adam_flume_cpu_euler_kernels

ADAM, FLUME CPU kernels of the Euler model.

The model-agnostic loop bodies (adam_flume_cpu_{face,aux}_kernels_agnostic.INC) instantiated on the Euler physics: the local arrays are sized by the Euler constants NV_K = NV_EULER, NV_AUX_K = NV_AUX (issue #41, section 4), plus the Euler signal-speed loop.

Source: src/app/flume/cpu/adam_flume_cpu_euler_kernels.F90

Dependencies

Contents

• compute_face_fluxes
• add_gravity_edge_correction
• compute_q_aux
• count_nonfinite
• compute_positivity_factors
• compute_seam_positivity_factors
• compute_backbone_fluxes
• positivity_cell_factor
• blend_positivity_fluxes
• blend_inadmissible_ghosts
• compute_lambda_max
• compute_lambda_max_dissipative
• face_split_fluxes
• backbone_face_flux
• cell_sources
• internal_energy

Subroutines

compute_face_fluxes

Compute the WENO face fluxes of direction d: face (i,j,k) lies between cells (i,j,k) and (i+di,j+dj,k+dk), so the face array starts at index 0 along d.

Per face: gather the stencil m = 1-S ... S into constant-bound locals, project and split it, reconstruct every field (the local v is the packed stencil of the WENO primitive), back-project.

subroutine compute_face_fluxes(d, di, dj, dk, ni, nj, nk, ngc, blocks_number, gamma, ch, is_characteristic, weno, q, q_aux, fl)

Arguments

Name	Type	Intent	Attributes	Description
d	integer(kind=I4P)	in		Direction, 1=x, 2=y, 3=z.
di	integer(kind=I4P)	in		Unit step along d.
dj	integer(kind=I4P)	in		Unit step along d.
dk	integer(kind=I4P)	in		Unit step along d.
ni	integer(kind=I4P)	in		Grid dimensions.
nj	integer(kind=I4P)	in		Grid dimensions.
nk	integer(kind=I4P)	in		Grid dimensions.
ngc	integer(kind=I4P)	in		Grid dimensions.
blocks_number	integer(kind=I4P)	in		Actual blocks number.
gamma	real(kind=R8P)	in		Specific heats ratio.
ch	real(kind=R8P)	in		GLM cleaning speed (models with GLM only).
is_characteristic	logical	in		Characteristic (or conservative) variables.
weno	type(weno_object)	in		WENO coefficients.
q	real(kind=R8P)	in		Conservative variables.
q_aux	real(kind=R8P)	in		Auxiliary variables.
fl	real(kind=R8P)	inout		Face fluxes of direction d.

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add_gravity_edge_correction

Add the faces beyond the block to the gravity energy correction of direction d (issue #73, M7-G2a): cell 1 takes -g_d F^rho / 24 of face -1 (between cells -1 and 0), cell n_d that of face n_d + 1 (between cells n_d + 1 and n_d + 2), the two terms of g_d (-F_{i-3/2} + F_{i-1/2} + F_{i+1/2} - F_{i+3/2}) / 24 whose faces the block does not hold. Each face is computed as compute_face_fluxes does (the same body, its mass component kept), from the ghosts: its stencil reaches S + 1 ghost cells, which the initialisation requires with gravity.

subroutine add_gravity_edge_correction(d, di, dj, dk, ni, nj, nk, ngc, blocks_number, gamma, ch, is_characteristic, weno, ir, gd, q, q_aux, gc)

Arguments

Name	Type	Intent	Attributes	Description
d	integer(kind=I4P)	in		Direction, 1=x, 2=y, 3=z.
di	integer(kind=I4P)	in		Unit step along d.
dj	integer(kind=I4P)	in		Unit step along d.
dk	integer(kind=I4P)	in		Unit step along d.
ni	integer(kind=I4P)	in		Grid dimensions.
nj	integer(kind=I4P)	in		Grid dimensions.
nk	integer(kind=I4P)	in		Grid dimensions.
ngc	integer(kind=I4P)	in		Grid dimensions.
blocks_number	integer(kind=I4P)	in		Actual blocks number.
gamma	real(kind=R8P)	in		Specific heats ratio.
ch	real(kind=R8P)	in		GLM cleaning speed (models with GLM only).
is_characteristic	logical	in		Characteristic (or conservative) variables.
weno	type(weno_object)	in		WENO coefficients.
ir	integer(kind=I4P)	in		Index of the density (mass) variable.
gd	real(kind=R8P)	in		Gravity along d.
q	real(kind=R8P)	in		Conservative variables.
q_aux	real(kind=R8P)	in		Auxiliary variables.
gc	real(kind=R8P)	inout		Gravity energy correction [1, ...].

