Title: An Interfacial Profile-Preserving Approach for Phase Field Modeling of Incompressible Two-Phase Flows Show Chinese title

Title: 一种保持界面轮廓的相场建模方法用于不可压缩两相流动

Abstract: In this paper, we introduce an interfacial profile-preserving approach for phase field modeling for simulating incompressible two-phase flows. While the advective Cahn-Hilliard equation effectively captures the topological evolution of complex interfacial structures, it tends to displace the fluid interface from its equilibrium state, impacting simulation accuracy. To tackle this challenge, we present an interfacial profile-preserving formulation that relies on a phase-field-related signed distance function, rather than the phase field function itself. It is solved iteratively to restore the equilibrium interface profile after each time step. This approach effectively minimizes discretization errors and enhances mass conservation accuracy for each phase. Our formulation is discretized using a second-order Total Variation Diminishing (TVD) Runge-Kutta method within iterations and a finite volume scheme in spatial discretization. We quantitatively compare our present profile-preserving method with the original method in terms of accuracy and convergence rate through simulations of a deforming drop in a single vortex and a rising bubble in quiescent fluid, and further validate the applicability through simulations of a two-dimensional contracting liquid filament, a drop impacting a deep liquid pool, and three-dimensional drop deformation in shear flow. Our results exhibit good agreement with analytical solutions, prior numerical results, and experimental data, demonstrating the effectiveness and accuracy of our proposed approach. Show Chinese abstract

Abstract: 在本文中，我们引入了一种界面轮廓保持方法，用于相场建模以模拟不可压缩两相流动。 虽然对流Cahn-Hilliard方程能够有效捕捉复杂界面结构的拓扑演变，但它倾向于将流体界面从其平衡状态移开，影响模拟精度。 为了解决这一挑战，我们提出了一种基于与相场相关的有符号距离函数而非相场函数本身的界面轮廓保持公式。 它通过迭代求解，在每个时间步后恢复平衡界面轮廓。 该方法有效减少了离散化误差，并提高了各相的质量守恒精度。 我们的公式在迭代中使用二阶总变差减少（TVD）龙格-库塔方法进行离散化，并在空间离散化中使用有限体积方案。 我们通过单个涡旋中的变形液滴和静止流体中的上升气泡的模拟，定量比较了我们当前的轮廓保持方法与原始方法在准确性和收敛速度方面的表现，并通过二维收缩液丝、液滴撞击深液池以及剪切流中的三维液滴变形的模拟进一步验证了其适用性。 我们的结果与解析解、先前的数值结果和实验数据表现出良好的一致性，证明了我们所提出方法的有效性和准确性。