6,426 research outputs found
Stable finite element pair for Stokes problem and discrete Stokes complex on quadrilateral grids
In this paper, we first construct a nonconforming finite element pair for the
incompressible Stokes problem on quadrilateral grids, and then construct a
discrete Stokes complex associated with that finite element pair. The finite
element spaces involved consist of piecewise polynomials only, and the
divergence-free condition is imposed in a primal formulation. Combined with
some existing results, these constructions can be generated onto grids that
consist of both triangular and quadrilateral cells
Complex flow patterns at the onset of annular electroconvection in a dielectric liquid subjected to an arbitrary unipolar injection
We numerically investigated the annular electroconvection that takes place in a dielectric liquid lying between two concentric cylinder electrodes. A uniform injection of arbitrary strengths either from the inner or outer cylinder introduces free charge carriers into the system, and the resulting Coulomb force induces electroconvection. The problem is characterized by a linear instability that corresponds to the onset of flow motion. The linear stability criteria were determined from direct numerical results and by linear stability analysis, and the results obtained with the two approaches show an excellent agreement. We focused on the fully developed flow pattern in the finite amplitude regime. We observed very different flow motions that were highly dependent on the injection strength.Ministerio de Ciencia y Tecnología FIS2011-25161Junta de Andalucía P10-FQM-5735Junta de Andalucía P09-FQM-458
Boundary-Conforming Free-Surface Flow Computations: Interface Tracking for Linear, Higher-Order and Isogeometric Finite Elements
The simulation of certain flow problems requires a means for modeling a free
fluid surface; examples being viscoelastic die swell or fluid sloshing in
tanks. In a finite-element context, this type of problem can, among many other
options, be dealt with using an interface-tracking approach with the
Deforming-Spatial-Domain/Stabilized-Space-Time (DSD/SST) formulation. A
difficult issue that is connected with this type of approach is the
determination of a suitable coupling mechanism between the fluid velocity at
the boundary and the displacement of the boundary mesh nodes. In order to avoid
large mesh distortions, one goal is to keep the nodal movements as small as
possible; but of course still compliant with the no-penetration boundary
condition. Standard displacement techniques are full velocity, velocity in a
specific coordinate direction, and velocity in normal direction. In this work,
we investigate how the interface-tracking approach can be combined with
isogeometric analysis for the spatial discretization. If NURBS basis functions
of sufficient order are used for both the geometry and the solution, both a
continuous normal vector as well as the velocity are available on the entire
boundary. This circumstance allows the weak imposition of the no-penetration
boundary condition. We compare this option with an alternative that relies on
strong imposition at discrete points. Furthermore, we examine several coupling
methods between the fluid equations, boundary conditions, and equations for the
adjustment of interior control point positions.Comment: 20 pages, 16 figure
Large Eddy Simulations in Astrophysics
In this review, the methodology of large eddy simulations (LES) is introduced
and applications in astrophysics are discussed. As theoretical framework, the
scale decomposition of the dynamical equations for neutral fluids by means of
spatial filtering is explained. For cosmological applications, the filtered
equations in comoving coordinates are also presented. To obtain a closed set of
equations that can be evolved in LES, several subgrid scale models for the
interactions between numerically resolved and unresolved scales are discussed,
in particular the subgrid scale turbulence energy equation model. It is then
shown how model coefficients can be calculated, either by dynamical procedures
or, a priori, from high-resolution data. For astrophysical applications,
adaptive mesh refinement is often indispensable. It is shown that the subgrid
scale turbulence energy model allows for a particularly elegant and physically
well motivated way of preserving momentum and energy conservation in AMR
simulations. Moreover, the notion of shear-improved models for inhomogeneous
and non-stationary turbulence is introduced. Finally, applications of LES to
turbulent combustion in thermonuclear supernovae, star formation and feedback
in galaxies, and cosmological structure formation are reviewed.Comment: 64 pages, 23 figures, submitted to Living Reviews in Computational
Astrophysic
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