A second order fully-discrete linear energy stable scheme for a binary compressible viscous fluid model
A second order fully-discrete linear energy stable scheme for a binary compressible viscous fluid model
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DOI：
10.1016/j.jcp.2019.06.030
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发表时间：
2018-09
期刊：
影响因子：
--
通讯作者：
Xueping Zhao;Qi Wang
中科院分区：
文献类型：
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作者：
Xueping Zhao;Qi Wang
根据广义Onsager原理，给出了二元可压缩流体流动的热力学一致相场模型在交错网格上的线性二阶完全离散数值格式。水动力模型不仅具有本构方程的变分结构，而且保证了质量守恒、线性动量守恒和能量耗散。首先利用能量二次化方法将模型转化为等价形式，然后利用时间上的Crank-Nicolson方法将模型离散得到半离散偏微分方程组。半离散数值格式在时间上保持了质量守恒和能量耗散规律。然后，利用二阶有限差分法在空间交错网格上对半离散PDE系统进行离散，得到一个完全离散格式，该格式遵循离散能量耗散规律。我们证明了由完全离散格式得到的线性系统的唯一可解性。通过对二元聚合物流体中旋量分解引起的相分离和气液混合物中界面演化的网格细化和数值算例，分别说明了该格式的收敛性和应用上的实用性。
We present a linear, second order fully discrete numerical scheme on a staggered grid for a thermodynamically consistent hydrodynamic phase field model of binary compressible fluid flows, derived from the generalized Onsager Principle. The hydrodynamic model possesses not only the variational structure in its constitutive equation, but also warrants the mass, linear momentum conservation as well as energy dissipation. We first reformulate the model using the energy quadratization method into an equivalent form and then discretize the reformulated model to obtain a semidiscrete partial differential equation system using the Crank-Nicolson method in time. The semi-discrete numerical scheme preserves the mass conservation and energy dissipation law in time. Then, we discretize the semi-discrete PDE system on a staggered grid in space to arrive at a fully discrete scheme using 2nd order finite difference methods, which respects a discrete energy dissipation law. We prove the unique solvability of the linear system resulting from the fully discrete scheme. Mesh refinements and numerical examples on phase separation due to spinodal decomposition in binary polymeric fluids and interface evolution in the gas-liquid mixture are presented to show the convergence property and the usefulness of the new scheme in applications, respectively.