An upwind method for genuine weakly hyperbolic systems
Naveen Kumar Garg, Michael Junk, S.V. Raghurama Rao, M. Sekhar
TL;DR
This paper introduces an upwind numerical scheme based on Flux Difference Splitting and Jordan canonical forms to effectively simulate genuine weakly hyperbolic systems, accurately capturing shocks.
Contribution
It develops a novel FDS-J scheme utilizing Jordan canonical forms to handle defective eigenvector sets in weakly hyperbolic systems.
Findings
Accurately captures various shocks in weakly hyperbolic systems
Uses Jordan canonical forms to address eigenvector deficiencies
Demonstrates effectiveness of the proposed scheme
Abstract
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.
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Taxonomy
TopicsComputational Fluid Dynamics and Aerodynamics · Numerical methods for differential equations · Fluid Dynamics and Turbulent Flows