adam_weno_object

ADAM, WENO class definition. Detailed reference of this implementation in contained into NASA/CR-97-206253 ICASE Report No. 97-65 "Essentially Non-Oscillatory and Weighted Essentially Non-Oscillatory Schemes for Hyperbolic Conservation Laws" of Chi-Wang Shu (1997). The stencil is arragnged as the following where for the sake of simplicity the case S=3 for interface 1/2 is sketched:

                       1/2
                       L|R
      -2     -1      0  |   1      2      3
...|------|------|------|------|------|------|...
    -^  ^+ -^  ^+ -^  ^+ -^  ^+ -^  ^+ -^  ^+
      \/     \/     \/     \/     \/     \/
...|------|------|------|------|------|------|...
   |stencil 0 R         |      |      |      |
   |____________________|      |      |      |
   |      |stencil 1 R         |      |      |
   |      |____________________|      |      |
   |      |      |stencil 2 R         |      |
   |      |      |____________________|      |
   |      |stencil 0 L         |      |      |
   |      |____________________|      |      |
   |             |stencil 1 L         |      |
   |             |____________________|      |
   |                    |stencil 2 L         |
   |                    |____________________|
   |centered (big) stencil                   |
   |_________________________________________|

Note that:

• For upwind reconstruction the right (+) cell values are [-2,-1,0,1,2 ];
• For upwind reconstruction the left (-) cell values are [-1, 0,1,2,3 ];
• For centered reconstruction the cell values are [-2,-1,0,1,2,3];

To simplify the calculation for the upwind reconstruction the cell values for the left (-) reconstruction are passed in array shifted to left with the same bounds of the right (+) values, i.e. [-2:2] or [1-S:-1+S], while for the centered reconstruction the big stencil [-2:3] or [1-S:S] is passed.

Non TBP procedures are also provided for use without class object in device backend kernels.

Source: src/lib/common/adam_weno_object.F90

Dependencies

Contents

• weno_object
• initialize
• load_from_file
• reconstruct_upwind
• initialize_centered_S1
• initialize_centered_S2
• initialize_centered_S3
• initialize_centered_S4
• initialize_upwind_S1
• initialize_upwind_S2
• initialize_upwind_S3
• initialize_upwind_S4
• initialize_upwind_S5
• compute_polynomials_upwind
• compute_weights_upwind
• weno_compute_convolution
• weno_compute_polynomials_upwind
• weno_compute_weights_upwind
• weno_reconstruct_centered
• weno_reconstruct_upwind
• description

Variables

Name	Type	Attributes	Description
S_MAX	integer(kind=I4P)	parameter	Maximum number/dimensions of stencils.
S_MAX_M1	integer(kind=I4P)	parameter	Maximum number/dimensions of stencils minus 1.
WENO_U_1	character(len=8)	parameter	Parameter of WENO scheme, upwind S=1, order 1.
WENO_U_3	character(len=8)	parameter	Parameter of WENO scheme, upwind S=2, order 3.
WENO_U_5	character(len=8)	parameter	Parameter of WENO scheme, upwind S=3, order 5.
WENO_U_7	character(len=8)	parameter	Parameter of WENO scheme, upwind S=4, order 7.
WENO_U_9	character(len=8)	parameter	Parameter of WENO scheme, upwind S=5, order 9.
WENO_C_2	character(len=8)	parameter	Parameter of WENO scheme, centered S=1, order 2.
WENO_C_4	character(len=8)	parameter	Parameter of WENO scheme, centered S=2, order 4.
WENO_C_6	character(len=8)	parameter	Parameter of WENO scheme, centered S=3, order 6.
WENO_C_8	character(len=8)	parameter	Parameter of WENO scheme, centered S=4, order 8.
INI_SECTION_NAME	character(len=4)	parameter	INI (config) file section name containing time configs.

Derived Types

weno_object

WENO class definition.

Components

Name	Type	Attributes	Description
mpih	type(mpih_object)		MPI handler.
scheme	character(len=:)	allocatable	WENO scheme.
S	integer(kind=I4P)		Stencils number/dimensions, 2S-1 order of accuracy.
is_centered	logical		Centered scheme flag.
a	real(kind=R8P)	allocatable	Optimal weights [1:2,0:S-1,1:S].
p	real(kind=R8P)	allocatable	Polinomials coefficients [1:2,0:S-1,0:S-1,1:S].
d	real(kind=R8P)	allocatable	Smoothness indicators coefficients [0:S-1,0:S-1,0:S-1,1:S].
c	real(kind=R8P)	allocatable	Centered polynomials coefficients [1-S:S,1:S].
zeps	real(kind=R8P)		Parameter for avoiding division by zero in computing IS.
sodd	integer(kind=I4P)		Branching between odd and even number of stencils (mod(S,2)).
wexp	integer(kind=I4P)		Exponent for growing the diffusive part of weights.
ror_number	integer(kind=I4P)		Number of ROR iterations.
ror_schemes	integer(kind=I4P)	allocatable	Scheme (S value) for each ROR iteration.
ror_threshold	real(kind=R8P)		ROR threshold triggering.
ror_vars_number	integer(kind=I4P)		Number of variables to check in ROR iterations.
ror_ivar	integer(kind=I4P)	allocatable	Index of each variable to check in ROR iterations.
enable_ror_stats	logical		Enable ror statistic saving.
ib_reduction_extent	integer(kind=I4P)		Extent of order reduction close to IB solids.
ib_reduced_order	integer(kind=I4P)		Reduced order (S value) close to IB solids.
ror_stats	integer(kind=I4P)	allocatable	ROR statistics.
cell_scheme	integer(kind=I4P)	allocatable	Local-cell WENO scheme: S everywhere, but modified close to solids.

