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A conservative finite difference method and its application for the analysis of a transient flow around a square prism. (English) Zbl 0966.76061
Summary: We present detailed results of numerical calculations of transient two-dimensional incompressible flow around and in the wake of a square prism at $\text{Re}= 100$, 200 and 500. An implicit finite difference operator-splitting method, a version of the known SIMPLEC-like method on a staggered grid, is described. The method has second-order accuracy in space, and conserves mass, momentum and kinetic energy. A new modification of the multigrid method is employed to solve the elliptic pressure problem. Calculations are performed on a sequence of spatial grids with up to $401\times 321$ grid points, at sequentially halved time steps, to ensure grid-independent results. Three types of flow are shown to exist at $\text{Re}= 500$: a steady-state unstable flow, and two flows which are transient, fully periodic and asymmetric about the centre line, but symmetric to each other. We also present discrete frequency spectra of drag and lift coefficients.

76M20Finite difference methods (fluid mechanics)
76D25Wakes and jets (viscous fluids)
76D05Navier-Stokes equations (fluid dynamics)
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