CONVERGENCE OF NUMERICAL-SOLUTIONS FOR 2-D FLOWS IN A CAVITY AT LARGE RE

Convergence properties of various finite-difference schemes for solving the equations of motion for recirculating flow of an incompressible fluid in a square 2-D cavity are examined at Reynolds numbers up to 10'. Stream function-vorticity forms of the governing equations are approximated by means of second-order-correct central-difference approximations and solved by means of alternating-direction-implicit iteration. The effects of grid-altering coordinate transformations, spatially nonuniforn ADI relaxation parameters, and order-correct treatments of the vorticity boundary condition on such issues as accuracy and rate of convergence are established. Differences in results occurring with upwind versus central differencing at high Reynolds numbers are explained with consideration in particular for the sizes of the secondary vortices. Formulation of the advective terms in convective, divergence, and Arakawa-conservative forms is discussed in terms of global conservation of vorticity, kinetic energy, and square vorticity. © 1979.