Efficient Finite Difference WENO Scheme for Hyperbolic Systems with Non-conservative Products

Higher order finite difference Weighted Essentially Non-Oscillatory (WENO) schemes have been constructed for conservation laws. For multidimensional problems, they offer high accuracy at a fraction of the cost volume WENO or DG scheme comparable accuracy. This makes them quite attractive several science and engineering applications. But, to best our knowledge, such not extended non-linear hyperbolic systems with non-conservative products. In this paper, we perform an extension which improves domain applicability schemes. The is carried out by writing in fluctuation form. We use HLLI Riemann solver Dumbser Balsara (2016) as building block carrying extension. Because HLL block, resulting has proper supersonic limit. anti-diffusive fluxes ensures that stationary discontinuities can be preserved scheme, thus expanding its applicability. Our new formulation uses same reconstruction was used classical versions, making it very easy users transition over present formulation. laws, shown well version WENO, two major advantages:- 1) It capture jumps linearly degenerate wave families exactly. 2) only requires applied once. Several examples from PDE products are indicate works achieves design smooth flows. Stringent ... *Abstract truncated, see PDF*