Mathematical interpretation of moving particle semi-implicit method

Abstract

This paper seeks to reformulate moving particle semi-implicit method (MPS) in order to provide a mathematical interpretation of the method. It is shown that gradient and Laplace operators are evaluated by using volume integral of the Taylor series expansion of a target function and that the form of the volume integral evaluation of the differential operators is similar to MPS, suggesting that the volume integral evaluation is a mathematical interpretation of MPS. Numerical experiments using one-dimensional setting indicate a possibility of improving the accuracy of computing the differential operators when the reformulated MPS is used. Remarks on directions towards improving the accuracy of MPS are made.