Showing papers by "Walter Boscheri published in 2019"

Central WENO Subcell Finite Volume Limiters for ADER Discontinuous Galerkin Schemes on Fixed and Moving Unstructured Meshes

Abstract: We present a novel a posteriori subcell finite volume limiter for high order discontinuous Galerkin (DG) finite element schemes for the solution of nonlinear hyperbolic PDE systems in multiple space dimensions on fixed and moving unstructured simplex meshes. The numerical method belongs to the family of high order fully discrete one-step ADER-DG schemes [12, 45] and makes use of an element-local spacetime Galerkin finite element predictor. Our limiter is based on the MOOD paradigm, in which the discrete solution of the high order DG scheme is checked a posteriori against a set of physical and numerical admissibility criteria, in order to detect spurious oscillations or unphysical solutions and in order to identify the so-called troubled cells. Within the detected troubled cells the discrete solution is then discarded and recomputed locally with a more robust finite volume method on a fine subgrid. In this work, we propose for the first time to use a high order ADER-CWENO finite volume scheme as subcell finite volume limiter on unstructured simplex meshes, instead of a classical second order TVD scheme. Our new numerical scheme has been developed both for fixed Eulerian meshes as well as for moving Lagrangian grids. It has been carefully validated against a set of typical benchmark problems for the compressible Euler equations of gas dynamics and for the equations of ideal magnetohydrodynamics (MHD). AMS subject classifications: 65Mxx, 65Zxx

FORCE schemes on moving unstructured meshes for hyperbolic systems

Abstract: The aim of this paper is to propose a new simple and robust numerical flux of the centered type in the context of Arbitrary-Lagrangian–Eulerian (ALE) finite volume schemes. The work relies on the FORCE flux of Toro and Billet and is concerned with the solution of general hyperbolic systems of nonlinear equations involving both conservative and non-conservative terms as well as sources which might become stiff. The proposed approach is formulated in a general way using a path-conservative method and the Roe-type system matrix is computed numerically in order to provide a numerical flux function that can be applied to any given hyperbolic system. Furthermore, one great advantage of the FORCE flux is that no information about the eigenstructure of the system is needed, not even eigenvalues, but only information regarding the geometry of the control volumes are required, which are automatically available in the moving mesh framework. Our method is of the finite volume type, high order accurate in space, thanks to a WENO reconstruction operator, and even in time, due to a fully-discrete ADER one-step discretization. The algorithm applies to moving multidimensional unstructured meshes composed by triangles and tetrahedra. Both accuracy and robustness of the scheme are assessed on a series of test problems for the Euler equations of compressible gas dynamics, for the magnetohydrodynamics equations as well as for the Baer–Nunziato model of compressible multi-phase flows.