Type-Bound Procedures

Name	Attributes	Description
description	pass(self)	Return pretty-printed object description.
initialize	pass(self)	Initialize class.
load_from_file	pass(self)	Load config from file.
reconstruct_upwind	pass(self)	Return WENO upwind reconstruction of 2S-1 order.
initialize_centered_S1	pass(self)	Initialize centered coefficients for S=1.
initialize_centered_S2	pass(self)	Initialize centered coefficients for S=2.
initialize_centered_S3	pass(self)	Initialize centered coefficients for S=3.
initialize_centered_S4	pass(self)	Initialize centered coefficients for S=4.
initialize_upwind_S1	pass(self)	Initialize upwind coefficients for S=1.
initialize_upwind_S2	pass(self)	Initialize upwind coefficients for S=2.
initialize_upwind_S3	pass(self)	Initialize upwind coefficients for S=3.
initialize_upwind_S4	pass(self)	Initialize upwind coefficients for S=4.
initialize_upwind_S5	pass(self)	Initialize upwind coefficients for S=5.
compute_polynomials_upwind	pass(self)	Compute WENO polynomials upwind.
compute_weights_upwind	pass(self)	Compute WENO weights.

Subroutines

initialize

Initialize class.

subroutine initialize(self, file_parameters, scheme, nb, ngc, ni, nj, nk)

Arguments

Name	Type	Intent	Attributes	Description
self	class(weno_object)	inout		WENO object.
file_parameters	type(file_ini)	in	optional	Simulation parameters ini file handler.
scheme	character(len=*)	in	optional	WENO scheme.
nb	integer(kind=I4P)	in		Total blocks number for MPI.
ngc	integer(kind=I4P)	in		Number of ghost cells.
ni	integer(kind=I4P)	in		Number of cells in i direction.
nj	integer(kind=I4P)	in		Number of cells in j direction.
nk	integer(kind=I4P)	in		Number of cells in k direction.

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load_from_file

Load config from file.

subroutine load_from_file(self, file_parameters, go_on_fail)

Arguments

Name	Type	Intent	Attributes	Description
self	class(weno_object)	inout		WENO object.
file_parameters	type(file_ini)	in		Simulation parameters ini file handler.
go_on_fail	logical	in	optional	Go on if load fails.

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reconstruct_upwind

Reconstruct by WENO upwind method of 2S-1 order.

Attributes: pure

subroutine reconstruct_upwind(self, S, v, vr)

Arguments

Name	Type	Intent	Attributes	Description
self	class(weno_object)	in		WENO object.
S	integer(kind=I4P)	in		Number of stencils used.
v	real(kind=R8P)	in		Variables to be reconstructed.
vr	real(kind=R8P)	out		Left and right (1,2) interface value of reconstructed v.

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initialize_centered_S1

Initialize coefficients for centered S=1, 2S=2th order.

subroutine initialize_centered_S1(self)

Arguments

Name	Type	Intent	Attributes	Description
self	class(weno_object)	inout		WENO object.

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initialize_centered_S2

Initialize coefficients for centered S=2, 2S=4th order.

subroutine initialize_centered_S2(self)

Arguments

Name	Type	Intent	Attributes	Description
self	class(weno_object)	inout		WENO object.

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initialize_centered_S3

Initialize coefficients for centered S=3, 2S=6th order.

subroutine initialize_centered_S3(self)

Arguments

Name	Type	Intent	Attributes	Description
self	class(weno_object)	inout		WENO object.

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initialize_centered_S4

Initialize coefficients for centered S=4, 2S=8th order.

subroutine initialize_centered_S4(self)

Arguments

Name	Type	Intent	Attributes	Description
self	class(weno_object)	inout		WENO object.

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initialize_upwind_S1

Initialize coefficients for upwind S=1.

subroutine initialize_upwind_S1(self)

Arguments

Name	Type	Intent	Attributes	Description
self	class(weno_object)	inout		WENO object.

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initialize_upwind_S2

Initialize coefficients for upwind S=2, 2S-1=3rd order.

subroutine initialize_upwind_S2(self)

Arguments

Name	Type	Intent	Attributes	Description
self	class(weno_object)	inout		WENO object.

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initialize_upwind_S3

Initialize coefficients for upwind S=3, 2S-1=5th order.

subroutine initialize_upwind_S3(self)

Arguments

Name	Type	Intent	Attributes	Description
self	class(weno_object)	inout		WENO object.

