A mass-conserved diffuse interface method and its application for incompressible multiphase flows with large density ratio
A mass-conserved diffuse interface method and its application for incompressible multiphase flows with large density ratio
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DOI：
10.1016/j.jcp.2015.03.005
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发表时间：
2015-06
期刊：
影响因子：
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通讯作者：
Y. Wang;C. Shu;J. Shao;Jie Wu;X. Niu
中科院分区：
文献类型：
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作者：
Y. Wang;C. Shu;J. Shao;Jie Wu;X. Niu
本文提出了一种质量守恒的扩散界面法，用于模拟大密度比二元流体的不可压缩流动。该方法在Cahn-Hilliard方程中引入质量修正项，以补偿数值扩散和模拟扩散引起的质量损失或质量增加。由于质量损失或增加是通过相界面，在每个时间步，它们的值是非常小的，以保持质量守恒，质量源或质量汇被引入并均匀分布在扩散层的体积。在均匀分布的情况下，应用质量守恒原理，解析地导出了代表质量源或质量汇的质量修正项。通过引入质量修正，采用五阶迎风格式求解修正的Cahn-Hilliard方程，得到了粘性流体的相场。通过新开发的多相格子Boltzmann通量求解器[20]模拟流场。通过对拉普拉斯定律、两气泡合并、瑞利-泰勒不稳定性和密度比为1000、粘度比为100的重力作用下气泡上升过程的数值模拟，验证了该方法的有效性。数值计算结果表明，界面形状和流动特性与文献中的解析解和基准数据吻合良好。数值结果还表明，在所有情况下考虑的质量是良好的守恒。此外，还证明了每个时间步的质量修正项大约为10 - 4 10 - 5，与序参数的大小相比，这个数字很小。
In this work a mass-conserved diffuse interface method is proposed for simulating incompressible flows of binary fluids with large density ratio. In the method, a mass correction term is introduced into the Cahn–Hilliard equation to compensate the mass losses or offset the mass increases caused by the numerical and modeling diffusion. Since the mass losses or increases are through the phase interfaces and at each time step, their values are very small, to keep mass conservation, mass sources or sinks are introduced and uniformly distributed in the volume of diffuse layer. With the uniform distribution, the mass correction term representing mass sources or sinks is derived analytically by applying mass conservation principle. By including the mass correction, the modified Cahn–Hilliard equation is solved by the fifth-order upwind scheme to capture the phase field of the bindery fluids. The flow field is simulated by the newly-developed multiphase lattice Boltzmann flux solver [20]. The proposed approach is validated by simulating the Laplace law, the merging of two bubbles, Rayleigh–Taylor instability and bubble rising under gravity with density ratio of 1000 and viscosity ratio of 100. Numerical results of interface shapes and flow properties agree well with both analytical solutions and benchmark data in the literature. Numerical results also show that the mass is well-conserved in all cases considered. In addition, it is demonstrated that the mass correction term at each time step is in the order of 10− 4∼ 10− 5, which is a small number compared with the magnitude of order parameter.