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Calculation of two-dimensional shear-driven cavity flows at high Reynolds numbers. (English) Zbl 0753.76116
Summary: The time-dependent Navier-Stokes equations are numerically integrated for two-dimensional incompressible viscous flow in a shear-driven square cavity. Using a time-splitting method and finite differences on a staggered mesh, the momentum and pressure equations are directly solved by a tensor product method where one finite difference direction is diagonalized by eigenvalue decomposition. The effects of increasing Reynolds number are studied and the developing boundary layer is captured by using a finely clustered mesh. At $$Re=30 000$$ the flow is in a continuously developing unsteady regime. Power spectrum plots indicate that the unsteady flow oscillates with one fundamental frequency and exhibits some characteristics of transition between laminar and turbulent states.

MSC:
 76M20 Finite difference methods applied to problems in fluid mechanics 76D05 Navier-Stokes equations for incompressible viscous fluids
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