To increase the reliability of simulations by particle methods for incompressible viscous flow
problems, convergence studies and improvements in accuracy are considered for a fully …

To facilitate the numerical analysis of particle methods, we derive truncation error estimates
for the approximate operators in a generalized particle method. Here, a generalized particle …

Unique solvability and stability analysis is conducted for a generalized particle method for a
Poisson equation with a source term given in divergence form. The general-ized particle …

This paper considers several approximate operators used in a particle method based on a
Voronoi diagram. We introduce and study our approximate operators on gradient and …

When introducing an implicit scheme in time based on the predictor-corrector method for the
incompressible Navier–Stokes equations, we need to solve the pressure Poisson equation …

Numerical analysis of a generalized particle method is considered for convection-diffusion
equations. A generalized particle method have been introduced as a class of particle …