New computational techniques for finite-difference Weighted Essentially Non-Oscillatory schemes and related problems

2014

High-Resolution Shock-Capturing (HRSC) schemes constitute the state of the art for computing accurate numerical approximations to the solution of many hyperbolic systems of conservation laws, especially in computational fluid dynamics. A drawback of these schemes is that most of them use the spectral decomposition of the Jacobian matrix of the system to compute the numerical approximations by local projections to characteristic fields. The numerical solutions obtained are often excellent in terms of resolution, but the computational effort needed may be too high for some problems, especially those for which the spectral information of the flux Jacobian matrix is not available or is quite di…