Weighted Essentially Non-oscillatory Schemes on Triangular Meshes

In this paper we construct high-order weighted essentially non-oscillatory schemes on two-dimensional unstructured meshes (triangles) in the finite volume formulation. We present third-order schemes using a combination of linear polynomials and fourth-order schemes using a combination of quadratic polynomials. Numerical examples are shown to demonstrate the accuracies and robustness of the methods for shock calculations.