adam_riemann_euler_library

ADAM, Riemann Problem for Euler equations solvers and convective fluxes computations library.

Source: src/lib/common/adam_riemann_euler_library.F90

Dependencies

Contents

• compute_riemann_euler_exact
• compute_riemann_euler_hllc
• compute_riemann_euler_hllc_lm
• compute_riemann_euler_hllem
• compute_riemann_euler_llf
• compute_riemann_euler_ts
• compute_conservatives_euler
• compute_convective_fluxes_euler
• compute_eigeinvectors_left
• compute_eigeinvectors_right

Subroutines

compute_riemann_euler_exact

Solve the Riemann problem between the state 1 (left) and 4 (right) using exact Integral/Rainkine-Hugonoit relations.

subroutine compute_riemann_euler_exact(si, sir, uni, ut1, ut2, nv, q_aux1, q_aux4, f, lmax)

Arguments

Name	Type	Intent	Attributes	Description
si	integer(kind=I4P)	in		Directional (1=x,2=y,3=z) increment.
sir	real(kind=R8P)	in		Directional (1=x,2=y,3=z) increment.
uni	integer(kind=I4P)	in		Index of normal and tangential velocities.
ut1	integer(kind=I4P)	in		Index of normal and tangential velocities.
ut2	integer(kind=I4P)	in		Index of normal and tangential velocities.
nv	integer(kind=I4P)	in		Number of conservative varibales.
q_aux1	real(kind=R8P)	in		Left state, auxiliary variables.
q_aux4	real(kind=R8P)	in		Left state, auxiliary variables.
f	real(kind=R8P)	inout		Resulting fluxes.
lmax	real(kind=R8P)	out	optional	Maximum wave speed estimation.

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compute_riemann_euler_hllc

Solve the Riemann problem between the state 1 (left) and 4 (right) using the HLLC solver.

subroutine compute_riemann_euler_hllc(si, sir, uni, ut1, ut2, nv, q_aux1, q_aux4, f, lmax)

Arguments

Name	Type	Intent	Attributes	Description
si	integer(kind=I4P)	in		Directional (1=x,2=y,3=z) increment.
sir	real(kind=R8P)	in		Directional (1=x,2=y,3=z) increment.
uni	integer(kind=I4P)	in		Index of normal and tangential velocities.
ut1	integer(kind=I4P)	in		Index of normal and tangential velocities.
ut2	integer(kind=I4P)	in		Index of normal and tangential velocities.
nv	integer(kind=I4P)	in		Number of conservative varibales.
q_aux1	real(kind=R8P)	in		Left state, auxiliary variables.
q_aux4	real(kind=R8P)	in		Left state, auxiliary variables.
f	real(kind=R8P)	inout		Resulting fluxes.
lmax	real(kind=R8P)	out	optional	Maximum wave speed estimation.

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compute_riemann_euler_hllc_lm

Solve the Riemann problem between the state 1 (left) and 4 (right) using the HLLC-LM solver. The algorithm is based on the Low Mach (LM) modification, see "A shock-stable modification of the HLLC Riemann solver with reduced numerical dissipation", Nico Fleischmann, Stefan Adami, Nikolaus A. Adams, 2020.

subroutine compute_riemann_euler_hllc_lm(si, sir, uni, ut1, ut2, nv, q_aux1, q_aux4, f, lmax)

Arguments

Name	Type	Intent	Attributes	Description
si	integer(kind=I4P)	in		Directional (1=x,2=y,3=z) increment.
sir	real(kind=R8P)	in		Directional (1=x,2=y,3=z) increment.
uni	integer(kind=I4P)	in		Index of normal and tangential velocities.
ut1	integer(kind=I4P)	in		Index of normal and tangential velocities.
ut2	integer(kind=I4P)	in		Index of normal and tangential velocities.
nv	integer(kind=I4P)	in		Number of conservative varibales.
q_aux1	real(kind=R8P)	in		Left state, auxiliary variables.
q_aux4	real(kind=R8P)	in		Left state, auxiliary variables.
f	real(kind=R8P)	inout		Resulting fluxes.
lmax	real(kind=R8P)	out	optional	Maximum wave speed estimation.

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compute_riemann_euler_hllem

Solve the Riemann problem between the state 1 (left) and 4 (right) using the HLLEM solver. See Dumbser and Balsara "A new efficient formulation of the HLLEM Riemann solver for general conservative and non-conservative hyperbolic systems", 2016, Journal of Compuational Physics.

subroutine compute_riemann_euler_hllem(si, sir, uni, ut1, ut2, nv, q_aux1, q_aux4, f, lmax)

Arguments

Name	Type	Intent	Attributes	Description
si	integer(kind=I4P)	in		Directional (1=x,2=y,3=z) increment.
sir	real(kind=R8P)	in		Directional (1=x,2=y,3=z) increment.
uni	integer(kind=I4P)	in		Index of normal and tangential velocities.
ut1	integer(kind=I4P)	in		Index of normal and tangential velocities.
ut2	integer(kind=I4P)	in		Index of normal and tangential velocities.
nv	integer(kind=I4P)	in		Number of conservative varibales.
q_aux1	real(kind=R8P)	in		Left state, auxiliary variables.
q_aux4	real(kind=R8P)	in		Left state, auxiliary variables.
f	real(kind=R8P)	inout		Resulting fluxes.
lmax	real(kind=R8P)	out	optional	Maximum wave speed estimation.

