ p_star_two_rarefaction()

◆ p_star_failsafe()

◆ riemann_data_from_state()

Member Data Documentation

◆ problem_dimension

◆ riemann_data_size