8,940 research outputs found
XFEM based fictitious domain method for linear elasticity model with crack
Reduction of computational cost of solutions is a key issue to crack
identification or crack propagation problems. One of the solution is to avoid
re-meshing the domain when the crack position changes or when the crack
extends. To avoid re-meshing, we propose a new finite element approach for the
numerical simulation of discontinuities of displacements generated by cracks
inside elastic media. The approach is based on a fictitious domain method
originally developed for Dirichlet conditions for the Poisson problem and for
the Stokes problem, which is adapted to the Neumann boundary conditions of
crack problems. The crack is represented by level-set functions. Numerical
tests are made with a mixed formulation to emphasize the accuracy of the
method, as well as its robustness with respect to the geometry enforced by a
stabilization technique. In particular an inf-sup condition is theoretically
proven for the latter. A realistic simulation with a uniformly pressurized
fracture inside a volcano is given for illustrating the applicability of the
method.Comment: 27 pages, 15 figure
A local projection stabilized method for fictitious domains
In this work a local projection stabilization method is proposed to solve a
fictitious domain problem. The method adds a suitable fluctuation term to the
formulation thus rendering the natural space for the Lagrange multiplier
stable. Stability and convergence are proved and these results are illustrated
by a numerical experiment.Comment: Submitted Preprin
A CutFEM method for two-phase flow problems
In this article, we present a cut finite element method for two-phase
Navier-Stokes flows. The main feature of the method is the formulation of a
unified continuous interior penalty stabilisation approach for, on the one
hand, stabilising advection and the pressure-velocity coupling and, on the
other hand, stabilising the cut region. The accuracy of the algorithm is
enhanced by the development of extended fictitious domains to guarantee a well
defined velocity from previous time steps in the current geometry. Finally, the
robustness of the moving-interface algorithm is further improved by the
introduction of a curvature smoothing technique that reduces spurious
velocities. The algorithm is shown to perform remarkably well for low capillary
number flows, and is a first step towards flexible and robust CutFEM algorithms
for the simulation of microfluidic devices
Combining Boundary-Conforming Finite Element Meshes on Moving Domains Using a Sliding Mesh Approach
For most finite element simulations, boundary-conforming meshes have
significant advantages in terms of accuracy or efficiency. This is particularly
true for complex domains. However, with increased complexity of the domain,
generating a boundary-conforming mesh becomes more difficult and time
consuming. One might therefore decide to resort to an approach where individual
boundary-conforming meshes are pieced together in a modular fashion to form a
larger domain. This paper presents a stabilized finite element formulation for
fluid and temperature equations on sliding meshes. It couples the solution
fields of multiple subdomains whose boundaries slide along each other on common
interfaces. Thus, the method allows to use highly tuned boundary-conforming
meshes for each subdomain that are only coupled at the overlapping boundary
interfaces. In contrast to standard overlapping or fictitious domain methods
the coupling is broken down to few interfaces with reduced geometric dimension.
The formulation consists of the following key ingredients: the coupling of the
solution fields on the overlapping surfaces is imposed weakly using a
stabilized version of Nitsche's method. It ensures mass and energy conservation
at the common interfaces. Additionally, we allow to impose weak Dirichlet
boundary conditions at the non-overlapping parts of the interfaces. We present
a detailed numerical study for the resulting stabilized formulation. It shows
optimal convergence behavior for both Newtonian and generalized Newtonian
material models. Simulations of flow of plastic melt inside single-screw as
well as twin-screw extruders demonstrate the applicability of the method to
complex and relevant industrial applications
Simulation of cell movement through evolving environment: a fictitious domain approach
A numerical method for simulating the movement of unicellular organisms which respond to chemical signals is presented. Cells are modelled as objects of finite size while the extracellular space is described by reaction-diffusion partial differential equations. This modular simulation allows the implementation of different models at the different scales encountered in cell biology and couples them in one single framework. The global computational cost is contained thanks to the use of the fictitious domain method for finite elements, allowing the efficient solve of partial differential equations in moving domains. Finally, a mixed formulation is adopted in order to better monitor the flux of chemicals, specifically at the interface between the cells and the extracellular domain
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