A Projection Preconditioner for Solving the Implicit Immersed Boundary Equations

作者：Zhang Qinghai^*; Guy Robert D; Philip Bobby

来源：Numerical Mathematics: Theory, Methods and Applications , 2014, 7(4): 473-498.

DOI：10.4208/nmtma.2014.1304si

• Fluid-structure interaction
• immersed boundary method
• projection method
• preconditioning

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.

• 出版日期2014-11