A novel approach to rigid spheroid models in viscous flows using operator splitting methods

TL;DR

This paper introduces a second-order symmetric operator splitting method for simulating rigid spheroidal particles in viscous flows, improving accuracy and stability over traditional methods especially in stiff and perturbed systems.

Contribution

The paper develops and analyzes a novel operator splitting approach for rigid spheroid models in viscous flows, demonstrating enhanced accuracy and stability in challenging regimes.

Findings

Splitting method significantly improves solution accuracy for perturbed systems.

Method retains stability in stiff regimes where conventional methods fail.

Global error behavior varies with system stiffness, from d7h^2/d7 in non-stiff to d7h in stiff regimes.

Abstract

Calculating cost-effective solutions to particle dynamics in viscous flows is an important problem in many areas of industry and nature. We implement a second-order symmetric splitting method on the governing equations for a rigid spheroidal particle model with torques, drag and gravity. The method splits the operators into a vector field that is conservative and one that takes into account the forces of the fluid. Error analysis and numerical tests are performed on perturbed and stiff particle-fluid systems. For the perturbed case, the splitting method greatly improves the solution accuracy, when compared to a conventional multi-step method, and the global error behaves as $\mathcal{O}(\varepsilon h^2)$ for roughly equal computational cost. For stiff systems, we show that the splitting method retains stability in regimes where conventional methods blow up. In addition, we show through numerical experiments that the global order is reduced from $\mathcal{O}(h^2/\varepsilon)$ in the non-stiff regime to $\mathcal{O}(h)$ in the stiff regime.