Central Weighted ENO Schemes for Hyperbolic Conservation Laws on Fixed and Moving Unstructured Meshes

We present a novel family of arbitrary high order accurate central Weighted ENO (CWENO) finite volume schemes for the solution of nonlinear systems of hyperbolic conservation laws on fixed and moving unstructured simplex meshes in two and three space dimensions. Starting from the given cell averages of a function on a triangular or tetrahedral control volume and its neighbors, the nonlinear CWENO reconstruction yields a high order accurate and essentially nonoscillatory polynomial that is defined everywhere in the cell. Compared to other WENO schemes on unstructured meshes, the total stencil size is the minimum possible one, as in classical pointwise WENO schemes of Jiang and Shu. However, the linear weights can be chosen arbitrarily, which makes the practical implementation on general unstructured meshes particularly simple. We make use of the piecewise polynomials generated by the CWENO reconstruction operator inside the framework of fully discrete and high order accurate one-step ADER finite volume sch...

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