A numerical approach for fluid deformable surfaces with conserved enclosed volume

Abstract

We consider surface finite elements and a semi-implicit time stepping scheme to simulate fluid deformable surfaces. Such surfaces are modeled by incompressible surface Navier-Stokes equations with bending forces. Here, we consider closed surfaces and enforce conservation of the enclosed volume. The numerical approach builds on higher order surface parameterizations, a Taylor-Hood element for the surface Navier-Stokes part, appropriate approximations of the geometric quantities of the surface mesh redistribution and a Lagrange multiplier for the constraint. The considered computational examples highlight the solid-fluid duality of fluid deformable surfaces and demonstrate convergence properties that are known to be optimal for different sub-problems.

References in corpus (20)

• Mechanics of active surfaces
• Theory of defect-mediated morphogenesis
• Modelling fluid deformable surfaces with an emphasis on biological interfaces
• Incompressible fluid problems on embedded surfaces: Modeling and variational formulations
• Higher-order surface FEM for incompressible Navier-Stokes flows on manifolds
• A structure-preserving parametric finite element method for surface diffusion
• Solving the incompressible surface Navier-Stokes equation by surface finite elements
• Geometrical control of active turbulence in curved topographies
• A finite element approach for vector- and tensor-valued surface PDEs
• Hydrodynamic Flows on Curved Surfaces: Spectral Numerical Methods for Radial Manifold Shapes
• Arbitrary Lagrangian--Eulerian finite element method for curved and deforming surfaces. I. General theory and application to fluid interfaces
• Numerical computations of the dynamics of fluidic membranes and vesicles
• Analysis of Finite Element Methods for Vector Laplacians on Surfaces
• A numerical approach for fluid deformable surfaces
• Finite element discretization methods for velocity-pressure and stream function formulations of surface Stokes equations
• Anomalous chained turbulence in actively driven flows on spheres
• Divergence-free tangential finite element methods for incompressible flows on surfaces
• Liquid Crystals on Deformable Surfaces
• Active Flows on Curved Surfaces
• Dune-CurvedGrid -- A Dune module for surface parametrization

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• A curvilinear surface ALE formulation for self-evolving Navier-Stokes manifolds -- General theory and analytical solutions
• A parametric finite element method for the incompressible Navier--Stokes equations on an evolving surface