AD: fix OLAF treecode near-core regularization floor and TwrInfl OpenMP data race

[luwang00]

Feature or improvement description
FVW treecode: the wake path used Tree%DistanceDirect = 2*mean(RegParam), averaged over an over-allocated array whose sentinel tail drove it negative during wake buildup, disabling the near-core direct-evaluation fallback. Replace it with a per-node maxRegParam (max eps over the cell's particles); each branch now uses distDirect = BranchFactor*radius + 2*maxRegParam so control points inside a regularization core fall back to direct evaluation. Applied to both the particle and segment trees.

TwrInflArray: make FirstWarn_TowerStrike firstprivate and ErrStat2/ErrMsg2 private in the OpenMP loop to avoid a data race.

In ui_part_nograd_11, the idRegExp mollifier (1-exp(-(r/rc)^3))/r^3 differs from 1/r^3 by <exp(-8)~3.4e-4 once r>2*rc, which is exactly the accuracy the far-field multipole already accepts at its BranchFactor*radius+2*maxRegParam floor. Treat the mollifier as 1 beyond that boundary (new PART_REG_NRAD/PART_REG_CUT3 params) so the near-field direct kernel and the far-field multipole share the same 2*rc cutoff. Since most near-field tree pairs have r>>rc, this skips exp() for the majority of evaluations, giving ~25-32 percent serial speedup on the treecode path with the output unchanged to ~1.8e-5 relative. Also caches r^2/r^3/rc^3 to drop redundant calculations; the compact-support branch is refactored identically (bit-for-bit).

Related issue, if one exists
There are several reported issues with OLAF. Unclear if this fix addresses any of them.

Impacted areas of the software
OLAF

Generative AI usage
Co-authored-by: Microsoft Copilot copilot@microsoft.com
Co-authored-by: Anthropic Claude claude@anthropic.com

Test results, if applicable
One r-test needs rebasing: ad_BAR_OLAF. Very small differences.

• r-test branch merging required

[Copilot]

Pull request overview

This PR adjusts OLAF/FVW induced-velocity computation to make near-core/direct-evaluation behavior robust during wake buildup, removes an OpenMP data race in tower-influence calculations, and optimizes the particle exponential-regularization kernel to reduce expensive exp() calls while keeping results within the stated tolerance.

Changes:

• Replace the global tree “direct-eval distance” floor (based on a mean regularization parameter) with a per-node maxRegParam floor used during traversal for both particle and segment trees.
• Fix an OpenMP data race in TwrInflArray by making loop-local state (FirstWarn_TowerStrike, ErrStat2/ErrMsg2) thread-safe.
• Optimize ui_part_nograd_11 by reusing r^2/r^3/rc^3 and skipping the exponential mollifier computation for r > 2*rc.

Reviewed changes

Copilot reviewed 4 out of 4 changed files in this pull request and generated no comments.

File	Description
modules/aerodyn/src/FVW_VortexTools.f90	Adds per-node maxRegParam and applies it in tree traversal to enforce a near-core direct-evaluation floor.
modules/aerodyn/src/FVW_Subs.f90	Restricts DEV NaN/sentinel checks to active particle ranges to avoid false negatives from preallocated tails.
modules/aerodyn/src/FVW_BiotSavart.f90	Speeds up particle exponential regularization by sharing the same 2*rc cutoff as the far-field floor and caching powers of r/rc.
modules/aerodyn/src/AeroDyn.f90	Removes an OpenMP data race in TwrInflArray via firstprivate/private scoping.

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