Research and improvement on the accuracy of discontinuous smoothed particle hydrodynamics (DSPH) method

Discontinuous smoothed particle hydrodynamics (DSPH) method based on traditional SPH method, which can be used to simulate discontinuous physics problems near interface or boundary. Previous works showed that DSPH method has a good application prospect [Xu et al, 2013], but further verification and improvement are demanded. In this paper, we investigate the accuracy of DSPH method by some numerical models. Moreover, to improve the accuracy of D-SPH method, first order and second order multidimensional RDSPH methods are proposed by following the idea of restoring particle consistency in SPH (RSPH) method which has shown good results in the improvement of particle consistency and accuracy for non-uniform particles. This restoring particle consistency in DSPH (RDSPH) method has the advantages from both RSPH method and D-SPH method. In addition, the accuracy of RDSPH methods near the interface, boundary and in non-uniform interior region are tested in one-dimensional and twodimensional spaces.