Optimized incompressible smoothed particle hydrodynamics methods and validations

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.