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A stable numerical method for the dynamics of fluidic membranes
John W Barrett1, Harald Garcke2, Robert Nürnberg1
1Department of Mathematics, Imperial College London, London, SW7 2AZ UK.
Numerische Mathematik
|June 13, 2017
Summary
This study introduces a novel finite element method for simulating fluidic membranes in Navier-Stokes flow. The robust numerical scheme accurately captures membrane dynamics and conservation properties in 2D and 3D simulations.
Area of Science:
- Computational Fluid Dynamics (CFD)
- Numerical Analysis
- Fluid-Structure Interaction
Background:
- Accurate simulation of fluidic membranes requires robust numerical methods.
- Existing methods face challenges in handling local inextensibility and surface viscosity.
- Free boundary problems involving elastic membranes in viscous flow are computationally intensive.
Purpose of the Study:
- To develop a stable and accurate finite element scheme for fluidic membrane dynamics.
- To incorporate local inextensibility and Boussinesq-Scriven surface viscosity.
- To simulate membrane evolution in 2D and 3D Navier-Stokes flow.
Main Methods:
- Unfitted finite element approximation for independent discretization of bulk and surface degrees of freedom.
- Solution of a tangential Navier-Stokes equation to enforce local inextensibility.
- Discretization of bending elastic forces using Dziuk's approximation (2008).
Main Results:
- The developed numerical scheme is stable and exhibits good mesh properties.
- Simulations in 2D and 3D demonstrate the method's robustness in various flow situations.
- High precision in fulfilling conservation properties is observed.
Conclusions:
- The proposed finite element method provides a reliable approach for simulating fluidic membranes.
- The method effectively handles complex membrane behaviors like inextensibility and surface viscosity.
- This work offers a valuable tool for studying fluid-membrane interactions in diverse applications.
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