Eigenstructure-preserving scheme for a hyperbolic system

TL;DR

This paper introduces an eigenstructure-preserving numerical scheme for hyperbolic systems that guarantees real eigenvalues at the discrete level, maintaining eigenstructure despite truncation errors, and ensures local conservation.

Contribution

The paper presents a novel scheme that preserves eigenstructure and guarantees real eigenvalues in numerical simulations of hyperbolic systems, even with discretization errors.

Findings

Always generates real eigenvalues in simulations

Maintains eigenstructure despite truncation errors

Ensures local conservation through skew-symmetric operators

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.