A stable discretization of the lattice Boltzmann equation for simulation of incompressible two-phase flows at high density ratio
A stable discretization of the lattice Boltzmann equation for simulation of incompressible two-phase flows at high density ratio
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DOI：
10.1016/j.jcp.2004.12.001
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发表时间：
2005-06-10
影响因子：
4.1
通讯作者：
Lin, CL
中科院分区：
文献类型：
--
作者：
Lee, T;Lin, CL
本文提出了一种非理想气体格子Boltzmann方程（LBE）的稳定离散方法，用于模拟具有高密度和粘度比的不可压缩两相流。非理想气体LBE中离散强迫项的刚性会引发严重的数值不稳定性，限制了LBE方法的实际应用。使用一个适当的压力更新计划也是至关重要的LBE方法的稳定性，因为不可忽略的跨相界面的压力变化。为了处理这些问题，我们提出了一个稳定的离散方案，它假设低马赫数近似，并利用应力和潜在形式的表面张力，不可压缩变换，和一致的离散化的分子间强迫项。采用该稳定离散格式模拟了一维平流方程中的源项、静止液滴、液滴振荡以及液滴在密度比为1000的薄膜上的溅射和沉积。静止和振荡液滴的数值解与解析解包括拉普拉斯定律吻合得很好。在液滴撞击之后喷射的液体片的扩展因子的时间历程也遵循已知的扩展幂定律。(c)2004年爱思唯尔公司All rights reserved.
A stable discretization of the lattice Boltzmann equation (LBE) for non-ideal gases is presented for simulation of incompressible two-phase flows having high density and viscosity ratios. The stiffness of the discretized forcing terms in LBE for non-ideal gases is known to trigger severe numerical instability and restrict practical application of the LBE method. Use of a proper pressure updating scheme is also crucial to the stability of the LBE method because of non-negligible pressure variation across the phase interface. To deal with these issues, we propose a stable discretization scheme, which assumes the low Mach number approximation, and utilizes the stress and potential forms of the surface tension force, the incompressible transformation, and the consistent discretization of the intermolecular forcing terms. The proposed stable discretization scheme is applied to simulate 1-D advection equation with a source term, a stationary droplet, droplet oscillation and droplet splashing and deposition on a thin film at a density ratio of 1000 with varying Reynolds numbers. The numerical solutions of stationary and oscillatory droplets agree well with analytic solutions including the Laplace's law. The time history of the spread factor of the liquid sheet emitted after the droplet impact also follows the known spreading power law. (c) 2004 Elsevier Inc. All rights reserved.