adam_flume_seam_sync_object

ADAM, FLUME per-stage seam flux synchronisation data of the positivity limiter (issue #50, D1).

Why. The positivity limiter keeps every forward-Euler stage admissible cell by cell, but at a 2:1 AMR seam the end-of-step Berger-Colella reflux then replaces the coarse face flux by the restricted fine one, a correction no cell factor bounds: on the Balsara-Spicer blast across a refined box it drives coarse seam cells to rho e < 0 (issue #50). The limited runs therefore synchronise the seam flux at every stage, before the update:

• the fine faces of the seam take as backbone F^LF(q_C, q_f), with the coarse donor cell q_C as outer state;
• the coarse face takes the means of the fine high-order and backbone fluxes, F_H and F_LF (2x2 fine faces per coarse face cell, 2x1 on a quadtree face normal to x or y): the coarse backbone update with the mean of F^LF(q_C, q_f) is a convex combination of standard Lax-Friedrichs partial updates of q_C, hence admissible, so the coarse cell factor Lambda_C is computed with this pair;
• both sides blend with one factor theta_s = min(Lambda_C, min Lambda_f), so each side stays in its corner box and the coarse flux is exactly the mean of the fine ones: conservative at every stage, the reflux reduces to round-off.

What this object holds. The register's intra-realm AMR faces are replicated on every rank (flux_register_object, issue #28), so per-face skins indexed like the register are complete after one MPI_ALLREDUCE each: the coarse donor states qc (SUM: one owner writes), the fine means flo, fhi (SUM over the fine quadrants), the fine factors lmin (MIN) and the seam factors th (SUM: the coarse owner writes). The fine seam faces of this rank keep their backbone and high-order fluxes in a compact store (fine_lo, fine_hi): the blend overwrites the face fluxes before the seam faces are set. The skin cell c runs over the two tangential axes, inner fastest, the register order.

Source: src/app/flume/common/adam_flume_seam_sync_object.F90

Dependencies

Contents

• flume_seam_sync_object
• reduce_states
• reduce_fluxes
• reduce_factors
• reduce_theta
• seam_weno5_sensor
• seam_weno5_cell_ratio
• build
• seam_face_cells
• seam_skin_index
• seam_fine_to_coarse

Derived Types

flume_seam_sync_object

Per-stage seam flux synchronisation data (host).

Components

Name	Type	Attributes	Description
nv	integer(kind=I4P)		Variables number.
ncells	integer(kind=I4P)		Skin cells of all intra-realm AMR register faces.
nfine	integer(kind=I4P)		Face cells of this rank's fine seam faces.
off	integer(kind=I4P)	allocatable	Skin offset of each register face (-1: not intra-realm AMR).
fine_off	integer(kind=I4P)	allocatable	Compact offset of each (block, face) fine seam face (-1: none).
qc	real(kind=R8P)	allocatable	Coarse donor states [nv, ncells].
flo	real(kind=R8P)	allocatable	Mean fine backbone fluxes [nv, ncells].
fhi	real(kind=R8P)	allocatable	Mean fine high-order fluxes [nv, ncells].
lmin	real(kind=R8P)	allocatable	Smallest fine factor [ncells].
th	real(kind=R8P)	allocatable	Seam factors [ncells].
fine_lo	real(kind=R8P)	allocatable	Fine seam face backbone fluxes [nv, nfine].
fine_hi	real(kind=R8P)	allocatable	Fine seam face high-order fluxes [nv, nfine].

Type-Bound Procedures

Name	Attributes	Description
build	pass(self)	Size the skins from the register, reset them; .true. if any seam.
reduce_states	pass(self)	Complete the coarse donor states over the ranks.
reduce_fluxes	pass(self)	Complete the fine means over the ranks.
reduce_factors	pass(self)	Complete the smallest fine factors over the ranks.
reduce_theta	pass(self)	Complete the seam factors over the ranks.

Subroutines

reduce_states

Complete the coarse donor states over the ranks (each skin cell written by its coarse owner only).

subroutine reduce_states(self)

Arguments

Name	Type	Intent	Attributes	Description
self	class(flume_seam_sync_object)	inout		The synchronisation data.

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reduce_fluxes

Complete the fine means over the ranks (each quadrant written by its fine owner only).

subroutine reduce_fluxes(self)

Arguments

Name	Type	Intent	Attributes	Description
self	class(flume_seam_sync_object)	inout		The synchronisation data.

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reduce_factors

Complete the smallest fine factors over the ranks.

subroutine reduce_factors(self)

Arguments

Name	Type	Intent	Attributes	Description
self	class(flume_seam_sync_object)	inout		The synchronisation data.

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reduce_theta

Complete the seam factors over the ranks (each skin cell written by its coarse owner only).

subroutine reduce_theta(self)

Arguments

Name	Type	Intent	Attributes	Description
self	class(flume_seam_sync_object)	inout		The synchronisation data.

