High-order inverse Lax-Wendroff procedure for compressible fluid-structure interaction problems

Abstract

In this study, we propose a global high-order approach for fluid-structure interaction (FSI) problems involving compressible inviscid flows and deformable elastic solids. A partitioned coupling strategy is employed to solve the fluid and solid equations. The compressible Euler equations in the fluid domain are solved using a high-order finite difference weighted essentially non-oscillatory (WENO) method on fixed Cartesian Eulerian grids. In the solid domain, the linear elastodynamic equations are discretized via the Lagrangian discontinuous Galerkin (DG) finite element method on unstructured meshes. To handle the moving interface between the fluid and solid domains, we develop a high-order treatment derived from the inverse Lax-Wendroff (ILW) boundary scheme. This approach avoids the need for mesh generation and sub-iterations at each time step, simplifying implementation. Furthermore, the specialized interface treatment ensures stability in challenging cases, such as those involving light solids coupled with heavy fluids. Stability analysis for linear systems further demonstrates the robustness of the method. We validate the proposed approach through numerical tests on one- and two-dimensional problems. The results demonstrate that our method could achieve third-order accuracy for smooth solutions, handle shock induced FSI problems without oscillation, and remain stable across a wide range of material parameters.