Flow force and torque on submerged bodies in lattice-Boltzmann via momentum exchange

TL;DR

This paper introduces a generalized derivation of the momentum exchange method for calculating flow force and torque on submerged bodies in lattice Boltzmann simulations, applicable to various boundary conditions.

Contribution

It provides a boundary-condition-independent derivation of the momentum exchange method, including corrections and validation through numerical tests.

Findings

Correct formulas for static and moving bodies derived

Numerical tests confirm the accuracy of the formulas

Method applicable to various boundary condition implementations

Abstract

We present a new derivation of the momentum exchange method to compute the flow force and torque on a submerged body in lattice Boltzmann methods. Our derivation does not depend on a particular implementation of the boundary conditions at the body surface and relies on general principles. We recover some well known expressions, in some cases with slight corrections, to treat the cases of static and moving bodies. We also present some numerical tests that support the correctness of the formulas derived.