Year: 2013
East Asian Journal on Applied Mathematics, Vol. 3 (2013), Iss. 3 : pp. 247–262
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.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/eajam.250713.150813a
East Asian Journal on Applied Mathematics, Vol. 3 (2013), Iss. 3 : pp. 247–262
Published online: 2013-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 16
Keywords: Immersed boundary method unconditionally energy stable inextensible vesicle Navier-Stokes flow.
-
Simulation of a Soap Film Möbius Strip Transformation
Kim, Yongsam | Lai, Ming-Chih | Seol, YunchangEast Asian Journal on Applied Mathematics, Vol. 7 (2017), Iss. 3 P.615
https://doi.org/10.4208/eajam.070217.120617a [Citations: 1] -
Arbitrarily high-order unconditionally energy stable SAV schemes for gradient flow models
Gong, Yuezheng | Zhao, Jia | Wang, QiComputer Physics Communications, Vol. 249 (2020), Iss. P.107033
https://doi.org/10.1016/j.cpc.2019.107033 [Citations: 42] -
Unconditionally Energy Stable Schemes for the Inextensible Interface Problem with Bending
Lai, Ming-Chih | Ong, Kian ChuanSIAM Journal on Scientific Computing, Vol. 41 (2019), Iss. 4 P.B649
https://doi.org/10.1137/18M1210277 [Citations: 6] -
A second-order stable explicit interface advancing scheme for FSI with both rigid and elastic structures and its application to fish swimming simulations
Liu, Jie
Computers & Fluids, Vol. 118 (2015), Iss. P.274
https://doi.org/10.1016/j.compfluid.2015.06.002 [Citations: 2] -
An Energy Stable Immersed Boundary Method for Deformable Membrane Problem with Non-uniform Density and Viscosity
Wang, Qinghe | Pan, Mingyang | Tseng, Yu-Hau | He, DongdongJournal of Scientific Computing, Vol. 94 (2023), Iss. 2
https://doi.org/10.1007/s10915-022-02092-3 [Citations: 0] -
Arbitrarily high-order linear energy stable schemes for gradient flow models
Gong, Yuezheng | Zhao, Jia | Wang, QiJournal of Computational Physics, Vol. 419 (2020), Iss. P.109610
https://doi.org/10.1016/j.jcp.2020.109610 [Citations: 58]