Consistent projection methods for variable density incompressible Navier-Stokes equations with continuous surface forces on a rectangular collocated mesh
Consistent projection methods for variable density incompressible Navier-Stokes equations with continuous surface forces on a rectangular collocated mesh
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DOI：
10.1016/j.jcp.2009.06.004
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发表时间：
2009-10
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影响因子：
--
通讯作者：
M. Ni
中科院分区：
文献类型：
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作者：
M. Ni
针对具有连续表面力的变密度纳维-斯托克斯方程，在矩形并置网格上开发了两种二阶时间和空间精度的一致投影方法。与原始投影方法（本文中表示为算法 I 和 II）不同，在原始投影方法中，根据中间速度和压力梯度更新的单元中心速度不能保证是螺线管的，一致投影方法（表示为算法 III 和 IV）基于周围单元表面上具有速度单位的保守通量的插值来获得单元中心速度。根据连续表面力的处理，算法 III 中的压力梯度或算法 IV 中的压力梯度与表面力之和在单元中心处由一致投影方法中更新的速度和中间速度之间的差值得出。对具有一系列密度比的非粘性 3D 静态液滴进行了数值模拟。使用一致的投影方法，可以大大减少杂散电流，并且可以准确捕获界面上的压力跃变，而不会出现振荡。所开发的一致投影方法还应用于模拟由表面张力驱动的初始椭圆和由浮力驱动的初始球气泡的界面演化，具有良好的精度和分辨率。
Two consistent projection methods of second-order temporal and spatial accuracy have been developed on a rectangular collocated mesh for variable density Navier–Stokes equations with a continuous surface force. Instead of the original projection methods (denoted as algorithms I and II in this paper), in which the updated cell center velocity from the intermediate velocity and the pressure gradient is not guaranteed solenoidal, the consistent projection methods (denoted as algorithms III and IV) obtain the cell center velocity based on an interpolation from a conservative fluxes with velocity unit on surrounding cell faces. Dependent on treatment of the continuous surface force, the pressure gradient in algorithm III or the sum of the pressure gradient and the surface force in algorithm IV at a cell center is then conducted from the difference between the updated velocity and the intermediate velocity in a consistent projection method. A non-viscous 3D static drop with serials of density ratios is numerically simulated. Using the consistent projection methods, the spurious currents can be greatly reduced and the pressure jump across the interface can be accurately captured without oscillations. The developed consistent projection method are also applied for simulation of interface evolution of an initial ellipse driven by the surface tension and of an initial sphere bubble driven by the buoyancy with good accuracy and good resolution.