Improved procedure for the computation of Lamb's coefficients in the Physalis method for particle simulation

TL;DR

This paper presents an improved, faster, and more memory-efficient procedure for computing Lamb's coefficients in the Physalis method, enhancing particle flow simulations with better conservation properties.

Contribution

It introduces a scalar product-based approach for calculating Lamb's coefficients, replacing the SVD method, with comparable accuracy and improved computational efficiency.

Findings

The new method is significantly faster than the original SVD-based approach.

It requires less memory while maintaining accuracy.

The approach effectively conserves fluid angular momentum in rotating particle cases.

Abstract

The Physalis method is suitable for the simulation of flows with suspended spherical particles. It differs from standard immersed boundary methods due to the use of a local spectral representation of the solution in the neighborhood of each particle, which is used to bridge the gap between the particle surface and the underlying fixed Cartesian grid. This analytic solution involves coefficients which are determined by matching with the finite-difference solution farther away from the particle. In the original implementation of the method this step was executed by solving an over-determined linear system via the singular-value decomposition. Here a more efficient method to achieve the same end is described. The basic idea is to use scalar products of the finite-difference solutions with spherical harmonic functions taken over a spherical surface concentric with the particle. The new approach is tested on a number of examples and is found to posses a comparable accuracy to the original one, but to be significantly faster and to require less memory. An unusual test case that we describe demonstrates the accuracy with which the method conserves the fluid angular momentum in the case of a rotating particle.