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compute_q_aux

Compute the auxiliary variables on every cell, ghost cells included.

subroutine compute_q_aux(ni, nj, nk, ngc, blocks_number, gamma, R, q, q_aux)

Arguments

Name	Type	Intent	Attributes	Description
ni	integer(kind=I4P)	in		Grid dimensions.
nj	integer(kind=I4P)	in		Grid dimensions.
nk	integer(kind=I4P)	in		Grid dimensions.
ngc	integer(kind=I4P)	in		Grid dimensions.
blocks_number	integer(kind=I4P)	in		Actual blocks number.
gamma	real(kind=R8P)	in		Specific heats ratio.
R	real(kind=R8P)	in		Gas constant.
q	real(kind=R8P)	in		Conservative variables.
q_aux	real(kind=R8P)	inout		Auxiliary variables.

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count_nonfinite

Count the non-finite (NaN or infinite) conservative values of the interior cells (issue #45): the exponent field has all its bits set. Tested on the bit pattern, so that no floating point mode can fold the test away.

subroutine count_nonfinite(ni, nj, nk, ngc, blocks_number, q, n)

Arguments

Name	Type	Intent	Attributes	Description
ni	integer(kind=I4P)	in		Grid dimensions.
nj	integer(kind=I4P)	in		Grid dimensions.
nk	integer(kind=I4P)	in		Grid dimensions.
ngc	integer(kind=I4P)	in		Grid dimensions.
blocks_number	integer(kind=I4P)	in		Actual blocks number.
q	real(kind=R8P)	in		Conservative variables.
n	integer(kind=I8P)	out		Non-finite values number.

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compute_positivity_factors

Compute the cell factor Lambda of every interior cell into lam(1,:,:,:,:) (the other components untouched) and count the cells whose backbone is not admissible (Lambda = 0 there: the floors, if enabled, take over) and those with a non-finite high-order face flux (Lambda = 0 too: a NaN or infinite flux carries no information, and every comparison with it is false, so the corner factors would keep it; tested on the bit pattern as count_nonfinite).

subroutine compute_positivity_factors(ni, nj, nk, ngc, blocks_number, gamma, ch, damping, hs, dt, g, has_phi, phi, dxyz, is_null, q, q_aux, flx, fly, flz, gc, lam, bad, nonfinite)

Arguments

Name	Type	Intent	Attributes	Description
ni	integer(kind=I4P)	in		Grid dimensions.
nj	integer(kind=I4P)	in		Grid dimensions.
nk	integer(kind=I4P)	in		Grid dimensions.
ngc	integer(kind=I4P)	in		Grid dimensions.
blocks_number	integer(kind=I4P)	in		Actual blocks number.
gamma	real(kind=R8P)	in		Specific heats ratio.
ch	real(kind=R8P)	in		GLM cleaning speed (EGLM only).
damping	real(kind=R8P)	in		GLM damping rate (EGLM only).
hs	integer(kind=I4P)	in		Half stencil of the high-order sources.
dt	real(kind=R8P)	in		Forward-Euler step of the stage.
g	real(kind=R8P)	in		Gravity (issue #73), zero without it.
has_phi	logical	in		The cell potential is applied (issue #81).
phi	real(kind=R8P)	in		Gravitational potential (read with has_phi).
dxyz	real(kind=R8P)	in		Blocks space steps [3, nb].
is_null	logical	in		Null directions.
q	real(kind=R8P)	in		Conservative variables (ghosts updated).
q_aux	real(kind=R8P)	in		Auxiliary variables.
flx	real(kind=R8P)	in		X-face high-order fluxes.
fly	real(kind=R8P)	in		Y-face high-order fluxes.
flz	real(kind=R8P)	in		Z-face high-order fluxes.
gc	real(kind=R8P)	in		Gravity energy correction (zero without it).
lam	real(kind=R8P)	inout		Cell factors (component 1).
bad	integer(kind=I4P)	out		Cells with an inadmissible backbone.
nonfinite	integer(kind=I4P)	out		Cells with a non-finite high-order face flux.

