A Projection Preconditioner for Solving the Implicit Immersed Boundary Equations. Issue 4 (9th August 2018)

• Record Type: Journal Article
• Authors: Zhang, Qinghai; Guy, Robert D.; Philip, Bobby
• Is Part Of: Numerical mathematics. Volume 7:Issue 4(2014)
• Page Start: 473
• Page End: 498
• Publication Date: 2018-08-09
• Subjects: 65M55, -- 65F08, -- 76M20, -- 76D99; Fluid-structure interaction, -- immersed boundary method, -- projection method, -- preconditioning; Numerical analysis -- Periodicals; Numerical analysis; Periodicals; 518.05
• DOI: 10.1017/S100489790000129X
• Languages: English
• ISSNs: 1004-8979

Abstract

Abstract: 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 methods. The 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 method. From 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 one. For low Reynolds number and high stiffness, one particular projection preconditioner yields an efficiency improvement of the explicit IB method by a factor around thirty. Substantial speed-ups over explicit-time method are achieved for Reynolds number below 100. This speedup increases as the Eulerian grid size and/or the Reynolds number are further reduced.