Coupling an Eulerian Fluid Calculation to a Lagrangian Solid Calculation with the Ghost Fluid Method

We propose a numerical method for modeling multimaterial flows where the domain is decomposed into separate Eulerian and Lagrangian subdomains. That is, the equations are written in Eulerian form in one subdomain and in Lagrangian form in the other subdomain. This is of interest, for example, when considering the effect of underwater explosions on the hull of a ship or the impact of a low speed projectile on a soft explosive target. On the one hand, high-speed fluid flows are traditionally modeled by applying shock-capturing schemes to the compressible Euler equations to avoid problems associated with tangling of a Lagrangian mesh. On the other hand, solid dynamics calculations are traditionally carried out using Lagrangian numerical methods to avoid problems associated with numerical smearing in Eulerian calculations. We use the ghost fluid method to create accurate discretizations across the Eulerian/Lagrangian interface. The numerical method is presented in both one and two spatial dimensions; three-dimensional extensions (to the interface coupling method) are straightforward.