Smoothed Particles Hydrodynamics – the implementations of the incompressibility

The Smoothed Particle Hydrodynamics (SPH) is a fully Lagrangian, grid-free technique for fluid-flow simulations. An important and open issue in the SPH is a proper implementation of the incompressibility constraint. Generally there are two ways to deal with this problem. The first Weakly Compressible SPH (WCSPH) is the most widespread technique. It involves governing equations closed by a suitably-chosen equation of state. The second, Truly Incompressible SPH (ISPH), utilizes Projection Method – the technique known from the grid methods. The purpose of the present study is quantitative comparison of both techniques. The Smoothed Particle Hydrodynamics (SPH) is a fully Lagrangian, grid-free technique for fluid-flow simulations. An important and open issue in the SPH is a proper implementation of the incompressibility constraint. Generally there are two ways to deal with this problem. The first Weakly Compressible SPH (WCSPH) is the most widespread technique. It involves governing equations closed by a suitably-chosen equation of state. The second, Truly Incompressible SPH (ISPH), utilizes Projection Method – the technique known from the grid methods. The purpose of the present study is quantitative comparison of both techniques.