A multi-physics algorithm for shocked viscous flows interacting with geometrically complex elastoplastic materials

We present an algorithm for the numerical simulation of compressible, shocked, viscous flows interacting with geometrically complex elastoplastic materials. A mathematical formulation is considered, where each material has its own equation of state and is governed by its own system of non-linear, inhomogeneous partial differential equations, which are solved simultaneously on the same computational mesh. To this end, we extend an existing algorithm, which was originally devised for inviscid flows interacting with elastoplastic solids, to account for viscous and heat transfer effects at material interfaces. This approach allows for the modeling of problems of interest to this work, where near-wall viscous effects are important to the external aerodynamics of the body, but which may induce a two-way dynamic and thermodynamic interaction with an elastoplastic material. In the special case of negligible two-way interaction, the algorithm reduces to an immersed interface scheme for viscous flow past rigid bodies. For both cases, we demonstrate the accuracy and robustness of the method through a wide range of multi-dimensional test problems. We demonstrate that the elastoplastic multi-physics simulations can accurately capture the external viscous fluid dynamics flow, while also being able to resolve the behavior of the substrate and interior of the geometry. For the rigid body simulations, we also highlight the differences in the solution when compared to the inviscid case. In all cases, the method operates on a single computational Cartesian mesh and integrates seamlessly with adaptive mesh refinement.