exact.hpp File Reference

Exact Riemann solver for GSPH (Toro 2009). More...

#include "shambackends/math.hpp"
#include "shambackends/sycl.hpp"
#include "shammodels/gsph/math/riemann/iterative.hpp"

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Classes
struct	shammodels::gsph::riemann::ExactState< Tscal >
	Left/right primitive state for the exact solver (velocity along pair axis). More...

Namespaces
namespace	shammodels
	namespace for models

Functions
template<class Tscal>
Tscal	shammodels::gsph::riemann::exact_v_xc_shock (Tscal LR, Tscal p2, Tscal p1, Tscal r1, Tscal gamma)
	Relative velocity jump across a shock wave (Rankine-Hugoniot).
template<class Tscal>
Tscal	shammodels::gsph::riemann::exact_v_xc_rarefaction (Tscal LR, Tscal p2, Tscal p1, Tscal r1, Tscal gamma)
	Relative velocity jump across a rarefaction wave (isentropic relation).
template<class Tscal>
Tscal	shammodels::gsph::riemann::exact_v_lr_ss (Tscal pS, ExactState< Tscal > left, ExactState< Tscal > right, Tscal gamma)
template<class Tscal>
Tscal	shammodels::gsph::riemann::exact_v_lr_rs (Tscal pS, ExactState< Tscal > left, ExactState< Tscal > right, Tscal gamma)
template<class Tscal>
Tscal	shammodels::gsph::riemann::exact_v_lr_sr (Tscal pS, ExactState< Tscal > left, ExactState< Tscal > right, Tscal gamma)
template<class Tscal>
Tscal	shammodels::gsph::riemann::exact_v_lr_rr (Tscal pS, ExactState< Tscal > left, ExactState< Tscal > right, Tscal gamma)
template<class Tscal>
i32	shammodels::gsph::riemann::exact_judge_wave_pattern (ExactState< Tscal > left, ExactState< Tscal > right, Tscal gamma)
	Wave pattern codes: 11=shock/shock, 21=rarefaction/shock, 12=shock/rarefaction, 22=rarefaction/rarefaction.
template<class Tscal, class ResidualFn>
Tscal	shammodels::gsph::riemann::exact_bisection_generic (Tscal posi, Tscal nega, Tscal v_lr_0, Tscal tol, u32 max_iter, ResidualFn residual)
	Shared bisection loop for a single wave-pattern's residual function.
template<class Tscal>
Tscal	shammodels::gsph::riemann::exact_bisection_ss (ExactState< Tscal > left, ExactState< Tscal > right, Tscal gamma, Tscal tol, u32 max_iter)
	Bisection solve for the shock/shock (11) wave pattern.
template<class Tscal>
Tscal	shammodels::gsph::riemann::exact_bisection_rs (ExactState< Tscal > left, ExactState< Tscal > right, Tscal gamma, Tscal tol, u32 max_iter)
	Bisection solve for the rarefaction/shock (21) wave pattern.
template<class Tscal>
Tscal	shammodels::gsph::riemann::exact_bisection_sr (ExactState< Tscal > left, ExactState< Tscal > right, Tscal gamma, Tscal tol, u32 max_iter)
	Bisection solve for the shock/rarefaction (12) wave pattern.
template<class Tscal>
Tscal	shammodels::gsph::riemann::exact_bisection_rr (ExactState< Tscal > left, ExactState< Tscal > right, Tscal gamma, Tscal tol, u32 max_iter)
	Bisection solve for the rarefaction/rarefaction (22) wave pattern.
template<class Tscal>
RiemannResult< Tscal >	shammodels::gsph::riemann::exact_solver (Tscal u_L, Tscal rho_L, Tscal p_L, Tscal u_R, Tscal rho_R, Tscal p_R, Tscal gamma, Tscal tol=Tscal{1.0e-8}, u32 max_iter=100)
	Exact Riemann solver for the 1D Euler equations (ideal gas).

Detailed Description

Exact Riemann solver for GSPH (Toro 2009).

Author

Guo Yansong (guo.y.nosp@m.anso.nosp@m.ng.ng.nosp@m.y@gm.nosp@m.ail.c.nosp@m.om)

Timothée David–Cléris (tim.s.nosp@m.hamr.nosp@m.ock@p.nosp@m.roto.nosp@m.n.me)

Yona Lapeyre (yona..nosp@m.lape.nosp@m.yre@e.nosp@m.ns-l.nosp@m.yon.f.nosp@m.r)

Implements the exact solution of the 1D Riemann problem for an ideal gas: the wave pattern (shock/rarefaction on each side) is classified first from the initial states, then the matching closed-form shock (Rankine-Hugoniot) or rarefaction (isentropic) relation is solved to convergence via bisection.

References:

• Toro, E.F. (2009) "Riemann Solvers and Numerical Methods for Fluid Dynamics"

Definition in file exact.hpp.

Function Documentation

exact_bisection_generic()

template<class Tscal, class ResidualFn>

Tscal shammodels::gsph::riemann::exact_bisection_generic ( Tscal posi, Tscal nega, Tscal v_lr_0, Tscal tol, u32 max_iter, ResidualFn residual )

inline

Shared bisection loop for a single wave-pattern's residual function.

