Oblique impact of a jet on a plane surface solved by SPH:suggestions to improve the results of the pressure profiles

Smoothed Particle Hydrodynamics method is well suited for simulations of un-compressible fluid systems with free surfaces or quickly varying boundary conditions A very convenient approach in the SPH framework is the one assuming a weak compressibility of the fluid: in this case the numerical solution procedure is simple and explicit. We study the case of a jet of water on an inclined rigid wall. This problem has an analytical solutions and therefore it is possible to make an accurate, comparison of the SPH results with the analytical ones. In the standard SPH implementations, it is well known that the pressure values exhibit a consistent noisy behavior, since small density variations are amplified by the large sound speed, therefore producing random pressure spikes. We propose a simple therapy that produces more regular and accurate pressure profiles. Essentially we add to the continuity equation a diffusive term, with a coefficient proportional to the sound speed, the kernel of the particles and to the particles size. This new term is analogous to the artificial viscosity that appears into the momentum equation. It is purely numerical and in the continuum limits it goes to zero and the general conservation properties of the algorithm are not changed. We find that the best results are obtained with » h cs (Wik=Wii)2 where » is an a-dimensional coefficient of the order ¼ 0:1, h is the particle smoothing length, cs is the sound speed and Wik is the kernel at the i position evaluated at the k position. We have verified the improvements is excellent in many cases. Here These comparisons testify the quality of the improvements. The computational cost of the proposed therapy is quite small since the diffusion the can be calculated at the same time level of the other spatial derivatives.