Third Order WENO Scheme on Three Dimensional Tetrahedral Meshes (Communications in Computational Physics, 2018)
We extend the weighted essentially non-oscillatory (WENO) schemes ontwo dimensional triangular meshes developed in [7] to three dimensions, and construct a third order finite volume WENO scheme on three dimensional tetrahedralmeshes. We use the Lax-Friedrichs monotone flux as building blocks, third order reconstructions made from combinations of linear polynomials which are constructed ondiversified small stencils of a tetrahedral mesh, and non-linear weights using smoothness indicators based on the derivatives of these linear polynomials. Numerical examples are given to demonstrate stability and accuracy of the scheme.