H. Liu et al., UPWIND COMPACT METHOD AND DIRECT NUMERICAL-SIMULATION OF DRIVEN FLOW IN A SQUARE CAVITY, Science in China. Series A, Mathematics, Physics, Astronomy & Technological Sciences, 36(11), 1993, pp. 1347-1357
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.