Eigenstructure-preserving scheme for a hyperbolic system

Takashi Shiroto; Akinobu Matsuyama; Nobuyuki Aiba

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arXiv · 1906.07320

Eigenstructure-preserving scheme for a hyperbolic system

Takashi Shiroto·Akinobu Matsuyama·Nobuyuki Aiba

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Abstract

A hyperbolic system must have a set of linearly independent eigenvectors and corresponding real eigenvalues. In numerical simulations, however, the eigenvalues can be complex because truncation errors pollute a characteristic polynomial of the hyperbolic system. Here we propose an eigenstructure-preserving scheme which always generates the real eigenvalues, even in discrete level. Although the eigenstructure is discussed in a non-conservative formulation, the proposed scheme is locally conservative owing to the skew-symmetric operators.

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Takashi Shiroto, Akinobu Matsuyama, Nobuyuki Aiba. 2019-06-18. Eigenstructure-preserving scheme for a hyperbolic system. https://arxiv.org/abs/1906.07320

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