UPWIND COMPACT METHOD AND DIRECT NUMERICAL-SIMULATION OF DRIVEN FLOW IN A SQUARE CAVITY

A high-order accurate finite-difference scheme, the upwind compact met hod, is proposed. The 2-D unsteady incompressible Navier-Stokes equati ons are solved in primitive variables. The nonlinear convection terms in the governing equations are approximated by using upwind biased com pact difference, and other spatial derivative terms are discretized by using the fourth-order compact difference. The upwind compact method is used to solve the driven flow in a square cavity. Solutions are obt ained for Reynolds numbers as high as 10000. When Re less than or equa l to 5000, the results agree well with those in literature. When Re = 7500 and Re = 10000, there is no convergence to a steady laminar solut ion, and the flow becomes unsteady and periodic.