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An Unconditionally Energy Stable Immersed Boundary Method with Application to Vesicle Dynamics

Published online by Cambridge University Press:  28 May 2015

Wei-Fan Hu  and
Ming-Chih Lai
Wei-Fan Hu*
Affiliation:
Center of Mathematical Modeling and Scientific Computing & Department of Applied Mathematics, National Chiao Tung University, 1001, Ta Hsueh Road, Hsinchu 300, Taiwan
Ming-Chih Lai*
Affiliation:
Center of Mathematical Modeling and Scientific Computing & Department of Applied Mathematics, National Chiao Tung University, 1001, Ta Hsueh Road, Hsinchu 300, Taiwan
*
Corresponding author. Email Address: weifanhu.am95g@g2.nctu.edu.tw
Corresponding author. Email Address: mclai@math.nctu.edu.tw
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Abstract

We develop an unconditionally energy stable immersed boundary method, and apply it to simulate 2D vesicle dynamics. We adopt a semi-implicit boundary forcing approach, where the stretching factor used in the forcing term can be computed from the derived evolutional equation. By using the projection method to solve the fluid equations, the pressure is decoupled and we have a symmetric positive definite system that can be solved efficiently. The method can be shown to be unconditionally stable, in the sense that the total energy is decreasing. A resulting modification benefits from this improved numerical stability, as the time step size can be significantly increased (the severe time step restriction in an explicit boundary forcing scheme is avoided). As an application, we use our scheme to simulate vesicle dynamics in Navier-Stokes flow.

Keywords

65M0676D07Immersed boundary methodunconditionally energy stableinextensible vesicleNavier-Stokes flow
Type
Research Article
Information
East Asian Journal on Applied Mathematics , Volume 3 , Issue 3 , August 2013 , pp. 247 - 262
Copyright
Copyright © Global-Science Press 2013

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