The current paper describes a rapid and impressive numerical technique to simulate the flows with multiple phases and components based upon the Shan-Chen model. The Shan-Chen model is a generalization of the incompressible Navier-Stokes equation with the variable density. The local radial basis function-generated finite difference method or local RBF-FD approach has been developed to solve the considered model. Furthermore, to get acceptable results, an extra diffusion term has been added to the density equation with a small coefficient. A reduced order technique e.g. proper orthogonal decomposition (POD) idea has been utilized to achieve a fast numerical procedure and to decrease the elapsed CPU time. The proposed numerical experiments show the ability, efficiency and acceptable results of the presented numerical scheme.

本文介绍了一种快速而令人印象深刻的数值技术，它基于Shan-Chen模型来模拟具有多个相和成分的流。Shan-Chen模型是具有可变密度的不可压缩Navier-Stokes方程的推广。已经开发了局部径向基函数生成的有限差分法或局部RBF-FD方法来求解所考虑的模型。此外，为了获得可接受的结果，将额外的扩散项以较小的系数添加到了密度方程中。降低阶数的技术（例如适当的正交分解（POD）构想）已用于实现快速数值过程并减少经过的CPU时间。所提出的数值实验表明了所提出数值方案的能力，效率和可接受的结果。