2013/04/17 by Michael Dumbser, Walter Boscheri, Dumbser, Michael +1 · 2 citations
Earth and Planetary Sciences · Engineering · #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Fluid Dynamics Simulations and Interactions #Numerical Analysis (math.NA) #Tropical and Extratropical Cyclones Research
paper · pdf · doi:10.48550/arxiv.1304.4816
openalex publication_date 2013/04/17 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28
In this article we present the first better than second order accurate\nunstructured Lagrangian-type one-step WENO finite volume scheme for the\nsolution of hyperbolic partial differential equations with non-conservative\nproducts. The method achieves high order of accuracy in space together with\nessentially non-oscillatory behavior using a nonlinear WENO reconstruction\noperator on unstructured triangular meshes. High order accuracy in time is\nobtained via a local Lagrangian space-time Galerkin predictor method that\nevolves the spatial reconstruction polynomials in time within each element. The\nfinal one-step finite volume scheme is derived by integration over a moving\nspace-time control volume, where the non-conservative products are treated by a\npath-conservative approach that defines the jump terms on the element\nboundaries. The entire method is formulated as an Arbitrary-Lagrangian-Eulerian\n(ALE) method, where the mesh velocity can be chosen independently of the fluid\nvelocity.\n The new scheme is applied to the full seven-equation Baer-Nunziato model of\ncompressible multi-phase flows in two space dimensions. The use of a Lagrangian\napproach allows an excellent resolution of the solid contact and the resolution\nof jumps in the volume fraction. The high order of accuracy of the scheme in\nspace and time is confirmed via a numerical convergence study. Finally, the\nproposed method is also applied to a reduced version of the compressible\nBaer-Nunziato model for the simulation of free surface water waves in moving\ndomains. In particular, the phenomenon of sloshing is studied in a moving water\ntank and comparisons with experimental data are provided.\n