Rouhollah Fatehi

Improving the accuracy and convergence rate of the smoothed particle hydrodynamics (SPH) method is still one of the challenges that researchers are trying to achieve. In this research, the first- and second-order convergence schemes have been used for the first and second spatial derivatives, respectively, in continuity and linear momentum conservation equations to increase accuracy and convergence rate. These schemes have been implemented in the open-source code of DualSPHysics, one of the prominent and powerful software of the SPH to calculate the particle velocity and pressure of the Taylor–Green vorticity benchmark problem. Both the standard and the improved solvers were evaluated with the same numerical settings, different particle spacing, and Reynolds numbers of 100 and 1000 with the same dimensionless time. Up to three orders of magnitude improvement in the accuracy were achieved in the results of the improved solver, as well as a significant increase in convergence rate.