A Numerical Framework for Fast Transient Compressible Flows Using Lattice Boltzmann and Immersed Boundary Methods

Abstract

This article is dedicated to the development of a model to simulate fast transient compressible flows on solid structures using immersed boundary method (IBM) and a lattice Boltzmann solver. Ultimately, the proposed model aims at providing an efficient algorithm to simulate strongly-coupled fluid-structure interactions (FSI). Within this goal, it is necessary to propose a precise and robust numerical framework and validate it on stationary solid cases first, which is the scope of the present study. Classical FSI methods, such as body-fitted approaches, are facing challenges with moving or complex geometries in realistic conditions, requiring computationally expensive re-meshing operations. IBM offers an alternative by treating the solid structure geometry independently from the fluid mesh. This study focuses on the extension of the IBM to compressible flows, and a particular attention is given to the enforcement of various thermal boundary conditions. A hybrid approach, combining diffuse forcing for Dirichlet-type boundary conditions and ghost-nodes forcing for Neumann-type boundary conditions is introduced. Finally, a simplified model, relying only on diffuse IBM forcing, is investigated to treat specific cases where the fluid solid interface is considered as adiabatic. The accuracy of the method is validated through various test cases of increasing complexity.