Simulating an Elastic Ring with Bend and Twist by an Adaptive Generalized Immersed Boundary Method
作者机构：Leon H.Charney Division of CardiologyDepartment of MedicineNew York University School ofMedicine550 First AvenueNew YorkNew York 10016USA Department of Mathematical SciencesUniversity of Cincinnati839 Old Chemistry BuildingCincinnatiOhio 45221USA
出 版 物：《Communications in Computational Physics》 (计算物理通讯（英文）)
年 卷 期：2012年第12卷第7期
页 面：433-461页
核心收录：
学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学]
基 金：support from American Heart Association award 10SDG4320049 National Science Foundation awards DMS 1016554 and OCI 1047734.S.L
主 题：Immersed boundary method Kirchhoff rod theory adaptive mesh refinement
摘 要：Many problems involving the interaction of an elastic structure and a viscous fluid can be solved by the immersed boundary(IB)*** the IB approach to such problems,the elastic forces generated by the immersed structure are applied to the surrounding fluid,and the motion of the immersed structure is determined by the local motion of the ***,the IB method has been extended to treatmore general elasticity models that include both positional and rotational degrees of *** such models,force and torque must both be applied to the *** positional degrees of freedomof the immersed structuremove according to the local linear velocity of the fluid,whereas the rotational degrees of freedom move according to the local angular *** paper introduces a spatially adaptive,formally second-order accurate version of this generalized immersed boundary *** use this adaptive scheme to simulate the dynamics of an elastic ring immersed in *** describe the elasticity of the ring,we use an unconstrained version of Kirchhoff rod *** demonstrate empirically that our numerical scheme yields essentially second-order convergence rates when applied to such *** also study dynamical instabilities of such fluid-structure systems,and we compare numerical results produced by our method to classical analytic results from elastic rod theory.
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