Frictwork fix #21
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Frictwork fix #21
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Backscatter code using the equivalent barotropic (EBT) mode documented in Yankovsky et al. (2024).
- Separate FrictWork and FrictWork_bh loops - Simplified the computation for MEKE%mom_src and MEKE%mom_src_bh when MEKE%backscatter_Ro_c /= 0. (cherry picked from commit 8ffc6a8)
Modifications to MOM_hor_visc:
This patch modifies the calculation of `src_btm_drag` to avoid
additional division operations.
We first note the following variable renames:
* `Isfac` is now `damping`, since it describes the net damping or
reduction of any damped fields. `sfac` has been removed since it no
longer appears in the expressions.
* `ldamping` is now `damp_rate`. This is primarily to avoid confusion
with `damping`, but also to more accurately describe its role.
* `ldamping_Strang1` is replaced to `damp_rate_s1`. It is used for a
similar purpose (cacheing of values from the first stage) but now
holds a slightly different value.
The following modifications were made.
1. The conditional split of `sdt` into `sdt_damping` substeps is
quantified by a new term, `damp_step` which is equal to 0.5 or 1.
`sdt_damp` is computed as `sdt * damp_step`.
The presence of `sdt_damp / sdt` in our expressions is replaced with
`damp_step`, which avoids an extra division.
2. The first expression (using new notation) was originally
sfac = 1 + sdt_damp * damp_rate
D = M * (1 - sfac) / (sdt * sfac)
where `D` is `src_btm_drag` and `M` is `MEKE_current(i,j)`
This has been transformed to
D = - M * (sdt_damp * damp_rate)
/ (sdt * (1 + sdt_damp * damp_rate))
= - M * (sdt_damp / sft) * damp_rate
* (1 / (1 + sdt_damp * damp_rate))
= - M * damp_step * damp_rate * damping
This new expression for `D` no longer requires a division.
3. In the second stage expression for `src_btm_drag`, we again use
`damp_rate` to replace `ldamping`. We also use `damp_rate1` to
denote the original value of `ldaming_Strang1`.
sfac = (1 + sdt_damp * damp_rate1) * (1 + sdt_damp * damp_rate)
D = M * (1 - sfac) / (sdt * sfac)
Using `damping1` to denote the damping from the first stage, `D` can
be transformed as follows.
D = -M * (sdt_damp * damp_rate + sdt_damp * damp_rate1
+ sdt_damp**2 * damp_rate * damp_rate1)
/ (sdt * (1 + sdt_damp * damp_rate) * (1 + sdt_damp * damp_rate1))
= -M * (sdt_damp / sdt) * (1 / (1 + sdt_damp * damp_rate))
* (damp_rate + damp_rate1 + sdt_damp * damp_rate * damp_rate1)
/ (1 + sdt_damp * damp_rate1)
= -M * damp_step * damping
* (damp_rate * (1 + sdt_damp * damp_rate1) + damp_rate1)
/ (1 + sdt_damp * damp_rate1)
= -M * damp_step * damping * (damp_rate + damp_rate1 * damping1)
We now store `damp_rate1 * damping1` in `damp_rate_s1(:,:)` rather
than just `damping1`, and can reduce this expression to
D = -M * damp_step * damping * (damp_rate + damp_rate_s1(i,j))
which requires no division. It also requires no additional
read or writes.
Assuming there are no mistakes here, this should only cause negligible
bitwise differences in the results.
Also, comments have been added which explain that we cannot modify the
existing expressions for `MEKE%MEKE`, since they would alter the bitwise
results of existing runs.
In the second stage of Strang splitting, there is a check for `sdt > sdt_damping`, following a check for nonzero `KH` or `K4`. However, `sdt_damp` can only be less than `sdt` when these are nonzero. Otherwise, `sdt_damping` equals `sdt`. Best as I can tell, this check is unnecessary and potentially problematic for optimization. This patch removes the redundant check.
MEKE: No-division implementation of src_btm_drag
(TODO: Explain changes here) * `visc_limit_h_flag` was redefined as a mask, rather than a flag, and we multiply it by FrictWork to apply the mask. TODO: * Rename `visc_limit_h_flag` to `visc_limit_h_mask` * Verify parentheses of expressions, eliminate conflicts.
marshallward
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