Numerical study of phase transition in van der Waals fluid
Numerical study of phase transition in van der Waals fluid
复制标题
DOI：
10.3934/dcdsb.2018174
复制
发表时间：
2018-06
影响因子：
1.2
通讯作者：
Q. He;Chang Liu;Xiaoding Shi
中科院分区：
文献类型：
--
作者：
Q. He;Chang Liu;Xiaoding Shi
在这篇文章中，我们使用守恒律的松弛方案来研究由货车der Waals方程模拟的液-汽相变，该方程引入了一个小参数$e$和一个新的变量。我们在一维拉格朗日坐标系下求解松弛方程组，在二维欧拉坐标系下求解松弛方程组。时间离散采用二阶TVD Runge-Kutta分裂格式，空间离散采用迎风格式或MUSCL格式。对流体的长期行为进行了数值研究。当初始数据属于椭圆区域时，解收敛于两个麦克斯韦态.当初始数据处于亚稳区时，解要么保持同相，要么收敛到麦克斯韦态，这取决于初始扰动。如果初始状态处于稳定区域，则解始终保持在该区域。
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.