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 $e$ and 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 fluid 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.
Highlights
Van der Waals equation in dealing with the behavior of phase transition is very important
We use relaxation scheme to study the dynamics of liquid-vapor phase transition for a van der Waals fluids
If the initial data belongs to elliptic region, the solution converges to two Maxwell states
Summary
Van der Waals equation in dealing with the behavior of phase transition is very important. Van der Waals, relaxation scheme, conservation laws, phase transition. The authors in [13]–[14] use another kind of state of equation to theoretically and numerically study the phase transition.
Sign-in/Register to view highlights & summary 
Published Version (
Free)
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call