A Robust TVD-WENO Scheme for Conservation Laws
The ultimate goal of this article is to develop a robust and accurate numerical method for solving hyperbolic conservation laws in one and two dimensions. A hybrid numerical method, coupling a cheap fourth order total variation diminishing (TVD) scheme  for smooth region and a Robust seventh-order weighted non-oscillatory (WENO) scheme  near discontinuities, is considered. High order multi-resolution analysis is used to detect the high gradients regions of the numerical solution in order to capture the shocks with the WENO scheme, while the smooth regions are computed with fourth order total variation diminishing (TVD). For time integration, we use the third order TVD Runge-Kutta scheme. The accuracy of the resulting hybrid high order scheme is comparable with these of WENO, but with significant decrease of the CPU cost. Numerical demonstrates that the proposed scheme is comparable to the high order WENO scheme and superior to the fourth order TVD scheme. Our scheme has the added advantage of simplicity and computational efficiency. Numerical tests are presented which show the robustness and effectiveness of the proposed scheme.
Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1328098Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1649
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