A Precise Calculation Method of the Gradient Operator in Numerical Computation with the MPS

Abstract

A highly precise numerical calculation method of the gradient as a differential operator in a computational method with the MPS has been proposed in this study. The method is not dependent on the particle arrangement. Gradient calculations of a linear and nonlinear function have been introduced in the proposed method to verify the numerical accuracy. The results show high accuracy on the boundary in regular grid arrangement case but on both the boundary and inside in random arrangement case. High accuracy and computational stability are also obtained when applied to the calculations of the hydrostatic pressure and free surface of water.