Two Dimensional Finite Volume and Finite Difference Weighted Essentially Non-Oscillatory Euler Schemes/2006

ABSTRACT

Weighted Essentially Non-Oscillatory schemes are high order accurate schemes designed for problems with piecewise smooth solutions containing discontinuities. Those schemes are mainly presented in two formulations, finite difference and finite volume. The aim of this paper is to see the advantages of the finite volume over the finite difference schemes. In this paper, finite difference WENO code for Cartesian grids is modified to run for general grids and finite volume WENO code is developed. Those codes are implemented for solving one-dimensional and two dimensional Euler equations. The results obtained from each scheme are compared with each other. Three numerical examples are tested: one dimensional shock tube problem, two-dimensional supersonic channel flow and supersonic staggered wedge cascade.

 

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