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Volume 3, Issue 3
An Unconditionally Energy Stable Immersed Boundary Method with Application to Vesicle Dynamics

Wei-Fan Hu & Ming-Chih Lai

East Asian J. Appl. Math., 3 (2013), pp. 247-262.

Published online: 2018-02

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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.

  • AMS Subject Headings

65M06, 76D07

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{EAJAM-3-247, author = {Wei-Fan Hu and Ming-Chih Lai}, title = {An Unconditionally Energy Stable Immersed Boundary Method with Application to Vesicle Dynamics}, journal = {East Asian Journal on Applied Mathematics}, year = {2018}, volume = {3}, number = {3}, pages = {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.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.250713.150813a}, url = {http://global-sci.org/intro/article_detail/eajam/10857.html} }
TY - JOUR T1 - An Unconditionally Energy Stable Immersed Boundary Method with Application to Vesicle Dynamics AU - Wei-Fan Hu & Ming-Chih Lai JO - East Asian Journal on Applied Mathematics VL - 3 SP - 247 EP - 262 PY - 2018 DA - 2018/02 SN - 3 DO - http://doi.org/10.4208/eajam.250713.150813a UR - https://global-sci.org/intro/article_detail/eajam/10857.html KW - Immersed boundary method, unconditionally energy stable, inextensible vesicle, Navier-Stokes flow. AB -

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.

Wei-Fan Hu and Ming-Chih Lai. (2018). An Unconditionally Energy Stable Immersed Boundary Method with Application to Vesicle Dynamics. East Asian Journal on Applied Mathematics. 3 (3). 247-262. doi:10.4208/eajam.250713.150813a
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