A Secular Equation for the Jacobian Matrix of Certain Multispecies Kinematic Flow Models

作者：Donat Rosa; Mulet Pep^*

来源：Numerical Methods for Partial Differential Equations, 2010, 26(1): 159-175.

DOI：10.1002/num.20423

• secular equation
• kinematic flows
• conservation laws

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 niatrix of the systern. This analysis call be considerably simplified by realizing that the flLlXeS in these models have a particular algebraic structure than 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.

• 出版日期2010-1