一种适合迭代求解的反馈力浸入边界法

Feedback forcing immersed boundary method for iterative calculations

对Goldstein提出的反馈力浸入边界法进行了新的思考,改进了其对力源项的计算,拓展了该浸入边界法的使用范围。传统的反馈力浸入边界法在进行力源项的计算时,含有对速度误差的时间积分项,只能用于含时间项的Navier-Stokes(N-S)方程的求解,且在显式时间推进时有严格的时间步长限制。本文改进的方法则直接通过迭代过程中的速度误差求和来计算力源项,避免了时间相关的参数,使其不仅能适合非定常隐式时间推进,还能与不含时间项的定常NS方程求解方法结合。为了验证改进方法的可靠性,对二维静止圆柱绕流、静止流体中的振荡圆柱、运动椭圆翼以及三维静止圆球的流场进行了计算,计算结果均与文献结果符合较好,表明本文改进的方法是有效的。得出的结论为:可以直接基于迭代次数进行反馈力源项的计算,改进的反馈力浸入边界法不仅可与非定常N-S方程结合,进行隐式求解,还可以与定常N-S方程结合用于定常流动的模拟,可将改进的方法运用到更多的流动问题当中。

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.