Abstract We develop a two-phase flow model for solving the nonlinear level set (LS) equation and Navier-Stokes equations in two dimension. In the proposed one-step LS method, the sharp interface is captured by implicitly representing the zero LS contour. The nonlinear LS equation is solved by upwinding Combined Compact Difference (CCD) scheme for the convection terms and center difference scheme for the other terms in space for predicting propagation of interface. Within the framework of Navier-Stokes solver, the semi-implicit Gear algorithm on a semi-staggered fixed grid is used for velocity-pressure coupling. The interface normal and curvature are calculated in terms of a hyperbolic tangent profile across the interface. To verify the proposed LS method, we consider reversed single vortex and Zalesak’s cases which are amenable to exact solutions. The proposed two-phase model is also investigated by solving the dam-break, Rayleigh-Taylor instability and bubble rising problems.

中文翻译：

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不可压缩界面流动的一步水平集数值研究

摘要 我们开发了一个用于求解二维非线性水平集 (LS) 方程和 Navier-Stokes 方程的两相流模型。在提出的一步 LS 方法中，通过隐式表示零 LS 轮廓来捕获锐利的界面。非线性 LS 方程通过对流项的迎风组合紧致差分 (CCD) 方案和空间中其他项的中心差分方案求解，以预测界面的传播。在 Navier-Stokes 求解器框架内，采用半交错固定网格上的半隐式 Gear 算法进行速度-压力耦合。界面法线和曲率是根据跨界面的双曲正切剖面计算的。为了验证所提出的 LS 方法，我们考虑了适用于精确解的反向单涡流和 Zalesak 的情况。