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initialize_upwind_S4

Initialize coefficients for upwind S=4, 2S-1=7th order.

subroutine initialize_upwind_S4(self)

Arguments

Name	Type	Intent	Attributes	Description
self	class(weno_object)	inout		WENO object.

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initialize_upwind_S5

Initialize coefficients for upwind S=5, 2S-1=9th order.

subroutine initialize_upwind_S5(self)

Arguments

Name	Type	Intent	Attributes	Description
self	class(weno_object)	inout		WENO object.

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compute_polynomials_upwind

Compute WENO polynomials upwind.

Attributes: pure

subroutine compute_polynomials_upwind(self, S, v, vp)

Arguments

Name	Type	Intent	Attributes	Description
self	class(weno_object)	in		WENO object.
S	integer(kind=I4P)	in		Number of stencils used.
v	real(kind=R8P)	in		Variable to be reconstructed.
vp	real(kind=R8P)	out		Polynomial reconstructions.

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compute_weights_upwind

Compute WENO weights upwind.

Attributes: pure

subroutine compute_weights_upwind(self, S, v, w)

Arguments

Name	Type	Intent	Attributes	Description
self	class(weno_object)	in		WENO object.
S	integer(kind=I4P)	in		Number of stencils used.
v	real(kind=R8P)	in		Variable to be reconstructed.
w	real(kind=R8P)	out		Weights of the stencils.

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weno_compute_convolution

Compute WENO convulution, non TBP.

Attributes: pure

subroutine weno_compute_convolution(S, vp, w, vr)

Arguments

Name	Type	Intent	Attributes	Description
S	integer(kind=I4P)	in		Number of stencils used.
vp	real(kind=R8P)	in		Polynomial reconstructions.
w	real(kind=R8P)	in		Weights of the stencils.
vr	real(kind=R8P)	out		Left and right (1,2) interface value of reconstructed v.

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weno_compute_polynomials_upwind

Compute WENO polynomials upwind, non TBP.

Attributes: pure

subroutine weno_compute_polynomials_upwind(S, weno_p, v, vp)

Arguments

Name	Type	Intent	Attributes	Description
S	integer(kind=I4P)	in		Number of stencils used.
weno_p	real(kind=R8P)	in		Polinomials coefficients.
v	real(kind=R8P)	in		Variable to be reconstructed.
vp	real(kind=R8P)	out		Polynomial reconstructions.

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weno_compute_weights_upwind

Compute WENO weights, non TBP.

Attributes: pure

subroutine weno_compute_weights_upwind(S, weno_a, weno_d, weno_zeps, v, w)

Arguments

Name	Type	Intent	Attributes	Description
S	integer(kind=I4P)	in		Number of stencils used.
weno_a	real(kind=R8P)	in		Optimal weights.
weno_d	real(kind=R8P)	in		Smoothness indicators coefficients.
weno_zeps	real(kind=R8P)	in		Parameter for avoiding division by zero in computing IS.
v	real(kind=R8P)	in		Variable to be reconstructed.
w	real(kind=R8P)	out		Weights of the stencils.

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weno_reconstruct_centered

Reconstruct by WENO centered method of 2S order, non TBP.

Attributes: pure

subroutine weno_reconstruct_centered(S, weno_a, weno_p, weno_d, weno_c, weno_zeps, v, vr)

Arguments

Name	Type	Intent	Attributes	Description
S	integer(kind=I4P)	in		Number of stencils used.
weno_a	real(kind=R8P)	in		Optimal weights.
weno_p	real(kind=R8P)	in		Polinomials coefficients.
weno_d	real(kind=R8P)	in		Smoothness indicators coefficients.
weno_c	real(kind=R8P)	in		Centered polinomials coefficients.
weno_zeps	real(kind=R8P)	in		Parameter for avoiding division by zero in computing IS.
v	real(kind=R8P)	in		Variables to be reconstructed.
vr	real(kind=R8P)	out		Left and right (1,2) interface value of reconstructed v.

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weno_reconstruct_upwind

Reconstruct by WENO upwind method of 2S-1 order, non TBP.

Attributes: pure

subroutine weno_reconstruct_upwind(S, weno_a, weno_p, weno_d, weno_zeps, v, vr)

Arguments

Name	Type	Intent	Attributes	Description
S	integer(kind=I4P)	in		Number of stencils used.
weno_a	real(kind=R8P)	in		Optimal weights.
weno_p	real(kind=R8P)	in		Polinomials coefficients.
weno_d	real(kind=R8P)	in		Smoothness indicators coefficients.
weno_zeps	real(kind=R8P)	in		Parameter for avoiding division by zero in computing IS.
v	real(kind=R8P)	in		Variables to be reconstructed.
vr	real(kind=R8P)	out		Left and right (1,2) interface value of reconstructed v.

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Functions

description

Return a pretty-formatted object description.

Attributes: pure

Returns: character(len=:)

function description(self) result(desc)

Arguments

Name	Type	Intent	Attributes	Description
self	class(weno_object)	in		WENO object.

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