Projection Preconditioner for Solving the Implicit Immersed Boundary Equations

作     者：Qinghai Zhang Robert D.Guy Bobby Philip 

作者机构：Department of MathematicsUniversity of UtahSalt Lake CityUT 84112USA Department ofMathematicsUniversity of California DavisDavisCA 95616USA Oak Ridge National LaboratoryOak RidgeTN 37831USA 

出 版 物：《Numerical Mathematics(Theory,Methods and Applications)》 (高等学校计算数学学报（英文版）)

年 卷 期：2014年第7卷第4期

页      面：473-498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：supported in part by NSF-DMS grants 1160438 and 1226386 to RDG 

主　　题：Fluid-structure interaction immersed boundary method projection method preconditioning 

摘      要：This paper presents a method for solving the linear semi-implicit immersed boundary equations which avoids the severe time step restriction presented by explicit-time *** Lagrangian variables are eliminated via a Schur complement to form a purely Eulerian saddle point system,which is preconditioned by a projection operator and then solved by a Krylov subspace *** the viewpoint of projection methods,we derive an ideal preconditioner for the saddle point problem and compare the efficiency of a number of simpler preconditioners that approximate this perfect *** low Reynolds number and high stiffness,one particular projection preconditioner yields an efficiency improvement of the explicit IB method by a factor around *** speed-ups over explicit-time method are achieved for Reynolds number below *** speedup increases as the Eulerian grid size and/or the Reynolds number are further reduced.