Parameters

posi	Initial bracket endpoint with positive residual
nega	Initial bracket endpoint with non-positive residual
v_lr_0	Target value (left.v - right.v) the residual must reach
residual	Wave-pattern-specific v_lr_XX(p, left, right, gamma) function

Definition at line 144 of file exact.hpp.

exact_bisection_rr()

template<class Tscal>

Tscal shammodels::gsph::riemann::exact_bisection_rr ( ExactState< Tscal > left, ExactState< Tscal > right, Tscal gamma, Tscal tol, u32 max_iter )

inline

Bisection solve for the rarefaction/rarefaction (22) wave pattern.

Definition at line 244 of file exact.hpp.

exact_bisection_rs()

template<class Tscal>

Tscal shammodels::gsph::riemann::exact_bisection_rs ( ExactState< Tscal > left, ExactState< Tscal > right, Tscal gamma, Tscal tol, u32 max_iter )

inline

Bisection solve for the rarefaction/shock (21) wave pattern.

Definition at line 208 of file exact.hpp.

exact_bisection_sr()

template<class Tscal>

Tscal shammodels::gsph::riemann::exact_bisection_sr ( ExactState< Tscal > left, ExactState< Tscal > right, Tscal gamma, Tscal tol, u32 max_iter )

inline

Bisection solve for the shock/rarefaction (12) wave pattern.

Definition at line 226 of file exact.hpp.

exact_bisection_ss()

template<class Tscal>

Tscal shammodels::gsph::riemann::exact_bisection_ss ( ExactState< Tscal > left, ExactState< Tscal > right, Tscal gamma, Tscal tol, u32 max_iter )

inline

Bisection solve for the shock/shock (11) wave pattern.

Definition at line 174 of file exact.hpp.

exact_judge_wave_pattern()

template<class Tscal>

i32 shammodels::gsph::riemann::exact_judge_wave_pattern ( ExactState< Tscal > left, ExactState< Tscal > right, Tscal gamma )

inline

Wave pattern codes: 11=shock/shock, 21=rarefaction/shock, 12=shock/rarefaction, 22=rarefaction/rarefaction.

Definition at line 113 of file exact.hpp.

exact_solver()

template<class Tscal>

RiemannResult< Tscal > shammodels::gsph::riemann::exact_solver ( Tscal u_L, Tscal rho_L, Tscal p_L, Tscal u_R, Tscal rho_R, Tscal p_R, Tscal gamma, Tscal tol = Tscal{1.0e-8}, u32 max_iter = 100 )

inline

Exact Riemann solver for the 1D Euler equations (ideal gas).

Classifies the wave pattern from the initial states, then solves the matching shock/rarefaction relation to convergence via bisection.

The left/right convention matches iterative_solver()/hllc_solver():

• Left state (L): particle on the "minus" side of the interface
• Right state (R): particle on the "plus" side of the interface
• Positive velocity points from L to R

Template Parameters

Tscal

Scalar type (f32 or f64)

Parameters

u_L	Left state velocity (normal component)
rho_L	Left state density
p_L	Left state pressure
u_R	Right state velocity (normal component)
rho_R	Right state density
p_R	Right state pressure
gamma	Adiabatic index
tol	Bisection convergence tolerance (default: 1e-8)
max_iter	Maximum bisection iterations (default: 100)

Returns

RiemannResult with p_star and v_star

Definition at line 281 of file exact.hpp.

exact_v_lr_rr()

template<class Tscal>

Tscal shammodels::gsph::riemann::exact_v_lr_rr ( Tscal pS, ExactState< Tscal > left, ExactState< Tscal > right, Tscal gamma )

inline

Definition at line 102 of file exact.hpp.

exact_v_lr_rs()

template<class Tscal>

Tscal shammodels::gsph::riemann::exact_v_lr_rs ( Tscal pS, ExactState< Tscal > left, ExactState< Tscal > right, Tscal gamma )

inline

Definition at line 88 of file exact.hpp.

exact_v_lr_sr()

template<class Tscal>

Tscal shammodels::gsph::riemann::exact_v_lr_sr ( Tscal pS, ExactState< Tscal > left, ExactState< Tscal > right, Tscal gamma )

inline

Definition at line 95 of file exact.hpp.

exact_v_lr_ss()

template<class Tscal>

Tscal shammodels::gsph::riemann::exact_v_lr_ss ( Tscal pS, ExactState< Tscal > left, ExactState< Tscal > right, Tscal gamma )

inline

Definition at line 81 of file exact.hpp.

exact_v_xc_rarefaction()

template<class Tscal>

Tscal shammodels::gsph::riemann::exact_v_xc_rarefaction ( Tscal LR, Tscal p2, Tscal p1, Tscal r1, Tscal gamma )

inline

Relative velocity jump across a rarefaction wave (isentropic relation).

Parameters

LR	-1 for the left wave, +1 for the right wave
p2	Trial star-region pressure
p1	Pressure of the state ahead of the wave
r1	Density of the state ahead of the wave
gamma	Adiabatic index

Definition at line 74 of file exact.hpp.

exact_v_xc_shock()

template<class Tscal>

Tscal shammodels::gsph::riemann::exact_v_xc_shock ( Tscal LR, Tscal p2, Tscal p1, Tscal r1, Tscal gamma )

inline

Relative velocity jump across a shock wave (Rankine-Hugoniot).

Parameters

LR	-1 for the left wave, +1 for the right wave
p2	Trial star-region pressure
p1	Pressure of the state ahead of the wave
r1	Density of the state ahead of the wave
gamma	Adiabatic index

Definition at line 56 of file exact.hpp.