Numerical Simulation of Shock-Tube Piston Problems with Adaptive, Anisotropic Meshes

Numerical simulations of the flow generated inside a shock-tube by the motion of a magnetically- driven piston are carried out using a novel finite volume adaptive scheme for dynamic meshes. Local modifications of the grid topology, including the addition or deletion of grid nodes are interpreted as a series of fictitious, continuous deformations of the mesh, thus allowing mesh adaptation to be described within the Arbitrary Lagrangian Eulerian (ALE) framework. The local deformations of the mesh elements are taken into account in a conservative fashion by adding additional fictitious fluxes to the ALE formulation of the governing equations for inviscid compressible flows. The solution on the new grid is recovered without any explicit interpolation. Therefore, the method automatically guarantees the solution to be conservative by construction. This peculiar capability is here exploited in preliminary Fluid-Structure Interaction (FSI) computations of compressible shocked flows with rigid, moving bodies. Anisotropic mesh adaptation is used to improve the computational efficiency. The solution compares fairly well with the analytical one-dimensional model.