High order accurate direct Arbitrary-Lagrangian-Eulerian ADER-WENO finite volume schemes on moving curvilinear unstructured meshes

摘要: Abstract In this article we present a new high order accurate fully discrete one-step Arbitrary-Lagrangian-Eulerian (ALE) finite volume scheme on moving unstructured curvilinear meshes in two and three space dimensions. The WENO reconstruction technique that is used to achieve of accuracy performed curved isoparametric triangular tetrahedral elements, which are not necessarily defined by straight boundaries. High time obtained via an element-local space-time Galerkin element predictor already developed [Boscheri W, Dumbser M. A direct arbitrary-lagrangian-eulerian ader-weno for conservative non-conservative hyperbolic systems 3d. Journal Computational Physics 2014;275(0):484–523.]. Our algorithm belongs the category cell-centered schemes, therefore nodal solver compute velocity at each vertex computational grid, as well additional degree freedom needed approximate geometry. To avoid mesh tangling or extremely distorted propose use modified version rezoning presented [Galera S, Maire P, Breil J. two-dimensional multi-material ale using vof interface reconstruction. 2010;229:5755-5787.], can deal with elements multiple rezoned geometry then taken into account directly during computation fluxes, thus resulting ALE method based conservation formulation governing PDE system. control step adopting approach, i.e. relying set basis functions desired scheme. way numerical solution configuration approximated same time. fully-discrete one single step, typical ADER approach. We apply our Euler equations compressible gas dynamics dimensions, considering classical test problems meshes. Furthermore convergence studies show proposed up fifth