基于嵌入式迭代的高精度浸入边界法

针对传统浸入边界法施加边界条件精度不高的情况,将附加体积力的求解内嵌到压强泊松方程的迭代当中,提出了基于嵌入式迭代的浸入边界法.将所提出的算法应用到圆柱绕流数值模拟中,并与他人的实验值和数值解进行了对比,验证了所提算法具有较高的计算精度.分析了插值函数是导致浸入边界法高估圆柱阻力系数的原因,并对阻力系数进行了修正,修正值与采用贴体网格得到的结果非常吻合.比较了本文算法和传统算法的圆柱迎流侧驻点附近的速度矢量和圆柱周围的流线,证实了本文算法在施加边界条件方面的优越性.比较了两种算法的计算效率,迭代计算附加体积力所导致的额外耗时不显著.

An Accurate Immersed Boundary Method Based on Built-in Iterations

To improve the accuracy of traditional immersed boundary method（IBM）on applying boundary conditions, a novel iterative IBM approach in which the body force updating is embedded into the iterations of pressure Poisson＇s equation is presented. The improved accuracy of presented method is verified by the numerical results of flow past a two-dimensional circular cylinder, and by the comparison between the experimental data and numerical results from the literature. It is indicated that the smearing effect of interpolation/distribution functions is a major factor for the over-predicted drag coefficient. Taking this smearing effect into account, the corrected drag coefficients agree well with the numerical results using body-conformal grids. Moreover, the velocity vector near the upwind stagnation and the streamlines around the cylinder show further evidence of the higher accuracy of the presented method on imposing boundary conditions. Finally, the computational efficiency of the presented method is investigated, which shows that the extra computing time consumed by iteratively updated body force is insignificant.