关键词: 浸入边界法, 反馈力源项, 隐式格式, 正交网格, 运动边界

Abstract: This paper proposes a novel idea of Goldstein’s virtual boundary method which improves the calculation of the feedback forcing term and extends the applicability of this immersed boundary method. The original virtual boundary method includes the time integration of velocity deviation, therefore confining this method to time-dependent Navier-Stokes (N-S)equations with a severe limitation of time steps for the explicit scheme. In contrast, this paper calculates the feedback forcing by the sum of velocity deviation in iteration to avoid time dependent parameters. Thus, the improved method is not only suitable for the unsteady implicit scheme, but can couple with the steady solver without any time-dependent terms. To verify this improved method, this paper simulated the flow past a stationary cylinder, the inline oscillation of a cylinder in a fluid at rest, a flapping ellipse wing and a stationary sphere. All results agree well with previous numerical results, verifying the accuracy of the present method. We come to the conclusions that the feedback force is dependent on the velocity deviation during iteration, and that the present method can couple with the implicit algorithm for unsteady flows as well as the steady Navier-Stokes solver, indicating wider applicability of the present method for extensive flow problems.

Key words: immersed boundary method, feedback forcing term, implicit scheme, orthogonal grid, moving boundary