adam_flume_cpu_mhd_eglm_kernels

ADAM, FLUME CPU kernels of the ideal MHD with EGLM 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_EGLM, NV_AUX_K = NV_AUX_MHD; the face-flux kernel is the shared body with the EGLM split (Derigs et al. 2018; issue #47, D-8, section 3.3). The energy includes psi^2 / 2 (the auxiliary variables and the floors read the thermal pressure from the energy without it); the nonconservative sources and the damping are local residual terms.

Source: src/app/flume/cpu/adam_flume_cpu_mhd_eglm_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
• compute_positivity_factors
• compute_seam_positivity_factors
• compute_backbone_fluxes
• positivity_cell_factor
• blend_positivity_fluxes
• blend_inadmissible_ghosts
• add_eglm_sources
• add_eglm_sources_limited
• add_glm_damping
• face_split_fluxes
• backbone_face_flux
• cell_sources
• eglm_source_scalars
• eglm_source_vector
• 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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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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add_eglm_sources

Add the nonconservative EGLM sources to the residuals of the interior cells (Derigs et al. 2018, eqs. 3.16-3.18; issue #47, section 3.3): -(div B) (0, B, u.B, u, 0) - (u.grad psi) (0, 0, psi, 0, 1) in the order (rho, rho u, E, B, psi). div B and grad psi are the centred finite differences of the library, half stencil hs (order 2 hs, the WENO order: second-order sources drop the Alfven wave to order 2.26, P0), null directions weighted zero. Local sources in every Runge-Kutta stage, never in the fluxes: momentum, energy and B are conserved up to these O(div B) terms. The 3-term sums are order-independent (mhd_sum3). The caller has refreshed the ghost cells and the auxiliary variables of q.

subroutine add_eglm_sources(ni, nj, nk, ngc, blocks_number, hs, dxyz, is_null, q, q_aux, 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.
hs	integer(kind=I4P)	in		Finite difference half stencil, <= ngc.
dxyz	real(kind=R8P)	in		Blocks space steps [3, nb].
is_null	logical	in		Null directions.
q	real(kind=R8P)	in		Conservative variables.
q_aux	real(kind=R8P)	in		Auxiliary variables.
dq	real(kind=R8P)	inout		Residuals.

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add_eglm_sources_limited

Add the EGLM sources with the positivity limiter (issue #47, D-9): in a cell with factor Lambda < 1 the second-order sources plus Lambda times the difference to the order-2 hs ones (the sources are linear in div B and u.grad psi, so the two scalars are blended); with Lambda = 1 the arithmetic of add_eglm_sources.

subroutine add_eglm_sources_limited(ni, nj, nk, ngc, blocks_number, hs, dxyz, is_null, q, q_aux, lam, 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.
hs	integer(kind=I4P)	in		Finite difference half stencil, <= ngc.
dxyz	real(kind=R8P)	in		Blocks space steps [3, nb].
is_null	logical	in		Null directions.
q	real(kind=R8P)	in		Conservative variables.
q_aux	real(kind=R8P)	in		Auxiliary variables.
lam	real(kind=R8P)	in		Cell factors (component 1).
dq	real(kind=R8P)	inout		Residuals.

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add_glm_damping

Add the damping source to the residuals of the interior cells, dq(psi) = dq(psi) - (alpha c_h / L) psi, as GLM (issue #47, section 3.3). Only psi is damped: the total energy is unchanged, so the removed cleaning energy psi^2 / 2 becomes thermal energy (the pressure grows) and the energy drift stays bounded by the div(B) sources.

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 alpha c_h / L.
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: the MHD split with EGLM 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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backbone_face_flux

Backbone adapter of the positivity limiter: the Lax-Friedrichs flux with the Wu speed, at least ch.

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 (EGLM): the nonconservative sources with second-order (s_lo, the backbone's) and order-2 hs (s_hi) centred differences, both with the damping of psi.

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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eglm_source_scalars

Return div B and u.grad psi of a cell by the centred differences of half stencil hs (the arithmetic of add_eglm_sources).

Attributes: pure

subroutine eglm_source_scalars(ngc, hs, dxyz, is_null, q, q_aux, i, j, k, b, divb, upsi)

Arguments

Name	Type	Intent	Attributes	Description
ngc	integer(kind=I4P)	in		Ghost cells number.
hs	integer(kind=I4P)	in		Half stencil.
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.
divb	real(kind=R8P)	out		div B, u.grad psi.
upsi	real(kind=R8P)	out		div B, u.grad psi.

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eglm_source_vector

Return the EGLM source vector of a cell from its div B and u.grad psi (linear in both).

Attributes: pure

subroutine eglm_source_vector(q, qa, divb, upsi, s)

Arguments

Name	Type	Intent	Attributes	Description
q	real(kind=R8P)	in		Conservative variables.
qa	real(kind=R8P)	in		Auxiliary variables.
divb	real(kind=R8P)	in		div B, u.grad psi.
upsi	real(kind=R8P)	in		div B, u.grad psi.
s	real(kind=R8P)	out		Sources.

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Functions

cleaning_energy

Cleaning-energy adapter of the floors kernel: psi^2 / 2, part of the EGLM energy.

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 positivity limiter: E minus the kinetic, magnetic and cleaning energies, 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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