An evolving pressure projection method for numerical computations of the weakly compressible Navier-Stokes equations is proposed. Fully explicit time integration is achieved using an independent pressure evolution equation. To damp the acoustic wave in a weakly compressible fluid flow, we iteratively compute the pressure evolution equation coupled with a projection step. Due to the simplicity and locality of this iteration procedure, it does not increase the computational amount too much. The computation is performed on a staggered Cartesian grid. By introducing the phase field model for interface capturing, this solver can be directly applied to two-phase flow simulations using a one-fluid model. Exact mass conservation is ensured by a finite-volume formulation of the conservative phase field equation. Various benchmarking problems are simulated to validate accuracy. The stability of a violent two-phase flow with large density and viscosity ratio is demonstrated in a three-dimensional dam break simulation. Numerical results show that the proposed method for weakly compressible Navier-Stokes equations can prevent oscillations of pressure and velocity.

提出了一种用于弱压缩Navier-Stokes方程数值计算的演化压力投影方法。使用独立的压力演化方程式可以实现完全明确的时间积分。为了衰减弱压缩流体中的声波，我们迭代计算了带有投影步长的压力演化方程。由于此迭代过程的简单性和局部性，因此不会过多增加计算量。该计算在交错的笛卡尔网格上执行。通过引入用于界面捕获的相场模型，该求解器可以直接用于使用单流体模型的两相流模拟。保守的相场方程的有限体积公式确保了精确的质量守恒。模拟各种基准测试问题以验证准确性。在三维溃坝模拟中证明了具有较大密度和粘度比的剧烈两相流的稳定性。数值结果表明，所提出的弱可压缩Navier-Stokes方程组方法可以防止压力和速度波动。