The solution of the Poisson's equation used by the incompressible smoothed particle hydrodynamics (ISPH) methods for estimating the pressure field is expensive in CPU time. The CPU time, consumed by the inversion of the operator ∇(1/ρ∇) and the estimation of the right hand side of the Poisson's equation, increases with the number N of particles used in a purely Lagrangian framework. In this work, this default of ISPH methods is overcome by solving the Poisson's equation on a Cartesian grid. This SPH‐mesh coupling is equivalent to the particle in cell method. In a first step, in order to analyze its efficiency, the optimized version of two ISPH methods (divergence free and density invariant) is compared with the standard weakly compressible SPH method through two benchmarks of incompressible bidimensional flows characterized by the Reynolds number Re, Lamb‐Oseen vortex (10 ≤Re≤ 100) and lid‐driven cavity flow (100 ≤Re≤ 1000). In a second step, the numerical results obtained by the three SPH methods are compared to laboratory experimental data of a dam break flow in order to show the performance of the SPH‐mesh coupling in a practical and complex flow problem. As in the configuration of the experimental setup, the numerical results are obtained for a Reynolds number Re = 3.8 10⁶.

中文翻译：

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优化的不可压缩的平滑粒子流体动力学方法和验证

不可压缩的平滑粒子流体动力学（ISPH）方法用于估计压力场的泊松方程的求解在CPU时间上很昂贵。的CPU时间，由操作员∇的反转消耗（1 / ρ ∇）和泊松方程的右手侧的估计，随着数量的增加Ñ纯拉格朗日框架中使用的粒子数。在这项工作中，通过在笛卡尔网格上求解泊松方程可以克服ISPH方法的默认设置。这种SPH网格耦合等效于单元中的粒子方法。第一步，为了分析其效率，通过以雷诺数Re，Lamb为特征的不可压缩二维流的两个基准，将两种ISPH方法（无散度和密度不变）的优化版本与标准的弱可压缩SPH方法进行比较。-Oseen涡旋（10≤重新≤100）和盖驱动空腔流（100≤再≤1000）。第二步，将通过三种SPH方法获得的数值结果与溃坝水流的实验室实验数据进行比较，以显示SPH网格耦合在实际和复杂水流问题中的性能。与实验装置的配置一样，对于雷诺数Re = 3.8 10 ⁶可获得数值结果。