Use of Jordan forms for convection-pressure split Euler solvers

Garg, NK and Maruthi, NH and Rao, SVR and Sekhar, M (2020) Use of Jordan forms for convection-pressure split Euler solvers. In: Journal of Computational Physics, 407 .

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Abstract

In this study, convection-pressure split Euler flux functions which contain weakly hyperbolic convective subsystems are analyzed. A system of first-order partial differential equations (PDEs) is said to be weakly hyperbolic if the corresponding flux Jacobian does not contain a complete set of linearly independent (LI) eigenvectors. Thus, the application of existing flux difference splitting (FDS) based schemes, which depend heavily on both eigenvalues and eigenvectors, are non-trivial to such systems. In the case of weakly hyperbolic systems, a required set of LI eigenvectors can be constructed through the addition of generalized eigenvectors by utilizing the theory of Jordan canonical forms. Once this is achieved for a weakly hyperbolic convective subsystem, an upwind solver can be constructed in the splitting framework. In the present work, the above approach is used for developing two new schemes. The first scheme is based on the Zha�Bilgen type splitting while the second is based on the Toro�Vázquez splitting. Both the schemes are tested on various benchmark problems in one-dimension (1-D) and two-dimensions (2-D). The concept of generalized eigenvectors based on Jordan forms is found to be useful in dealing with the weakly hyperbolic parts of the considered Euler systems.

Item Type:	Journal Article
Publication:	Journal of Computational Physics
Publisher:	Academic Press Inc.
Additional Information:	Copyright of this article belongs to Academic Press Inc.
Department/Centre:	Division of Mechanical Sciences > Aerospace Engineering(Formerly Aeronautical Engineering) Division of Mechanical Sciences > Civil Engineering
Date Deposited:	13 Feb 2020 10:03
Last Modified:	13 Feb 2020 10:03
URI:	http://eprints.iisc.ac.in/id/eprint/64499

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