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- Title
NUMERICAL STUDY OF PHASE TRANSITION IN VAN DER WAALS FLUID.
- Authors
He, Qiaolin; Liu, Chang; Shi, Xiaoding
- Abstract
In this article, we use a relaxation scheme for conservation laws to study liquid-vapor phase transition modeled by the van der Waals equation, which introduces a small parameter ϵand a new variable. We solve the relaxation system in Lagrangian coordinates for one dimension and solve the system in Eulerian coordinates for two dimension. A second order TVD Runge-Kutta splitting scheme is used in time discretization and upwind or MUSCL scheme is used in space discretization. The long time behavior of the uid is numerically investigated. If the initial data belongs to elliptic region, the solution converges to two Maxwell states. When the initial data lies in metastable region, the solution either remains in the same phase or converges to the Maxwell states depending to the initial perturbation. If the initial state is in the stable region, the solution remains in that region for all time.
- Subjects
PHASE transitions; VAN der Waals forces; VAN der Waals clusters; DIFFERENTIAL equations; MATHEMATICAL models; PARTIAL differential equations
- Publication
Discrete & Continuous Dynamical Systems - Series B, 2018, Vol 23, Issue 10, p4519
- ISSN
1531-3492
- Publication type
Article
- DOI
10.3934/dcdsb.2018174