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compute_seam_positivity_factors

Recompute the factor of the cells beside a 2:1 seam with the seam faces' backbone and high-order fluxes overridden (issue #50, D1: per-stage seam flux synchronisation). Cell n is cell(1:4,n) = (i, j, k, b); its face fec (1..6: -x, +x, -y, +y, -z, +z) takes olo(:,fec,n) and ohi(:,fec,n) where omask(fec,n), the backbone flux of q and the high-order flux of flx/fly/flz elsewhere, exactly as compute_positivity_factors. dbad and dnonfinite return the change of the two counts against the factors without the overrides, which compute_positivity_factors has already counted.

subroutine compute_seam_positivity_factors(ngc, gamma, ch, damping, hs, dt, g, has_phi, phi, dxyz, is_null, q, q_aux, flx, fly, flz, gc, ncells, cell, omask, olo, ohi, lam, dbad, dnonfinite)

Arguments

Name	Type	Intent	Attributes	Description
ngc	integer(kind=I4P)	in		Ghost cells number.
gamma	real(kind=R8P)	in		Specific heats ratio.
ch	real(kind=R8P)	in		GLM cleaning speed (EGLM only).
damping	real(kind=R8P)	in		GLM damping rate (EGLM only).
hs	integer(kind=I4P)	in		Half stencil of the high-order sources.
dt	real(kind=R8P)	in		Forward-Euler step of the stage.
g	real(kind=R8P)	in		Gravity (issue #73), zero without it.
has_phi	logical	in		The cell potential is applied (issue #81).
phi	real(kind=R8P)	in		Gravitational potential (read with has_phi).
dxyz	real(kind=R8P)	in		Blocks space steps [3, nb].
is_null	logical	in		Null directions.
q	real(kind=R8P)	in		Conservative variables (ghosts updated).
q_aux	real(kind=R8P)	in		Auxiliary variables.
flx	real(kind=R8P)	in		X-face high-order fluxes.
fly	real(kind=R8P)	in		Y-face high-order fluxes.
flz	real(kind=R8P)	in		Z-face high-order fluxes.
gc	real(kind=R8P)	in		Gravity energy correction (zero without it).
ncells	integer(kind=I4P)	in		Seam cells.
cell	integer(kind=I4P)	in		Seam cells (i, j, k, b) [4, ncells].
omask	logical	in		Overridden faces [6, ncells].
olo	real(kind=R8P)	in		Override backbone fluxes [nv, 6, ncells].
ohi	real(kind=R8P)	in		Override high-order fluxes [nv, 6, ncells].
lam	real(kind=R8P)	inout		Cell factors (component 1).
dbad	integer(kind=I4P)	out		Change of the inadmissible backbones count.
dnonfinite	integer(kind=I4P)	out		Change of the non-finite cells count.

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compute_backbone_fluxes

Compute the backbone flux of n face state pairs of direction d (issue #50: the fine faces of a 2:1 seam take the coarse donor cell as their outer state).

subroutine compute_backbone_fluxes(n, d, gamma, ch, qL, qR, flo)

Arguments

Name	Type	Intent	Attributes	Description
n	integer(kind=I4P)	in		Faces number.
d	integer(kind=I4P)	in		Direction, 1=x, 2=y, 3=z.
gamma	real(kind=R8P)	in		Specific heats ratio.
ch	real(kind=R8P)	in		GLM cleaning speed (EGLM only).
qL	real(kind=R8P)	in		Left states [nv, n].
qR	real(kind=R8P)	in		Right states [nv, n].
flo	real(kind=R8P)	out		Backbone fluxes [nv, n].

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positivity_cell_factor

The factor of one cell from its backbone update qb, the antidiffusive differences dlt(:,1:nf) of its active faces and the source difference dsrc: status 1 (and lc = 0) if the backbone is not admissible, 2 (and lc = 0) if a face difference is not finite (a NaN passes every comparison of the corners), else 0 with lc the largest factor of the corner box.

Attributes: pure

subroutine positivity_cell_factor(nf, qb, dlt, dsrc, lc, status)

Arguments

Name	Type	Intent	Attributes	Description
nf	integer(kind=I4P)	in		Active faces.
qb	real(kind=R8P)	in		Backbone update.
dlt	real(kind=R8P)	in		Antidiffusive differences.
dsrc	real(kind=R8P)	in		Source difference.
lc	real(kind=R8P)	out		Cell factor.
status	integer(kind=I4P)	out		0 admissible, 1 inadmissible backbone, 2 non-finite.

