An upwind method for genuine weakly hyperbolic systems
arXiv:1703.087511.22 citationsh-index: 26
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It provides a numerical method for simulating weakly hyperbolic systems, which are challenging due to defective eigenvectors, but the result is incremental as it extends existing upwind techniques.
The paper develops an upwind scheme (FDS-J) using Jordan canonical forms to handle genuine weakly hyperbolic systems, and demonstrates that it can accurately recognize various shocks.
In this article, we attempted to develop an upwind scheme based on Flux Difference Splitting using Jordan canonical forms to simulate genuine weakly hyperbolic systems. Theory of Jordan Canonical Forms is being used to complete defective set of linear independent eigenvectors. Proposed FDS-J scheme is capable of recognizing various shocks accurately.