Constructor function for the tdsops_t class.
'n_tds', 'delta', 'operation', 'scheme', 'bc_start', and 'bc_end' are necessary arguments. The remaining arguments are optional.
'stretch' is for obtaining the correct derivations in a stretched mesh 'stretch_correct' is for correcting the second derivative with the first
'from_to' is necessary for interpolation and staggered derivative, and it can be 'v2p' or 'p2v'. If the specific region the instance is operating is not a boundary region, then 'bc_start' and 'bc_end' are BC_HALO.
'sym' is relevant when the BC is free-slip. If sym is .true. then it means the field we operate on is assumed to be an even function (symmetric, cos type) across the boundary. If it is .false. it means the field is assumed to be an odd function (anti-symmetric, sin type).
'c_nu', 'nu0_nu' are relevant when operation is second order derivative and scheme is compact6-hyperviscous.
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| integer, | intent(in) | :: | n_tds |
Tridiagonal system size |
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| real(kind=dp), | intent(in) | :: | delta |
Grid spacing |
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| character(len=*), | intent(in) | :: | operation | |||
| character(len=*), | intent(in) | :: | scheme | |||
| integer, | intent(in) | :: | bc_start |
Boundary Cond. |
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| integer, | intent(in) | :: | bc_end |
Boundary Cond. |
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| real(kind=dp), | intent(in), | optional | :: | stretch(:) |
Stretching coefficients |
|
| real(kind=dp), | intent(in), | optional | :: | stretch_correct(:) |
Stretch correction |
|
| integer, | intent(in), | optional | :: | n_halo |
Number of halo cells |
|
| character(len=*), | intent(in), | optional | :: | from_to |
'v2p' or 'p2v' |
|
| logical, | intent(in), | optional | :: | sym |
(==npaire), only for Neumann BCs |
|
| real(kind=dp), | intent(in), | optional | :: | c_nu |
params for hypervisc. |
|
| real(kind=dp), | intent(in), | optional | :: | nu0_nu |
params for hypervisc. |
|
| real(kind=dp), | intent(in), | optional | :: | filter_alpha |
low-pass filter parameter |
return value of the function
Tridiagonal Solver Operators class.
| Type | Visibility | Attributes | Name | Initial | |||
|---|---|---|---|---|---|---|---|
| real(kind=dp), | public, | allocatable, dimension(:) | :: | dist_fw |
fw/bw phase back subs. the auxiliary factors |
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| real(kind=dp), | public, | allocatable, dimension(:) | :: | dist_bw |
fw/bw phase back subs. the auxiliary factors |
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| real(kind=dp), | public, | allocatable, dimension(:) | :: | dist_sa |
fw/bw phase back subs. the auxiliary factors |
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| real(kind=dp), | public, | allocatable, dimension(:) | :: | dist_sc |
fw/bw phase back subs. the auxiliary factors |
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| real(kind=dp), | public, | allocatable, dimension(:) | :: | dist_af |
fw/bw phase back subs. the auxiliary factors |
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| real(kind=dp), | public, | allocatable, dimension(:) | :: | thom_f | |||
| real(kind=dp), | public, | allocatable, dimension(:) | :: | thom_s | |||
| real(kind=dp), | public, | allocatable, dimension(:) | :: | thom_w | |||
| real(kind=dp), | public, | allocatable, dimension(:) | :: | thom_p | |||
| real(kind=dp), | public, | allocatable | :: | stretch(:) | |||
| real(kind=dp), | public, | allocatable | :: | stretch_correct(:) | |||
| real(kind=dp), | public, | allocatable | :: | coeffs(:) | |||
| real(kind=dp), | public, | allocatable | :: | coeffs_s(:,:) | |||
| real(kind=dp), | public, | allocatable | :: | coeffs_e(:,:) | |||
| real(kind=dp), | public | :: | alpha |
Compact scheme coeffs |
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| real(kind=dp), | public | :: | a |
Compact scheme coeffs |
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| real(kind=dp), | public | :: | b |
Compact scheme coeffs |
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| real(kind=dp), | public | :: | c | = | 0._dp |
Compact scheme coeffs |
|
| real(kind=dp), | public | :: | d | = | 0._dp |
Compact scheme coeffs |
|
| real(kind=dp), | public | :: | beta | = | 0._dp |
LHS 2nd off-diagonal (pentadiag LHS only) |
|
| real(kind=dp), | public | :: | beta_lhs_s | = | 0._dp |
j=1 backward-sub beta (0/2β Neumann, β otherwise) |
|
| logical, | public | :: | periodic | ||||
| logical, | public | :: | pentadiag | = | .false. |
.true. for pentadiagonal LHS schemes Solve with the serial Thomas algorithm instead of the distributed one. The distributed solver truncates a neighbour's influence at the subdomain edge, which is invisible for the well-conditioned derivative operators but not for the low-pass filter, whose system is only marginally diagonally dominant as alpha approaches 0.5. Thomas is serial along the line, so this is only valid when the direction is not decomposed. |
|
| logical, | public | :: | prefer_thomas | = | .false. | ||
| integer, | public | :: | n_tds |
Tridiagonal system size |
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| integer, | public | :: | n_rhs |
Right-hand-side builder size |
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| integer, | public | :: | move | = | 0 |
move between vertices and cell centres |
|
| integer, | public | :: | n_halo |
number of halo points |
| public function tdsops_init (n_tds, delta, operation, scheme, bc_start, bc_end, stretch, stretch_correct, n_halo, from_to, sym, c_nu, nu0_nu, filter_alpha) | Constructor function for the tdsops_t class. |
| procedure, public :: lowpass | |
| procedure, public :: stagder_1st | |
| procedure, public :: interpl_mid | |
| procedure, public :: deriv_2nd | |
| procedure, public :: deriv_1st | |
| procedure, public :: preprocess_thom | |
| procedure, public :: preprocess_penta_dist | |
| procedure, public :: preprocess_dist |
Directional tridiagonal solver container.