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blend_positivity_fluxes

Blend the face fluxes of direction d with the backbone: F <- F^LLF + theta (F - F^LLF), theta the smaller factor of the two cells (ghost factors from the exchange; a ghost never written keeps 1, so a physical-boundary face takes the interior cell's factor). Faces with theta = 1 are left untouched (bitwise), and counted otherwise; a face with theta = 0 takes the backbone flux itself (0 * NaN would keep a non-finite high-order flux).

subroutine blend_positivity_fluxes(d, di, dj, dk, ni, nj, nk, ngc, blocks_number, gamma, ch, q, lam, fl, limited)

Arguments

Name	Type	Intent	Attributes	Description
d	integer(kind=I4P)	in		Direction, 1=x, 2=y, 3=z.
di	integer(kind=I4P)	in		Unit step along d.
dj	integer(kind=I4P)	in		Unit step along d.
dk	integer(kind=I4P)	in		Unit step along d.
ni	integer(kind=I4P)	in		Grid dimensions.
nj	integer(kind=I4P)	in		Grid dimensions.
nk	integer(kind=I4P)	in		Grid dimensions.
ngc	integer(kind=I4P)	in		Grid dimensions.
blocks_number	integer(kind=I4P)	in		Actual blocks number.
gamma	real(kind=R8P)	in		Specific heats ratio.
ch	real(kind=R8P)	in		GLM cleaning speed (EGLM only).
q	real(kind=R8P)	in		Conservative variables.
lam	real(kind=R8P)	in		Cell factors (component 1).
fl	real(kind=R8P)	inout		Face fluxes of direction d.
limited	integer(kind=I4P)	out		Faces with theta < 1.

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blend_inadmissible_ghosts

Blend every inadmissible face ghost of q toward the adjacent interior cell and count the ghosts blended.

subroutine blend_inadmissible_ghosts(ni, nj, nk, ngc, blocks_number, is_null, q, blended)

Arguments

Name	Type	Intent	Attributes	Description
ni	integer(kind=I4P)	in		Grid dimensions.
nj	integer(kind=I4P)	in		Grid dimensions.
nk	integer(kind=I4P)	in		Grid dimensions.
ngc	integer(kind=I4P)	in		Grid dimensions.
blocks_number	integer(kind=I4P)	in		Actual blocks number.
is_null	logical	in		Null directions.
q	real(kind=R8P)	inout		Conservative variables (ghosts updated).
blended	integer(kind=I4P)	out		Ghosts blended.

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compute_lambda_max

Compute max(sum_d (|u_d| + a) / dx_d) over the interior cells (null directions excluded).

subroutine compute_lambda_max(ni, nj, nk, ngc, blocks_number, gamma, R, dxyz, is_null, q, lambda_max)

Arguments

Name	Type	Intent	Attributes	Description
ni	integer(kind=I4P)	in		Grid dimensions.
nj	integer(kind=I4P)	in		Grid dimensions.
nk	integer(kind=I4P)	in		Grid dimensions.
ngc	integer(kind=I4P)	in		Grid dimensions.
blocks_number	integer(kind=I4P)	in		Actual blocks number.
gamma	real(kind=R8P)	in		Specific heats ratio.
R	real(kind=R8P)	in		Gas constant.
dxyz	real(kind=R8P)	in		Blocks space steps [3, nb].
is_null	logical	in		Null directions.
q	real(kind=R8P)	in		Conservative variables.
lambda_max	real(kind=R8P)	out		Maximum of sum_d (|u_d| + a) / dx_d.

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compute_lambda_max_dissipative

Compute max(sum_d (|u_d| + a) / dx_d + 2 nu sum_d 1 / dx_d^2) over the interior cells (issue #65, D-M4-3), nu the largest diffusivity of the cell, with the maxima of the two parts and the minimum cell Reynolds number sum_d (|u_d| + a) / dx_d / (nu sum_d 1 / dx_d^2), (|u| + a) dx / nu on a uniform 1D grid.

subroutine compute_lambda_max_dissipative(ni, nj, nk, ngc, blocks_number, gamma, R, cp, mu0, k0, eta, t_wall, tref, omega_mu, omega_k, dxyz, is_null, q, lambda_max, lambda_hyp, lambda_dif, re_cell_min)

