A conservative coupling algorithm between a compressible flow and a rigid body using an Embedded Boundary method

TL;DR

This paper introduces a new explicit coupling algorithm for simulating interactions between a rigid body and unsteady compressible fluid flow using an Embedded Boundary method, ensuring conservation and stability.

Contribution

It presents a novel explicit coupling algorithm that maintains conservation laws and stability for rigid body-fluid interactions using an Embedded Boundary approach.

Findings

Ensures exact mass, momentum, and energy conservation.

Preserves uniform movement without numerical boundary roughness.

Demonstrates efficiency on 1D and 2D benchmark problems.

Abstract

This paper deals with a new solid-fluid coupling algorithm between a rigid body and an unsteady compressible fluid flow, using an Embedded Boundary method. The coupling with a rigid body is a first step towards the coupling with a Discrete Element method. The flow is computed using a Finite Volume approach on a Cartesian grid. The expression of numerical fluxes does not affect the general coupling algorithm and we use a one-step high-order scheme proposed by Daru and Tenaud [Daru V,Tenaud C., J. Comput. Phys. 2004]. The Embedded Boundary method is used to integrate the presence of a solid boundary in the fluid. The coupling algorithm is totally explicit and ensures exact mass conservation and a balance of momentum and energy between the fluid and the solid. It is shown that the scheme preserves uniform movement of both fluid and solid and introduces no numerical boundary roughness. The effciency of the method is demonstrated on challenging one- and two-dimensional benchmarks.