Arbitrary-Lagrangian-Eulerian One-Step WENO Finite Volume Schemes on Unstructured Triangular Meshes (Communications in Computational Physics, 2013)
In this article we present a new class of high order accurate ArbitraryEulerian-Lagrangian (ALE) one-step WENO finite volume schemes for solving nonlinear hyperbolic systems of conservation laws on moving two dimensional unstructured triangular meshes. A WENO reconstruction algorithm is used to achieve highorder accuracy in space and a high order one-step time discretization is achieved byusing the local space-time Galerkin predictor proposed in [25]. For that purpose, anew element-local weak formulation of the governing PDE is adopted on movingspace-time elements. The space-time basis and test functions are obtained considering Lagrange interpolation polynomials passing through a predefined set of nodes.Moreover, a polynomial mapping defined by the same local space-time basis functionsas the weak solution of the PDE is used to map the moving physical space-time element onto a space-time reference element. To maintain algorithmic simplicity, thefinal ALE one-step finite volume scheme uses moving triangular meshes with straightedges. This is possible in the ALE framework, which allows a local mesh velocity thatis different from the local fluid velocity. We present numerical convergence rates forthe schemes presented in this paper up to sixth order of accuracy in space and time andshow some classical numerical test problems for the two-dimensional Euler equationsof compressible gas dynamics.