33 research outputs found
The DUNE-ALUGrid Module
In this paper we present the new DUNE-ALUGrid module. This module contains a
major overhaul of the sources from the ALUgrid library and the binding to the
DUNE software framework. The main changes include user defined load balancing,
parallel grid construction, and an redesign of the 2d grid which can now also
be used for parallel computations. In addition many improvements have been
introduced into the code to increase the parallel efficiency and to decrease
the memory footprint.
The original ALUGrid library is widely used within the DUNE community due to
its good parallel performance for problems requiring local adaptivity and
dynamic load balancing. Therefore, this new model will benefit a number of DUNE
users. In addition we have added features to increase the range of problems for
which the grid manager can be used, for example, introducing a 3d tetrahedral
grid using a parallel newest vertex bisection algorithm for conforming grid
refinement. In this paper we will discuss the new features, extensions to the
DUNE interface, and explain for various examples how the code is used in
parallel environments.Comment: 25 pages, 11 figure
Wrinkling of fluid deformable surfaces
Wrinkling instabilities of thin elastic sheets can be used to generate
periodic structures over a wide range of length scales. Viscosity of the thin
elastic sheet or its surrounding medium has been shown to be responsible for
dynamic processes. While this has been explored for solid as well as liquid
thin elastic sheets we here consider wrinkling of fluid deformable surfaces,
which show a solid-fluid duality and have been established as model systems for
biomembranes and cellular sheets. We use this hydrodynamic theory and
numerically explore the formation of wrinkles and their coarsening, either by a
continuous reduction of the enclosed volume or the continuous increase of the
surface area. Both lead to almost identical results for wrinkle formation and
the coarsening process, for which a universal scaling law for the wavenumber is
obtained for a broad range of surface viscosity and rate of change of volume or
area. However, for large Reynolds numbers and small changes in volume or area
wrinkling can be suppressed and surface hydrodynamics allows for global shape
changes following the minimal energy configurations of the Helfrich energy for
corresponding reduced volumes
Numerical solution of steady-state groundwater flow and solute transport problems: Discontinuous Galerkin based methods compared to the Streamline Diffusion approach
In this study, we consider the simulation of subsurface flow and solute
transport processes in the stationary limit. In the convection-dominant case,
the numerical solution of the transport problem may exhibit non-physical
diffusion and under- and overshoots. For an interior penalty discontinuous
Galerkin (DG) discretization, we present a -adaptive refinement strategy
and, alternatively, a new efficient approach for reducing numerical under- and
overshoots using a diffusive -projection. Furthermore, we illustrate an
efficient way of solving the linear system arising from the DG discretization.
In -D and -D examples, we compare the DG-based methods to the streamline
diffusion approach with respect to computing time and their ability to resolve
steep fronts
Small deformations of spherical biomembranes
In this contribution to the proceedings of the 11th Mathematical Society of
Japan (MSJ) Seasonal Institute (July 2018) we give an overview of some recent
work on a mathematical model for small deformations of a spherical membrane.
The idea is to consider perturbations to minimisers of a surface geometric
energy. The model is obtained from consideration of second order approximations
to a perturbed energy. In particular, the considered problems involve particle
constraints and surface phase field energies.Comment: Submission to the proceedings of the 11th Mathematical Society of
Japan (MSJ) Seasonal Institute (July 2018
A numerical approach for fluid deformable surfaces with conserved enclosed volume
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. We here
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 and a Lagrange
multiplier for the constraint. The considered computational examples highlight
the solid-fluid duality of fluid deformable surfaces and demonstrate
convergence properties, partly known to be optimal for different sub-problems