An improved moving-particle semi-implicit (MPS) method was developed for numerical simulations of convective heat transfer problems. The MPS method, which is based on particles and their interactions, is a fully Lagrangian particle method for incompressible flows. A new Laplacian model and a new method for treating boundary conditions were proposed to solve numerical difficulties resulting from the original MPS method. Results of several numerical tests show the validity of the improved MPS method with the proposed model and method.
The application of the present MPS method to Rayleigh–Benard convection phenomena demonstrated the effectiveness of the proposed model and method on the numerical simulation of convective heat transfer problems. The dependence of the Nusselt number on the Rayleigh number was in good agreement with an empirical formula. The temperature contour and velocity distribution also agree well with the simulation results obtained with other methods. The roll pattern developed in the horizontal fluid layer as well as the convective heat transfer was successfully simulated with three-dimensional MPS calculations. Copyright © 2005 John Wiley & Sons, Ltd.