Feature/Improve the speed and accuracy of finding the ideal time step size

[camUrban]

Description

When using Movement's delta_time="optimize" flag, Ptera Software has previously attempted to find the optimal time step size that minimizes the difference in areas between the trailing-edge bound RingVortices and the wake RingVortices they shed. This works well for small Strouhal-number-experiments. However, I've noticed serious issues in finding an appropriate time step for simulations with high Strouhal numbers.

Motivation

Finding a good time step value is critical to running unsteady simulations and assessing the convergence of their simulation parameters.

Relevant Issues

None.

Changes

• Added the min_period property to Movement (along with caching and unit tests)
• Refactored Movement's private LCM methods to private functions
• Implemented _analytically_optimize_delta_time: fast analytical estimation of ideal delta_time by measuring wake displacement across a temporary Movement/UnsteadyProblem, including heuristics and warnings for low temporal resolution.
• Changed Movement.delta_time handling: default (None) now runs the analytical estimator; delta_time="optimize" runs the analytical estimator first then calls the iterative _optimize_delta_time using the analytical result as the initial guess.
• Adjusted iterative optimizer search bounds from sqrt(10) factor to +/- factor of 2.
• Separated static and dynamic delta_time optimization:
  • _optimize_delta_time now detects static vs non-static Movements and delegates to two helpers: _optimize_delta_time_static (uses scipy.optimize.minimize_scalar with early cutoff) and _optimize_delta_time_non_static (brute-force search over integer num_steps_per_lcm_cycle so delta_time cleanly divides the LCM period).
  • Added logging and warnings when the best integer step count sits on search bounds.
• Updated and expanded unit tests to cover analytical optimizer behavior, LCM functions, and adjust mocks/expectations accordingly.
• Switched from a sample-mean-based approach to using the trapezoid rule for calculating the final-cycle-mean and final-cycle-RMS loads and load coefficients. For cases where the LCM period is an integer multiple of the time step, sample-based and trapezoid-rule-based means are identical. However, this fix improves robustness if the the LCM period isn't an integer multiple of the time step.
• Updated PyCharm's "to inspect" inspection scope.

New Dependencies

None.

Change Magnitude

Moderate: Medium-sized change that adds or modifies a feature without large-scale impact.

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Checklist

• I am familiar with the current contribution guidelines.
• My branch is based on main and is up to date with the upstream main branch.
• All calculations use S.I. units.
• Code is formatted with black (line length = 88).
• Code is well documented with block comments where appropriate.
• Any external code, algorithms, or equations used have been cited in comments or docstrings.
• All new modules, classes, functions, and methods have docstrings in reStructuredText format, and are formatted using docformatter (--in-place --black). See the style guide for type hints and docstrings for more details.
• All new classes, functions, and methods in the pterasoftware package use type hints. See the style guide for type hints and docstrings for more details.
• If any major functionality was added or significantly changed, I have added or updated tests in the tests package.
• Code locally passes all tests in the tests package.
• After pushing, PR passes all automated checks (codespell, black, mypy, and tests).
• PR description links all relevant issues and follows this template.

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[codecov]

Codecov Report

❌ Patch coverage is 93.85475% with 11 lines in your changes missing coverage. Please review.
✅ Project coverage is 91.16%. Comparing base (e49d1df) to head (3116982).

Files with missing lines	Patch %	Lines
pterasoftware/movements/movement.py	93.82%	11 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main      #97      +/-   ##
==========================================
- Coverage   91.32%   91.16%   -0.16%     
==========================================
  Files          32       32              
  Lines        5818     5968     +150     
==========================================
+ Hits         5313     5441     +128     
- Misses        505      527      +22     

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