Two improved schemes for local solution reconstruction at the cell interface in discrete velocity method (DVM) are presented for simulation of flows in all flow regimes. Numerical results show that both the conventional DVM and the improved schemes can provide accurate prediction for rarefied flows, while in the continuum flow regime, the solution accuracy of two improved schemes is better than that of the conventional DVM. As far as the computational efficiency is concerned, the conventional DVM is better than the improved schemes.

A hybrid approach to couple finite difference method (FDM) with finite particle method (FPM) (ie, FDM-FPM) is developed to simulate viscous incompressible flows. The upper figure shows the computational model and pressure coefficients for the simulations of flows around an airfoil at Re 10 000, whereas the lower figure shows the vorticity field ω(H/g)_1/2 and kinetic energy for simulations of standing waves at Re = 50, respectively. The results show that FDM-FPM leverages the advantages of FDM in high efficiency with multiple resolutions and FPM in modeling free surfaces.

1. A 3D pure Lagrangian scheme for the ideal MHD equations is proposed on unstructured meshes.
2. We use a staggered discretization which the fluid velocity is located at the nodes while other variables are defined at the cell centers. We apply the classical subcell force method to MHD equations to compatibly construct the scheme and in which the artificial viscosity is based on Riemann solvers at the nodes. Besides, the magnetic divergence constraint is satisfied by projection method.
3. The scheme is capable to handle some stringent test problems, like 2D MHD rotor test and 2D and 3D MHD blast tests, and the results of these problems are comparable to those calculated by Eulerian or ALE schemes, which validate the accuracy and robustness of our scheme.