论文标题
使用一般压力方程的两相不可压缩粘性流的数值模拟
Numerical simulation of two-phase incompressible viscous flows using general pressure equation
论文作者
论文摘要
通用压力方程（GPE）是toutant最近提出的一种新方法（J.Comput。Phys。，374：822-842（2018）），用于不可压缩的流量模拟。它规定了压力的泊松方程，并且比经典的人工压缩方法更好。在这里，它概括为具有可变密度和粘度的两相不可压缩的粘性流。首先，修改压力演化方程以说明密度变化。其次，提出了定制的离散化来处理具有可变粘度的粘性应力术语。此外，还包括与散装粘度有关的其他术语以稳定模拟。界面演化和表面张力效应由相位场模型与基于GPE的流动方程式处理。使用以二阶为中心的方案在交错网格上离散压力和动量方程，并使用第三阶总变化降低runge-kutta方案进行游行。模拟了二维，轴对称和三维几何形状的几个不稳定的两相问题，在中间密度和粘度比下进行了模拟，结果与其他不可压缩的求解器和/或lattice-boltzmann方法（LBM）模拟的结果很好地达成了一致。与LBM相似，提出的基于GPE的方法是完全明确的，易于并行化。尽管比LBM慢，但所需的内存要比LBM少得多。因此，它可以是模拟具有有限的内存资源的两相流的好选择。
The general pressure equation (GPE) is a new method proposed recently by Toutant (J. Comput. Phys., 374:822-842 (2018)) for incompressible flow simulation. It circumvents the Poisson equation for the pressure and performs better than the classical artificial compressibility method. Here it is generalized for two-phase incompressible viscous flows with variable density and viscosity. First, the pressure evolution equation is modified to account for the density variation. Second, customized discretizations are proposed to deal with the viscous stress terms with variable viscosity. Besides, additional terms related to the bulk viscosity are included to stabilize the simulation. The interface evolution and surface tension effects are handled by a phase-field model coupled with the GPE-based flow equations. The pressure and momentum equations are discretized on a stagger grid using the second order centered scheme and marched in time using the third order total variation diminishing Runge-Kutta scheme. Several unsteady two-phase problems in two dimensional, axisymmetric and three dimensional geometries at intermediate density and viscosity ratios were simulated and the results agreed well with those obtained by other incompressible solvers and/or the lattice-Boltzmann method (LBM) simulations. Similar to the LBM, the proposed GPE-based method is fully explicit and easy to be parallelized. Although slower than the LBM, it requires much less memory than the LBM. Thus, it can be a good alternative to simulate two-phase flows with limited memory resource.
