adam_flume_cpu_mhd_glm_kernels

ADAM, FLUME CPU kernels of the ideal MHD with GLM cleaning model.

The model-agnostic auxiliary-variables loop (adam_flume_cpu_aux_kernels_agnostic.INC) and the MHD dt loop (adam_flume_cpu_mhd_kernels_agnostic.INC) instantiated with NV_K = NV_MHD_GLM, NV_AUX_K = NV_AUX_MHD (issue #41, section 4). The face-flux kernel is the shared body with the MHD split (M2-P3).

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

Dependencies

Contents

• compute_face_fluxes
• add_gravity_edge_correction
• compute_q_aux
• count_nonfinite
• compute_lambda_max
• compute_lambda_max_dissipative
• apply_floors
• compute_speed_max
• compute_divb_norms
• blend_inadmissible_ghosts
• add_glm_damping
• face_split_fluxes
• cleaning_energy
• 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_lambda_max

Compute max(sum_d (|u_d| + c_{f,d}) / dx_d) over the interior cells (null directions excluded), c_{f,d} the fast magnetosonic speed along d (issue #41, section 3.5).

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| + c_{f,d}) / dx_d.

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compute_lambda_max_dissipative

Compute max(sum_d (|u_d| + c_{f,d}) / 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 (Ohmic included), with the maxima of the two parts and the minimum cell Reynolds number; the MHD twin of the Euler compute_lambda_max_dissipative.

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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apply_floors

Apply the MHD positivity floors to the interior cells of a stage state, before its ghost exchange (issue #41, section 3.8): a cell with rho < rho_floor or p < p_floor gets rho = max(rho, rho_floor) at fixed velocity and p = max(p, p_floor) (internal energy added; the model's cleaning_energy adapter adds psi^2 / 2 under EGLM, zero otherwise). Interior only: the exchange then carries the floored values to the ghost cells, and ghost cells that no map fills (never read by the stencils) are not inspected. Returns the floored cells, the cells with a non-positive density or pressure (counted before flooring) and the minimum density and pressure. Floors are not conservative: the caller logs the counters.

subroutine apply_floors(ni, nj, nk, ngc, blocks_number, gamma, R, rho_floor, p_floor, q, floored, nonpositive, rho_min, p_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.
R	real(kind=R8P)	in		Gas constant.
rho_floor	real(kind=R8P)	in		Density and pressure floors.
p_floor	real(kind=R8P)	in		Density and pressure floors.
q	real(kind=R8P)	inout		Conservative variables.
floored	integer(kind=I4P)	out		Floored cells.
nonpositive	integer(kind=I4P)	out		Cells with non-positive density or pressure.
rho_min	real(kind=R8P)	out		Minimum density and pressure.
p_min	real(kind=R8P)	out		Minimum density and pressure.

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compute_speed_max

Compute max(|u_d| + c_{f,d}) over the interior cells and the active directions, the fastest wave speed (the GLM c_h check, issue #41, section 3.5).

subroutine compute_speed_max(ni, nj, nk, ngc, blocks_number, gamma, R, is_null, q, speed_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.
is_null	logical	in		Null directions.
q	real(kind=R8P)	in		Conservative variables.
speed_max	real(kind=R8P)	out		Maximum of |u_d| + c_{f,d}.

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compute_divb_norms

Compute the div(B) norms over the interior cells (issue #41, D-10): max|div B|, sum |div B| dV and the maximum over the seam-local cells (within band cells of a block face with seam(b,face) /= 0, a 2:1 AMR or inter-realm seam). div B is the centred finite difference of the library (half stencil hs), null directions weighted zero; the cell volume includes the null directions (issue #37). The caller has refreshed the ghost cells.

subroutine compute_divb_norms(ni, nj, nk, ngc, blocks_number, hs, band, dxyz, is_null, seam, q, divb_max, divb_l1, divb_seam_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.
hs	integer(kind=I4P)	in		Finite difference half stencil, <= ngc.
band	integer(kind=I4P)	in		Seam-local band width, in cells.
dxyz	real(kind=R8P)	in		Blocks space steps [3, nb].
is_null	logical	in		Null directions.
seam	integer(kind=I4P)	in		Seam faces flags [nb, 6] (0: not a seam face).
q	real(kind=R8P)	in		Conservative variables.
divb_max	real(kind=R8P)	out		Maximum of |div B|.
divb_l1	real(kind=R8P)	out		Sum of |div B| dV.
divb_seam_max	real(kind=R8P)	out		Maximum of |div B| over the seam-local cells.

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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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add_glm_damping

Add the GLM damping source to the residuals of the interior cells, dq(psi) = dq(psi) - (c_h^2 / c_p^2) psi (mixed GLM, Dedner et al. 2002; issue #41, section 3.1): a local source, in every Runge-Kutta stage and never in the fluxes, so the reflux and the conservation of the other variables are untouched.

subroutine add_glm_damping(ni, nj, nk, ngc, blocks_number, damping, q, dq)

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.
damping	real(kind=R8P)	in		Damping rate c_h^2 / c_p^2.
q	real(kind=R8P)	in		Conservative variables.
dq	real(kind=R8P)	inout		Residuals.

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face_split_fluxes

Split adapter of the shared face kernel (issue #41, M2-P3): the MHD split with GLM cleaning.

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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Functions

cleaning_energy

Cleaning-energy adapter of the floors kernel: zero, psi (if any) is not part of the energy of this model.

Attributes: pure

Returns: real(kind=R8P)

function cleaning_energy(q) result(e)

Arguments

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

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internal_energy

Internal-energy adapter of the ghost positivity blend: E minus the kinetic and magnetic energies, per unit volume (the mixed GLM keeps psi out of the energy).

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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