Numerical simulation of fluid-structure interaction using modified Ghost Fluid Method and Naviers equations

In this work, we deal with the 1D compressible fluid coupled with elastic solid in an Eulerian-Lagrangian system. To facilitate the analysis, the Naviers equation for elastic solid is cast into a 2x2 system similar to the Euler equation but in Lagrangian coordinate. The modified Ghost Fluid Method is employed to treat the fluid-elastic solid coupling, where an Eulerian-Lagrangian Riemann problem is defined and a nonlinear characteristic from the fluid and a Riemann invariant from the solid are used to predict and define the ghost fluid states. Theoretical analysis shows that the present approach is accurate in the sense of approximating the solution of the Riemann problem at the interface. Numerical validation of this approach is also accomplished by extensive comparison to 1D problems (both water-solid and gas-solid) with their respective analytical solutions.