Structure-Preserving Numerical Approximations to a Non-isothermal Hydrodynamic Model of Binary Fluid Flows
Structure-Preserving Numerical Approximations to a Non-isothermal Hydrodynamic Model of Binary Fluid Flows
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DOI：
10.1007/s10915-020-01229-6
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发表时间：
2020-06
影响因子：
2.5
通讯作者：
Shouwen Sun;Jun Li;Jia Zhao;Qi Wang
中科院分区：
文献类型：
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作者：
Shouwen Sun;Jun Li;Jia Zhao;Qi Wang
本文提出了两种二阶结构保持数值格式，用于求解不可压缩二元粘性流体流动的非等温流体动力学相场模型。该方案保持了各流体相的体积、总能量和正熵产生率。采用熵平方化方法设计了两种半离散的时间数值格式，同时保持了总能量和正熵产生率。第一个方案是弱非线性的，它是使用快速傅立叶算法辅助迭代方法求解。第二个方案是线性的，其中添加了一个依赖于时间的补充变量，以保持正的熵产生率。半离散格式在交错网格上用有限差分法进行空间离散，得到两个全离散格式。网格细化进行，以确认该计划的顺序和几个数值例子，以显示流体动力学以及解决热毛细对流在不可压缩的二元粘性流体流动的流体界面附近的热效应。
We present two second order, structure-preserving numerical schemes for a newly derived thermodynamically consistent, non-isothermal hydrodynamical phase field model for incompressible binary viscous fluid flows. The schemes preserve the volume of each fluid phase, the total energy and the positive entropy production rate. The entropy quadratization approach is employed to devise the two semi-discrete numerical schemes in time, preserving both the total energy and the positive entropy production rate. The first scheme is weakly nonlinear, which is solved using iterative methods aided by fast Fourier algorithms. The second scheme is linear, in which a time-dependent supplementary variable is added to preserve the positive entropy production rate. The semi-discrete schemes are discretized in space by a finite difference method on staggered grids subsequently to yield two fully discrete schemes. Mesh refinement is carried out to confirm the order of the schemes and several numerical examples are provided to show hydrodynamic as well as thermal effects in resolving thermocapillary convection near the fluid interface in the incompressible binary viscous fluid flow.