Mathematical base of Difference Operator of Particle Method
Provides a mathematical foundation for higher-order difference operators in MPS, addressing a gap in the literature, but the contribution is incremental.
The paper extends the Iribe-Nakaza method to higher-order difference operators for the Moving Particle Semi-implicit (MPS) method, showing it as a special case of the Discrete Differential Operators on Irregular Nodes (DDIN) framework. No concrete numerical results are provided.
Mathematical base of difference operators in Moving Particle Semi-implicit method (MPS) are not given sufficiently in contrast to Smooth Particle Hydrodynamics method (SPH). Iribe and Nakaza proposed a method to improve the accuracy of the gradient operator, and Khayyer and Gotoh gave an ingenuity also for gradient operator too. An extension to higher order difference operators of Iribe-Nakaza method is given in this paper. The proposed method is a special case of the author's method called Discrete Differential Operators on Irregular Nodes (DDIN).