Sharif Digital Repository

A modified weakly compressible smoothed particle hydrodynamics (WCSPH) is presented, which utilizes consistent discretization schemes for spatial derivatives in the flow equations. Here, each SPH particle is considered as a computational point that represents a specific part of the fluid. To overcome non-physical oscillations that usually arise in standard WCSPH, we modified the mass conservation equation by using a numerical filter. This modification is based on the difference between two discretization schemes used for the term ∇{dot operator}∇Pρ. Furthermore, a new implementation of wall boundary condition in SPH is introduced. This condition is imposed on the pressure of wall boundary... 

A new shock-detecting sensor for properly switching between a second-order and a higher-order filter is developed and assessed. The sensor is designed based on an order analysis. The nonlinear filter with the proposed sensor ensures damping of the high-frequency waves in smooth regions and at the same time removes the Gibbs oscillations around the discontinuities when using high-order compact finite difference schemes. In addition, a suitable scaling is proposed to have dissipation proportional to the shock strength and also to minimize the effects of the second-order filter on the very small scales. Several numerical experiments are carried out and the accuracy of the nonlinear filter with...