Analysis of a constant-coefficient pressure equation method for fast computations of two-phase flows at high density ratios
Analysis of a constant-coefficient pressure equation method for fast computations of two-phase flows at high density ratios
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快速计算高密度比两相流的恒系数压力方程法分析
DOI：
10.1016/j.jcp.2019.108904
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发表时间：
2019
期刊：
影响因子：
--
通讯作者：
P. Cifani
中科院分区：
文献类型：
--
作者：
P. Cifani
对用于快速模拟完全解析的不可压缩两相流的改进压力校正公式进行了分析。通过分裂密度加权压力梯度，压力方程被简化为常数系数泊松方程，可以使用高效的线性求解器。虽然加速的增益有据可查，但压力梯度的时间外推引入的误差需要进一步研究。本文表明，修正后的压力方程会导致非物理压力振荡和较大的误差。通过适当地将外推压力梯度与匹配的体积分数梯度网格相结合，可以恢复高密度比下的网格收敛。首先考虑一维前沿和平移球体的情况，从而将压力方程与动量方程解耦。随后，分析了上升流中气泡上升的情况，并求解了全套控制方程。已发现压力跃变外推误差取决于密度比和 CFL 数。最终，通过使用快速泊松解算器而实现的计算时间增益应通过减少上述误差可能需要的额外计算时间来加权。
An analysis of a modified pressure-correction formulation for fast simulations of fully resolved incompressible two-phase flows has been carried out. By splitting of the density weighted pressure gradient, the pressure equation is reduced to a constant-coefficient Poisson equation, for which efficient linear solvers can be used. While the gain in speed-up is well documented, the error introduced by the temporal extrapolation of the pressure gradient requires further investigations. In this paper it is shown that the modified pressure equation can lead to unphysical pressure oscillations and large errors. By appropriately combining the extrapolated pressure gradient with a matching volume fraction gradient grid convergence at high density ratios could be recovered. The cases of a one-dimensional front and a sphere translating at uniform velocity were first considered, allowing to decouple the pressure equation from the momentum equation. Subsequently, the case of a rising bubble in an upflow is analysed for which the full set of governing equations is solved. The pressure jump extrapolation error has been found dependent on the density ratio and the CFL number. Ultimately, the gain in the computational time, made possible by the use of fast Poisson solvers, should be weighted by the additional computational time the reduction of the aforementioned error may require.