Abstract In this paper a generalized conservative phase field-lattice Boltzmann model is proposed for immiscible incompressible flows with any number of components. In this phase field model, the each phase field variable satisfies a generalized eikonal equation and the volume fraction constraint. By introducing a quadratic functional, the dynamics of phase field variables can be treated as a gradient flow method. The phase field equations are reformulated based on the mass conservative law and the reduction-consistency conditions. Moreover, based on the generalized free energy functional, a family of generalized continuous surface tension force formulations is deduced by using the virtual work method. A lattice Boltzmann model (LBM) is developed to solve the generalized conservative phase field equations and the hydrodynamics equations. In the numerical simulation section, the motion of circular interfaces and Poiseuille flow with four phases are simulated first. The convergence rate and reduction-consistent of present model for the phase field equations are validated. The computational accuracy of present model for the hydrodynamics equations is also validated. Then serval two-dimensional (2D) examples with pairwise surface tension effect, including the droplets immersed in another fluid with four fluid phases, spreading of liquid lenses and spinodal decomposition with four fluid phases, are simulated. The obtained numerical results are in good agreement with the analytical solutions. Four continuous surface tension force formulations are also comparative studied. Finally, as a practical application, a three-dimensional (3D) bubble rising in a three-layer liquid is investigated.

中文翻译：

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多分量多相流的广义保守相场模型及其格子Boltzmann格式

摘要 本文提出了一个广义保守相场-格子Boltzmann模型，用于具有任意数量分量的不混溶不可压缩流动。在这个相场模型中，每个相场变量都满足一个广义的方程和体积分数约束。通过引入二次函数，相场变量的动力学可以被视为梯度流方法。相场方程是根据质量守恒定律和归约一致性条件重新制定的。此外，基于广义自由能泛函，利用虚功法推导出了一系列广义连续表面张力公式。格子玻尔兹曼模型 (LBM) 被开发用来求解广义保守相场方程和流体动力学方程。在数值模拟部分，首先模拟了圆形界面的运动和四相泊肃叶流。验证了相场方程模型的收敛速度和约简一致性。还验证了当前流体动力学方程模型的计算精度。然后模拟了具有成对表面张力效应的多个二维 (2D) 示例，包括浸入具有四种流体相的另一种流体中的液滴、液体透镜的扩散和具有四种流体相的旋节线分解。得到的数值结果与解析解非常吻合。还比较研究了四种连续的表面张力公式。最后，作为实际应用，研究了在三层液体中上升的三维 (3D) 气泡。