2020/01/28 by Friedemann Kemm, Elena Gaburro, Kemm, Friedemann +5 · 1 citation
Engineering · #Advanced Numerical Methods in Computational Mathematics #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Fluid Dynamics and Turbulent Flows #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.2001.10326
openalex publication_date 2020/01/28 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28
In this paper we propose a new diffuse interface model for the numerical\nsimulation of inviscid compressible flows around fixed and moving solid bodies\nof arbitrary shape. The solids are assumed to be moving rigid bodies, without\nany elastic properties. The model is a simplified case of the seven-equation\nBaer-Nunziato model of compressible multi-phase flows, and results in a\nnonlinear hyperbolic system with non-conservative products. The geometry of the\nsolid bodies is simply specified via a scalar field that represents the volume\nfraction of the fluid present in each control volume. This allows the\ndiscretization of arbitrarily complex geometries on simple uniform or adaptive\nCartesian meshes. Inside the solid bodies, the fluid volume fraction is zero,\nwhile it is unitary in the fluid phase. We prove that at the material\ninterface, i.e. where the volume fraction jumps from unity to zero, the normal\ncomponent of the fluid velocity assumes the value of the normal component of\nthe solid velocity. This result can be directly derived from the governing\nequations, either via Riemann invariants or from the generalized Rankine\nHugoniot conditions according to the theory of Dal Maso, Le Floch and Murat,\nwhich justifies the use of a path-conservative approach for treating the\nnonconservative products. The governing equations of our new model are solved\non uniform Cartesian grids via a high order path-conservative ADER\ndiscontinuous Galerkin (DG) method with a posteriori sub-cell finite volume\n(FV) limiter. Since the numerical method is of the shock capturing type, the\nfluid-solid boundary is never explicitly tracked by the numerical method,\nneither via interface reconstruction, nor via mesh motion. The effectiveness of\nthe proposed approach is tested on a set of numerical test problems, including\n1D Riemann problems as well as supersonic flows over fixed and moving rigid\nbodies.\n