Fluid‐structure coupling of linear elastic model with compressible flow models 
 
Authors:  Michael Herty Siegfried Müller Nils Gerhard Gaoming Xiang Bing Wang 
 
Institution:  1. Institut für Geometrie und Praktische Mathematik, RWTH Aachen University, 52056 Aachen, Germany;2. School of Aerospace Engineering, Tsinghua University, 100084 Beijing, China 
 
Abstract:  Cavitation erosion is caused in solids exposed to strong pressure waves developing in an adjacent fluid field. The knowledge of the transient distribution of stresses in the solid is important to understand the cause of damaging by comparisons with breaking points of the material. The modeling of this problem requires the coupling of the models for the fluid and the solid. For this purpose, we use a strategy based on the solution of coupled Riemann problems that has been originally developed for the coupling of 2 fluids. This concept is exemplified for the coupling of a linear elastic structure with an ideal gas. The coupling procedure relies on the solution of a nonlinear equation. Existence and uniqueness of the solution is proven. The coupling conditions are validated by means of quasi‐1D problems for which an explicit solution can be determined. For a more realistic scenario, a 2D application is considered where in a compressible single fluid, a hot gas bubble at low pressure collapses in a cold gas at high pressure near an adjacent structure. 
 
Keywords:  compressible flow coupled Riemann problem coupling conditions fluid‐structure coupling Lax curves linear elastic model 

