An HLLC-Type Riemann Solver for Multi-Component Elastic Materials

Accurate simulation of high-frequency wave interactions in elastic fluid-solid systems is crucial for applications such as medical ultrasound imaging and bubble cavitation in soft tissues. Existing approaches, including ALE-based fluid-structure solvers and interface-capturing five-equation models paired with an HLL Riemann solver, either require complex algorithms or produce material-interface smearing that demands very fine meshes. In this study, we introduce a new HLLC-type approximate Riemann solver tailored to the five-equation hypoelastic model. By analyzing the hyperbolic structure of the governing equations, we derive intermediate wave speeds and states that accurately capture shocks, contact discontinuities, and shear waves with reduced numerical dissipation while preserving stability. We couple this solver with high-order WENO reconstruction and validate it against canonical cases such as fluid-solid shock interaction and acoustic wave propagation through heterogeneous elastic media.