2009-08-012024-05-14https://scholars.lib.ntu.edu.tw/handle/123456789/657827Abstract: In this project we are aimed to derive a mathematically rigorous kernel function, which accounts for the interaction among particles, within the framework of moving particle semi-implicit (MPS) method to predict a computationally more accurate solution for the Navier-Stokes equations investigated at low as well as high Reynolds numbers. Determination of the functional dependence of kernel function on the distance vector between particles becomes therefore a key to success of the developed interaction model. The fact that the smoothed quantity for a scalar or for a vector at a particle location is mathematically identical to its collocated value provided that the kernel function is chosen as the delta function, which is unfortunately not implementable in the discrete context. Thanks to this underlying fact, our guideline of developing the modified kernel function is to make it closer to the delta function as much as possible in cases when diffusion dominates convection.kernel functionNavier-Stokes equationsdelta functionmoving particle semi-implicit method