Arguments

Name	Type	Intent	Attributes	Description
ni	integer(kind=I4P)	in		Grid dimensions.
nj	integer(kind=I4P)	in		Grid dimensions.
nk	integer(kind=I4P)	in		Grid dimensions.
ngc	integer(kind=I4P)	in		Grid dimensions.
blocks_number	integer(kind=I4P)	in		Actual blocks number.
gamma	real(kind=R8P)	in		Specific heats ratio, gas constant, cp.
R	real(kind=R8P)	in		Specific heats ratio, gas constant, cp.
cp	real(kind=R8P)	in		Specific heats ratio, gas constant, cp.
mu0	real(kind=R8P)	in		Dissipative coefficients.
k0	real(kind=R8P)	in		Dissipative coefficients.
eta	real(kind=R8P)	in		Dissipative coefficients.
t_wall	real(kind=R8P)	in		Hottest isothermal wall temperature, 0 if none.
tref	real(kind=R8P)	in		Temperature laws.
omega_mu	real(kind=R8P)	in		Temperature laws.
omega_k	real(kind=R8P)	in		Temperature laws.
dxyz	real(kind=R8P)	in		Blocks space steps [3, nb].
is_null	logical	in		Null directions.
q	real(kind=R8P)	in		Conservative variables.
lambda_max	real(kind=R8P)	out		Maximum of the sum.
lambda_hyp	real(kind=R8P)	out		Maximum of the hyperbolic part.
lambda_dif	real(kind=R8P)	out		Maximum of the diffusive part.
re_cell_min	real(kind=R8P)	out		Minimum cell Reynolds number.

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face_split_fluxes

Split adapter of the shared face kernel (issue #41, M2-P3): the Euler split, ch unused.

Attributes: pure

subroutine face_split_fluxes(gamma, ch, d, S, is_characteristic, qs, qas, fsplit, er, mu)

Arguments

Name	Type	Intent	Attributes	Description
gamma	real(kind=R8P)	in		Specific heats ratio.
ch	real(kind=R8P)	in		GLM cleaning speed.
d	integer(kind=I4P)	in		Direction, 1=x, 2=y, 3=z.
S	integer(kind=I4P)	in		WENO stencil half-width, S <= S_MAX.
is_characteristic	logical	in		Characteristic (or conservative) variables.
qs	real(kind=R8P)	in		Stencil conservative variables.
qas	real(kind=R8P)	in		Stencil auxiliary variables.
fsplit	real(kind=R8P)	out		Split fields in the WENO upwind layout.
er	real(kind=R8P)	out		Right eigenvectors.
mu	real(kind=R8P)	out		Magnitude of each field (WENO descaler).

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backbone_face_flux

Backbone adapter of the positivity limiter: the Rusanov flux, ch unused.

Attributes: pure

subroutine backbone_face_flux(gamma, ch, d, qL, qR, f)

Arguments

Name	Type	Intent	Attributes	Description
gamma	real(kind=R8P)	in		Specific heats ratio.
ch	real(kind=R8P)	in		GLM cleaning speed.
d	integer(kind=I4P)	in		Direction, 1=x, 2=y, 3=z.
qL	real(kind=R8P)	in		Left state.
qR	real(kind=R8P)	in		Right state.
f	real(kind=R8P)	out		Flux.

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cell_sources

Sources adapter of the positivity limiter: none (Euler).

Attributes: pure

subroutine cell_sources(ngc, hs, damping, dxyz, is_null, q, q_aux, i, j, k, b, s_lo, s_hi)

Arguments

Name	Type	Intent	Attributes	Description
ngc	integer(kind=I4P)	in		Ghost cells number.
hs	integer(kind=I4P)	in		Half stencil of the high-order sources.
damping	real(kind=R8P)	in		GLM damping rate.
dxyz	real(kind=R8P)	in		Block space steps.
is_null	logical	in		Null directions.
q	real(kind=R8P)	in		Conservative variables.
q_aux	real(kind=R8P)	in		Auxiliary variables.
i	integer(kind=I4P)	in		Cell indexes.
j	integer(kind=I4P)	in		Cell indexes.
k	integer(kind=I4P)	in		Cell indexes.
b	integer(kind=I4P)	in		Cell indexes.
s_lo	real(kind=R8P)	out		Backbone sources.
s_hi	real(kind=R8P)	out		High-order sources.

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Functions

internal_energy

Internal-energy adapter of the positivity limiter: E minus the kinetic energy, per unit volume.

Attributes: pure

Returns: real(kind=R8P)

function internal_energy(q) result(e)

Arguments

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

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