Numerical study of Riemann problem solutions and stability for a system of viscous conservation laws of mixed type

Document Type

Article

Publication Date

1-1-1991

Abstract

A numerical study of the isothermal fluid equations with a nonmonotone equation of state (like that of van der Waals) and with viscosity and capillarity terms is presented. This system is ill-posed (i.e., elliptic in x vs. t) in some regions of state space and well-posed (i.e., hyperbolic) in other regions. Thus, it may serve as a model for describing dynamic phase transitions. Numerical computations of phase jumps, shock waves, and rarefaction waves for this system are presented. Although the solution of the Riemann problem is not unique, all of these waves are found to be stable to infinitesimal initial perturbations. Criteria are found for instability after O(1) initial perturbations. An analytic argument is made for stability of phase transitions.

Identifier

0026172521 (Scopus)

Publication Title

SIAM Journal on Applied Mathematics

External Full Text Location

https://doi.org/10.1137/0151031

ISSN

00361399

First Page

605

Last Page

634

Issue

3

Volume

51

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