Premium
A secular equation for the Jacobian matrix of certain multispecies kinematic flow models
Author(s) -
Donat Rosa,
Mulet Pep
Publication year - 2010
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.20423
Subject(s) - jacobian matrix and determinant , mathematics , eigenvalues and eigenvectors , conservation law , matrix (chemical analysis) , nonlinear system , polynomial , flow (mathematics) , kinematics , algebraic number , shock (circulatory) , mathematical analysis , algebra over a field , pure mathematics , geometry , classical mechanics , medicine , physics , materials science , quantum mechanics , composite material
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