一种满足散度自由的隐式浸入边界法迭代求解格式  

Implicit divergence-free immersed boundary method based on iterations

作　　者：陈秀华 牟凯龙 赵兰浩[2] 周川 CHEN Xiu-hua;MU Kai-long;ZHAO Lan-hao;ZHOU Chuan(School of Harbor Engineering,Guangzhou Maritime University,Guangzhou 510725,China;College of Water Conservancy and Hydropower Engineering,Hohai University,Nanjing 210098,China;Guangdong Electric Power Design Institute Co.LTD,China Energy Engineering Group,Guangzhou 510663,China;Guangdong Kenuo Surveying Engineering Co.LTD,Guangzhou 510663,China)

机构地区：[1]广州航海学院航务工程学院,广州510725 [2]河海大学水利水电学院,南京210098 [3]中国能源建设集团广东省电力设计研究院有限公司,广州510663 [4]广东科诺勘测工程有限公司,广州510663

出　　处：《水动力学研究与进展（A辑）》2020年第6期775-780,共6页Chinese Journal of Hydrodynamics

基　　金：国家重点研发计划(2018YFC0407102)。

摘　　要：该文提出了一种同时满足散度自由和无滑边界条件的隐式浸入边界法迭代求解格式。首先,采用CBS算法(Characteristic-based Split scheme)对动量方程进行求解,然后构建满足散度自由的隐式浸入边界法迭代求解格式。其中,内迭代过程能够满足无滑边界条件,外迭代过程能够满足散度条件,在内迭代过程嵌入到外迭代过程时附加体积力项的计算考虑了速度增量的修正,根据更新后的附加体积力项求解压力,因此该方法能够同时满足散度自由和无滑条件。通过固壁旋转算例验证了该方法精度为1.5阶,通过圆柱绕流算例验证了该方法的精确性,通过颗粒沉降算例证明了该方法能够用于流固耦合问题的模拟。A novel implicit immersed boundary method which meets the divergence-free and no-slip conditions simultaneously is proposed. Firstly, the momentum equation is solved by the Characteristic-based Split scheme, then the iterative scheme with divergence-free properties is constructed. The inner iteration process can satisfy the no-slip boundary condition, while the outer iteration process can satisfy the divergence-free condition. The inner iteration process is embedded into the outer iteration process, so that the correction of the velocity increment is included in the calculation of the extra body force and the update of the force is incorporated into the iteration of the pressure. Therefore, the divergence-free and no-slip conditions are ensured fully at the same time. Finally, a numerical example of the rotation of a solid wall is used to verify the accuracy of the proposed method, which is about 1.5 order. The accuracy of the method is verified by the flow around a cylinder. It is proved that the method can be used to simulate the fluid structure coupling problems through the Sedimentation of particle.

关 键 词：浸入边界法 无滑条件 散度自由 隐式求解 迭代 

分 类 号：O35[理学—流体力学]