A novel solver for simulation of flows from continuum regime to rarefied regime at moderate Knudsen number

•It is the first time to present this new flow solver.•The new solver combines good features of discrete velocity method, gas kinetic flux solver and moment method.•It avoids solving a coupled and complicated set of partial differential equations for high order moments.•The solver is much more simple and stable than the conventional moment method.•It can simulate flows from continuum regime to rarefied regime at moderate Knudsen number.