Four open boundary conditions for incompressible unbounded flows are evaluated in the framework of the Leith type third-order upwind scheme (QUICKEST scheme), and the effectiveness of each is compared by two means, namely, the difference of flows among open boundary conditions, and between short and long open boundaries. Three test problems used for the open boundary condition evaluation are the backward-facing step flow, the blunt based body flow, and the rectangular cylinder obstacle flow in a channel. The investigated open boundary conditions are (1) the one first used by Thoman and Szewczyk (1966), (2) the one proposed by Mehta and Lavan (1975), (3) the Sommerfeld radiation condition first used by Orlanski (1976), and (4) the Sommerfeld radiation condition used by Bottaro (1990) and Kobayashi et al. (1993). Orlanski proposed a method which numerically evaluates the phase speed at the closest interior points every time. Bottaro and Kobayashi et al. proposed to use the mean channel velocity as the phase speed. The author proposes the uniform inlet velocity. As a result of numerical simulations, the author's approach shows the optimum open boundary condition in comparison with the four previous methods.
Comparison of effectiveness of four open boundary conditions for incompressible unbounded flows
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