Barrett, John W. and Garcke, Harald and Nurnberg, Robert (2016) A stable numerical method for the dynamics of fluidic membranes. NUMERISCHE MATHEMATIK, 134 (4). pp. 783-822. ISSN 0029-599X, 0945-3245
Full text not available from this repository. (Request a copy)Abstract
We develop a finite element scheme to approximate the dynamics of two and three dimensional fluidic membranes in Navier-Stokes flow. Local inextensibility of the membrane is ensured by solving a tangential Navier-Stokes equation, taking surface viscosity effects of Boussinesq-Scriven type into account. In our approach the bulk and surface degrees of freedom are discretized independently, which leads to an unfitted finite element approximation of the underlying free boundary problem. Bending elastic forces resulting from an elastic membrane energy are discretized using an approximation introduced by Dziuk (Numer Math 111:55-80, 2008). The obtained numerical scheme can be shown to be stable and to have good mesh properties. Finally, the evolution of membrane shapes is studied numerically in different flow situations in two and three space dimensions. The numerical results demonstrate the robustness of the method, and it is observed that the conservation properties are fulfilled to a high precision.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | FINITE-ELEMENT DISCRETIZATION; RED-BLOOD-CELLS; WILLMORE FLOW; PARAMETRIC APPROXIMATION; LIPID VESICLES; ELASTIC FLOW; 2-PHASE FLOW; STOKES-FLOW; LEVEL SET; SURFACE; |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics > Prof. Dr. Harald Garcke |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 12 Apr 2019 07:24 |
| Last Modified: | 12 Apr 2019 07:24 |
| URI: | https://pred.uni-regensburg.de/id/eprint/3920 |
Actions (login required)
 |
View Item |