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compute_riemann_euler_llf

Solve the Riemann problem between the state 1 (left) and 4 (right) using the Local-Lax-Friedrichs (LLF, Rusanov) solver.

subroutine compute_riemann_euler_llf(si, sir, uni, ut1, ut2, nv, q_aux1, q_aux4, f, lmax)

Arguments

Name	Type	Intent	Attributes	Description
si	integer(kind=I4P)	in		Directional (1=x,2=y,3=z) increment.
sir	real(kind=R8P)	in		Directional (1=x,2=y,3=z) increment.
uni	integer(kind=I4P)	in		Index of normal and tangential velocities.
ut1	integer(kind=I4P)	in		Index of normal and tangential velocities.
ut2	integer(kind=I4P)	in		Index of normal and tangential velocities.
nv	integer(kind=I4P)	in		Number of conservative varibales.
q_aux1	real(kind=R8P)	in		Left state, auxiliary variables.
q_aux4	real(kind=R8P)	in		Left state, auxiliary variables.
f	real(kind=R8P)	inout		Resulting fluxes.
lmax	real(kind=R8P)	out	optional	Maximum wave speed estimation.

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compute_riemann_euler_ts

Solve the Riemann problem between the state 1 (left) and 4 (right) using the Two-Shocks (TS) approximation.

subroutine compute_riemann_euler_ts(si, sir, uni, ut1, ut2, nv, q_aux1, q_aux4, f, lmax)

Arguments

Name	Type	Intent	Attributes	Description
si	integer(kind=I4P)	in		Directional (1=x,2=y,3=z) increment.
sir	real(kind=R8P)	in		Directional (1=x,2=y,3=z) increment.
uni	integer(kind=I4P)	in		Index of normal and tangential velocities.
ut1	integer(kind=I4P)	in		Index of normal and tangential velocities.
ut2	integer(kind=I4P)	in		Index of normal and tangential velocities.
nv	integer(kind=I4P)	in		Number of conservative varibales.
q_aux1	real(kind=R8P)	in		Left state, auxiliary variables.
q_aux4	real(kind=R8P)	in		Left state, auxiliary variables.
f	real(kind=R8P)	inout		Resulting fluxes.
lmax	real(kind=R8P)	out	optional	Maximum wave speed estimation.

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compute_conservatives_euler

Compute convervative variables from auxiliary ones.

Attributes: pure

subroutine compute_conservatives_euler(q_aux, q)

Arguments

Name	Type	Intent	Attributes	Description
q_aux	real(kind=R8P)	in		Auxiliary variables.
q	real(kind=R8P)	inout		Conservative varibales.

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compute_convective_fluxes_euler

Compute convective fluxes for Euler equations from auxiliary variables.

Attributes: pure

subroutine compute_convective_fluxes_euler(sir, q_aux, f)

Arguments

Name	Type	Intent	Attributes	Description
sir	real(kind=R8P)	in		Directional (1=x,2=y,3=z) increment.
q_aux	real(kind=R8P)	in		Auxiliary variables.
f	real(kind=R8P)	inout		Conservative fluxes.

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compute_eigeinvectors_left

Compute left eigenvectors matrix (L) of the Jacobian fluxes matrix $A=R\mathrm{\Lambda }L$ in primitive variables form. @note This function consider only the normal direction: $\frac{\partial P}{\partial t}+R\mathrm{\Lambda }L\frac{\partial P}{\partial n}=0$ where P are the primitive variables and n is the normal direction. R is the matrix of the right eigenvectors, $\mathrm{\Lambda }$ is the diagonal matrix of the eigenvalues and L is the matrix of the left eigenvectors.

Attributes: pure

subroutine compute_eigeinvectors_left(gm1, u, a, el)

Arguments

Name	Type	Intent	Attributes	Description
gm1	real(kind=R8P)	in		Specific heats ration minus one, g-1.
u	real(kind=R8P)	in		Normal velocity.
a	real(kind=R8P)	in		Speed of sound.
el	real(kind=R8P)	inout		Left eigenvectors matrix.

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compute_eigeinvectors_right

Compute right eigenvectors matrix (R) of the Jacobian fluxes matrix $A=R\mathrm{\Lambda }L$ in primitive variables form. @note This function consider only the normal direction: $\frac{\partial P}{\partial t}+R\mathrm{\Lambda }L\frac{\partial P}{\partial n}=0$ where P are the primitive variables and n is the normal direction. R is the matrix of the right eigenvectors, $\mathrm{\Lambda }$ is the diagonal matrix of the eigenvalues and L is the matrix of the left eigenvectors.

Attributes: pure

subroutine compute_eigeinvectors_right(H, u, a, er)

Arguments

Name	Type	Intent	Attributes	Description
H	real(kind=R8P)	in		Total specific entalpy.
u	real(kind=R8P)	in		Normal velocity.
a	real(kind=R8P)	in		Speed of sound.
er	real(kind=R8P)	inout		Right eigenvectors matrix.

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