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Functions

seam_weno5_sensor

Return the WENO-5 sensor of the face between v(3) and v(4) (issue #68 E1): r = min_k w_k / d_k of the right-interface reconstruction of cell 3 (v(1:5)) and of the left-interface one of cell 4 (v(2:6)), the Jiang-Shu weights of adam_weno_object (zeps = 1e-6, exponent 3, its smoothness-indicator table): about 1 on smooth data, near 0 where a stencil holds a discontinuity. The sensor of verification/amr-log/amr_log.py (A4) and of the weno-riemann flux correction (#47), threshold FLUX_CORRECTION_SENSOR_TAU. Whole-array argument: no array section crosses the device call boundary.

Attributes: pure

Returns: real(kind=R8P)

function seam_weno5_sensor(v) result(r)

Arguments

Name	Type	Intent	Attributes	Description
v	real(kind=R8P)	in		One variable on the 6 cells across the face, in order.

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seam_weno5_cell_ratio

Return min_k w_k / d_k of the WENO-5 reconstruction of cell c of v with the linear weights d0, d1, d2 of the stencils (c-2..c), (c-1..c+1), (c..c+2) (seam_weno5_sensor).

Attributes: pure

Returns: real(kind=R8P)

function seam_weno5_cell_ratio(v, c, d0, d1, d2) result(r)

Arguments

Name	Type	Intent	Attributes	Description
v	real(kind=R8P)	in		One variable on the 6 cells across the face.
c	integer(kind=I4P)	in		Cell (3 or 4).
d0	real(kind=R8P)	in		Linear weights.
d1	real(kind=R8P)	in		Linear weights.
d2	real(kind=R8P)	in		Linear weights.

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build

Size the skins of the register's intra-realm AMR faces and the compact store of this rank's fine seam faces, and reset them (qc, flo, fhi, th to 0, lmin to huge). The result depends on the replicated register only, so every rank takes the same branch and issues the same collectives.

Returns: logical

function build(self, flux_register, register_index, blocks_number, ni, nj, nk, nv) result(active)

Arguments

Name	Type	Intent	Attributes	Description
self	class(flume_seam_sync_object)	inout		The synchronisation data.
flux_register	type(flux_register_object)	in		Forest's flux register.
register_index	integer(kind=I4P)	in		(block, face) signed register index.
blocks_number	integer(kind=I4P)	in		Actual blocks number.
ni	integer(kind=I4P)	in		Grid dimensions.
nj	integer(kind=I4P)	in		Grid dimensions.
nk	integer(kind=I4P)	in		Grid dimensions.
nv	integer(kind=I4P)	in		Variables number.

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seam_face_cells

Cells of a block face fec (1..6: -x, +x, -y, +y, -z, +z).

Attributes: pure

Returns: integer(kind=I4P)

function seam_face_cells(fec, ni, nj, nk) result(n)

Arguments

Name	Type	Intent	Attributes	Description
fec	integer(kind=I4P)	in		Face.
ni	integer(kind=I4P)	in		Grid dimensions.
nj	integer(kind=I4P)	in		Grid dimensions.
nk	integer(kind=I4P)	in		Grid dimensions.

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seam_skin_index

Skin index of the interior cell (i, j, k) beside face fec (the inverse of seam_skin_cell).

Attributes: pure

Returns: integer(kind=I4P)

function seam_skin_index(fec, ni, nj, i, j, k) result(c)

Arguments

Name	Type	Intent	Attributes	Description
fec	integer(kind=I4P)	in		Face.
ni	integer(kind=I4P)	in		Grid dimensions.
nj	integer(kind=I4P)	in		Grid dimensions.
i	integer(kind=I4P)	in		Cell.
j	integer(kind=I4P)	in		Cell.
k	integer(kind=I4P)	in		Cell.

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seam_fine_to_coarse

Coarse skin cell covering the fine skin cell c of a fine block whose quadrant on the coarse face is (ioff, joff) (the convention of restrict_fine_face_to_quadrant: ri x ro fine face cells per coarse face cell, 2 per refined tangential axis, 1 with a zero offset along an axis the tree does not refine, z of a quadtree, issue #46).

Attributes: pure

Returns: integer(kind=I4P)

function seam_fine_to_coarse(fec, ni, nj, nk, ioff, joff, ri, ro, c) result(cc)

Arguments

Name	Type	Intent	Attributes	Description
fec	integer(kind=I4P)	in		Fine block face.
ni	integer(kind=I4P)	in		Grid dimensions.
nj	integer(kind=I4P)	in		Grid dimensions.
nk	integer(kind=I4P)	in		Grid dimensions.
ioff	integer(kind=I4P)	in		Quadrant offsets (inner, outer).
joff	integer(kind=I4P)	in		Quadrant offsets (inner, outer).
ri	integer(kind=I4P)	in		Refinement ratios along the inner and outer tangential axes.
ro	integer(kind=I4P)	in		Refinement ratios along the inner and outer tangential axes.
c	integer(kind=I4P)	in		Fine skin cell.

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