TY - JOUR T1 - A Projection Preconditioner for Solving the Implicit Immersed Boundary Equations JO - Numerical Mathematics: Theory, Methods and Applications VL - 4 SP - 473 EP - 498 PY - 2014 DA - 2014/07 SN - 7 DO - http://doi.org/10.4208/nmtma.2014.1304si UR - https://global-sci.org/intro/article_detail/nmtma/5885.html KW - Fluid-structure interaction, immersed boundary method, projection method, preconditioning. AB -
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.