| Type | Visibility | Attributes | Name | Initial | |||
|---|---|---|---|---|---|---|---|
| class(tdsops_t), | public, | allocatable | :: | der1st | |||
| class(tdsops_t), | public, | allocatable | :: | der1st_sym | |||
| class(tdsops_t), | public, | allocatable | :: | der2nd | |||
| class(tdsops_t), | public, | allocatable | :: | der2nd_sym | |||
| class(tdsops_t), | public, | allocatable | :: | stagder_v2p | |||
| class(tdsops_t), | public, | allocatable | :: | stagder_p2v | |||
| class(tdsops_t), | public, | allocatable | :: | interpl_v2p | |||
| class(tdsops_t), | public, | allocatable | :: | interpl_p2v | |||
| class(tdsops_t), | public, | allocatable | :: | lowpass | |||
| class(tdsops_t), | public, | allocatable | :: | lowpass_sym | |||
| integer, | public | :: | dir |
Constructor function for the tdsops_t class.
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| integer, | intent(in) | :: | n_tds |
Tridiagonal system size |
||
| real(kind=dp), | intent(in) | :: | delta |
Grid spacing |
||
| character(len=*), | intent(in) | :: | operation | |||
| character(len=*), | intent(in) | :: | scheme | |||
| integer, | intent(in) | :: | bc_start |
Boundary Cond. |
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| integer, | intent(in) | :: | bc_end |
Boundary Cond. |
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| real(kind=dp), | intent(in), | optional | :: | stretch(:) |
Stretching coefficients |
|
| real(kind=dp), | intent(in), | optional | :: | stretch_correct(:) |
Stretch correction |
|
| integer, | intent(in), | optional | :: | n_halo |
Number of halo cells |
|
| character(len=*), | intent(in), | optional | :: | from_to |
'v2p' or 'p2v' |
|
| logical, | intent(in), | optional | :: | sym |
(==npaire), only for Neumann BCs |
|
| real(kind=dp), | intent(in), | optional | :: | c_nu |
params for hypervisc. |
|
| real(kind=dp), | intent(in), | optional | :: | nu0_nu |
params for hypervisc. |
|
| real(kind=dp), | intent(in), | optional | :: | filter_alpha |
low-pass filter parameter |
return value of the function
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| class(tdsops_t), | intent(inout) | :: | self | |||
| real(kind=dp), | intent(in) | :: | delta | |||
| character(len=*), | intent(in) | :: | scheme | |||
| integer, | intent(in) | :: | bc_start | |||
| integer, | intent(in) | :: | bc_end | |||
| logical, | intent(in), | optional | :: | sym |
Tridiagonal low-pass filter, matching Incompact3d's filter.
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| class(tdsops_t), | intent(inout) | :: | self | |||
| real(kind=dp), | intent(in) | :: | af |
filter parameter, -0.5 < af < 0.5 |
||
| integer, | intent(in) | :: | bc_start | |||
| integer, | intent(in) | :: | bc_end | |||
| logical, | intent(in), | optional | :: | sym |
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| class(tdsops_t), | intent(inout) | :: | self | |||
| real(kind=dp), | intent(in) | :: | delta | |||
| character(len=*), | intent(in) | :: | scheme | |||
| integer, | intent(in) | :: | bc_start | |||
| integer, | intent(in) | :: | bc_end | |||
| logical, | intent(in), | optional | :: | sym | ||
| real(kind=dp), | intent(in), | optional | :: | c_nu | ||
| real(kind=dp), | intent(in), | optional | :: | nu0_nu |
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| class(tdsops_t), | intent(inout) | :: | self | |||
| character(len=*), | intent(in) | :: | scheme | |||
| character(len=*), | intent(in) | :: | from_to | |||
| integer, | intent(in) | :: | bc_start | |||
| integer, | intent(in) | :: | bc_end | |||
| logical, | intent(in), | optional | :: | sym |
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| class(tdsops_t), | intent(inout) | :: | self | |||
| real(kind=dp), | intent(in) | :: | delta | |||
| character(len=*), | intent(in) | :: | scheme | |||
| character(len=*), | intent(in) | :: | from_to | |||
| integer, | intent(in) | :: | bc_start | |||
| integer, | intent(in) | :: | bc_end | |||
| logical, | intent(in), | optional | :: | sym |
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| class(tdsops_t), | intent(inout) | :: | self | |||
| real(kind=dp), | intent(in), | dimension(:) | :: | dist_b |
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| class(tdsops_t), | intent(inout) | :: | self | |||
| real(kind=dp), | intent(in), | dimension(:) | :: | b |
LU preprocessing for non-periodic pentadiagonal Thomas algorithm.
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| class(tdsops_t), | intent(inout) | :: | self | |||
| integer, | intent(in) | :: | bc_start | |||
| integer, | intent(in) | :: | bc_end | |||
| logical, | intent(in) | :: | symmetry |