A Calibrated Reduced-Order Force Model for Bacterial Hydrodynamics in Free Space and Near a Planar Boundary

Abstract

Accurately resolving the near-field flow generated by many swimming bacteria while retaining computational efficiency remains challenging. Stokeslet-based models with many force points can capture detailed near-field hydrodynamics but are computationally expensive. Other approaches include far-field and low-order models that use fewer points but sacrifice near-field accuracy. We introduce a reduced-order framework based on the method of regularized Stokeslets that preserves important near-field flow features while using substantially fewer force points. The method replaces the force distribution of a high-fidelity model with forces on a sparse set of points whose strengths are determined by constrained least-squares calibration to the high-fidelity velocity field of a single bacterium. The calibrated forces yield an approximation that preserves the dominant reference-flow structure while satisfying the force-free and torque-free conditions of self-propelled swimming. Principal component analysis is then used to represent the phase-dependent variation of the calibrated forces using only a few dominant modes. By fitting the corresponding modal coefficients as continuous functions of flagellar phase, the reduced-order forces can be approximated at any phase of the flagellar cycle. The framework is applied in both free space and near a no-slip planar boundary, where it preserves the dominant flow structures and captures the wall-induced redirection of the surrounding fluid. The optimized cell-body regularization parameter depends weakly on wall distance, and the remaining velocity discrepancy is concentrated primarily near the cell body. By substantially reducing the number of force points, the reduced-order model lowers both the computational cost and memory requirements of velocity-field evaluation, making large-domain simulations of multi-swimmer flow fields more practical.