A New Revised Scheme for SPH

Based on the smoothed kernel approximation of the Smoothed Particle Hydrodynamics (SPH) method and Taylor series expansion, a new revised scheme for SPH method is proposed which significantly improves its accuracy, especially near the boundaries where the particle points do not entirely cover the compact support domain of kernel function and particles are irregularly distributed. The revised scheme is derived up to the first-and second-order derivatives both in one-dimensional and multi-dimensional cases. In order to demonstrate the ability of the proposed revised scheme, the scheme is applied to the interpolation of functions and the numerical solution of the convection–diffusion equations both in one- and two-dimensional cases.