Abstract: Finite-volume-based shock-capturing methods can most easily be constructed on structured Cartesian meshes. Implementations of higher-order discretizations on unstructured grids, on the other hand, can be quite cumbersome. In this talk, an approach in utilizing Cartesian schemes for real-world problems will be discussed that combines the ghost-fluid idea with block-structured adaptive mesh refinement. A scalar level set function storing the distance information to the boundary surface is used to consider arbitrary moving geometries on the Cartesian mesh without ambiguities. Although the presently used boundary incorporation is of first-order accuracy, several examples from compressible gas dynamics will be presented demonstrating that the utilization of mesh adaptation makes the overall approach suitable for serious computational investigations.
The method has been implemented in the generic fluid solver framework AMROC that is part of the Virtual Test Facility (VTF) software (http://www.cacr.caltech.edu/asc). In the VTF, a temporal splitting approach is used to couple the adaptive Eulerian finite volume method to explicit Lagrangian finite element schemes for computational solid dynamics. Three-dimensional fluid-structure interaction simulations involving large plastic deformations and/or fracture and fragmentation will be shown thereby confirming the applicability of the proposed techniques to problems with heavily evolving topology. Results obtained with different solid mechanics solvers, among them the general-purpose code DYNA3D, coupled to AMROC will be compared and the parallel performance and software engineering questions will be discussed briefly. Where they are non-standard, e.g., for gas-liquid flows or detonation waves with detailed chemical kinetics, the employed finite volume schemes and numerical flux functions will be sketched.