A secular equation for the Jacobian matrix of certain multispecies kinematic flow models

✍ Scribed by Rosa Donat; Pep Mulet

• Publisher: John Wiley and Sons
• Year: 2010
• Tongue: English
• Weight: 263 KB
• Volume: 26
• Category: Article
• ISSN: 0749-159X
• DOI: 10.1002/num.20423

✦ Synopsis

Abstract

Multispecies kinematic flow models lead to nonlinear systems of conservation laws with a possibly large number of unknowns, the concentrations or the densities of the different species. In recent years, the hyperbolic character of several of these models has been analyzed by considering the characteristic polynomial of the Jacobian matrix of the system. This analysis can be considerably simplified by realizing that the fluxes in these models have a particular algebraic structure that can be exploited within a systematic algebraic framework. The framework can serve to determine the eigenvalues, and even the eigenvectors, of the Jacobian matrix of the system, which allows the use of characteristic‐based high‐resolution shock capturing schemes in numerical simulations.© 2008 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2010