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 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 one hand, high speed fluid flows are traditionally modeled by applying shock capturing schemes to the compressible Euler equations avoiding problems associated with tangling of a Lagrangian mesh. On the other hand, solid dynamics calculations are traditionally carried out using Lagrangian numerical methods avoiding problems associated with numerical smearing in Eulerian calculations. We use the Ghost Fluid Method (GFM) to create accurate discretizations across the Eulerian/Lagrangian interface. The numerical method is presented in both one and two spatial dimensions noting that three dimensional extensions (to the interface coupling method) are straightforward. ∗Computer Science Department, Stanford University, Stanford, California 94305 †Research supported in part by the California Institute of Technology Center for Simulation of Dynamic Response of Materials which is sponsored by the US DOE as part of the Academic Strategic Alliances Program of the Accelerated Strategic Computing Initiative (subcontract B341492 of DOE contract W-7405-ENG-48) ‡Research supported in part by ONR N00014-97-1-0027