913 research outputs found
Immersed boundary methods for numerical simulation of confined fluid and plasma turbulence in complex geometries: a review
Immersed boundary methods for computing confined fluid and plasma flows in
complex geometries are reviewed. The mathematical principle of the volume
penalization technique is described and simple examples for imposing Dirichlet
and Neumann boundary conditions in one dimension are given. Applications for
fluid and plasma turbulence in two and three space dimensions illustrate the
applicability and the efficiency of the method in computing flows in complex
geometries, for example in toroidal geometries with asymmetric poloidal
cross-sections.Comment: in Journal of Plasma Physics, 201
Mode coupling in two-dimensional magnetohydrodynamic flows
The spectrum of incompressible waves and instabilities of two-dimensional plasma geometries with background flow is calculated. The equilibrium is solved numerically by the recently developed program FLow Equilibrium Solver (FLES). The spectra of the equilibria are computed by means of another ne vcr program, the INcompressible 2-dimensional FLow Eigenvalue Solver (IN2FLES). Magnetic instabilities and instabilities driven by the the two-dimensionality and the flow are found. For linear equilibria, the eigenvalues for elliptical geometries remain close to the curves on which the eigenvalues for circular geometries lie. These curves may be found for unbounded domains by a calculation in Fourier space [see Lifschitz, A. In: Proceedings of 1995 International Workshop on Operator Theory and Applications (ed. R. Mennicken and C. Tretter), pp. 97-117, Birkhauser, Boston, 1998]. Here the relation between a new continuous spectrum of unbounded domains and the discrete spectrum of bounded domains is investigated. Finally, it is found that the two-dimensionality and the background flow may lead to an overstable cluster point
Magnetohydrodynamic activity inside a sphere
We present a computational method to solve the magnetohydrodynamic equations
in spherical geometry. The technique is fully nonlinear and wholly spectral,
and uses an expansion basis that is adapted to the geometry:
Chandrasekhar-Kendall vector eigenfunctions of the curl. The resulting lower
spatial resolution is somewhat offset by being able to build all the boundary
conditions into each of the orthogonal expansion functions and by the
disappearance of any difficulties caused by singularities at the center of the
sphere. The results reported here are for mechanically and magnetically
isolated spheres, although different boundary conditions could be studied by
adapting the same method. The intent is to be able to study the nonlinear
dynamical evolution of those aspects that are peculiar to the spherical
geometry at only moderate Reynolds numbers. The code is parallelized, and will
preserve to high accuracy the ideal magnetohydrodynamic (MHD) invariants of the
system (global energy, magnetic helicity, cross helicity). Examples of results
for selective decay and mechanically-driven dynamo simulations are discussed.
In the dynamo cases, spontaneous flips of the dipole orientation are observed.Comment: 15 pages, 19 figures. Improved figures, in press in Physics of Fluid
Zonal flow scaling in rapidly-rotating compressible convection
The surface winds of Jupiter and Saturn are primarily zonal. Each planet
exhibits strong prograde equatorial flow flanked by multiple alternating zonal
winds at higher latitudes. The depth to which these flows penetrate has long
been debated and is still an unsolved problem. Previous rotating convection
models that obtained multiple high latitude zonal jets comparable to those on
the giant planets assumed an incompressible (Boussinesq) fluid, which is
unrealistic for gas giant planets. Later models of compressible rotating
convection obtained only few high latitude jets which were not amenable to
scaling analysis.
Here we present 3-D numerical simulations of compressible convection in
rapidly-rotating spherical shells. To explore the formation and scaling of
high-latitude zonal jets, we consider models with a strong radial density
variation and a range of Ekman numbers, while maintaining a zonal flow Rossby
number characteristic of Saturn.
All of our simulations show a strong prograde equatorial jet outside the
tangent cylinder. At low Ekman numbers several alternating jets form in each
hemisphere inside the tangent cylinder. To analyse jet scaling of our numerical
models and of Jupiter and Saturn, we extend Rhines scaling based on a
topographic -parameter, which was previously applied to an
incompressible fluid in a spherical shell, to compressible fluids. The
jet-widths predicted by this modified Rhines length are found to be in
relatively good agreement with our numerical model results and with cloud
tracking observations of Jupiter and Saturn.Comment: 17 pages, 12 figures, 3 tables, accepted for publication in PEP
Astrophysical turbulence modeling
The role of turbulence in various astrophysical settings is reviewed. Among
the differences to laboratory and atmospheric turbulence we highlight the
ubiquitous presence of magnetic fields that are generally produced and
maintained by dynamo action. The extreme temperature and density contrasts and
stratifications are emphasized in connection with turbulence in the
interstellar medium and in stars with outer convection zones, respectively. In
many cases turbulence plays an essential role in facilitating enhanced
transport of mass, momentum, energy, and magnetic fields in terms of the
corresponding coarse-grained mean fields. Those transport properties are
usually strongly modified by anisotropies and often completely new effects
emerge in such a description that have no correspondence in terms of the
original (non coarse-grained) fields.Comment: 88 pages, 26 figures, published in Reports on Progress in Physic
Prediction of high speed propeller flow fields using a three-dimensional Euler analysis
To overcome the limitations of classical propeller theory, a computer program, NASPROP-E, was developed which solves for the flow field surrounding a multibladed propeller and axisymmetric nacelle combination using a finite difference method. The governing equations are the three dimensional unsteady Euler equations written in a cylindrical coordinate system. They are marched in time until a steady state solution is obtained. The Euler equations require no special treatment to model the blade work vorticity. The equations are solved using an implicit approximate factorization method. Numerical results are presented which have greatly increased the understanding of high speed propeller flow fields. Numerical results for swirl angle downstream of the propeller and propeller power coefficient are higher than experimental results. The radial variation of coefficient are higher than experimental results. The radial variation of swirl angle, however, is in reasonable agreement with the experimental results. The predicted variation of power coefficient with blade angle agrees very well with data
Ideal magnetohydrodynamic simulations of unmagnetized dense plasma jet injection into a hot strongly magnetized plasma
We present results from three-dimensional ideal magnetohydrodynamic
simulations of unmagnetized dense plasma jet injection into a uniform hot
strongly magnetized plasma, with the aim of providing insight into core fueling
of a tokamak with parameters relevant for ITER and NSTX (National Spherical
Torus Experiment). Unmagnetized dense plasma jet injection is similar to
compact toroid injection but with much higher plasma density and total mass,
and consequently lower required injection velocity. Mass deposition of the jet
into the background appears to be facilitated via magnetic reconnection along
the jet's trailing edge. The penetration depth of the plasma jet into the
background plasma is mostly dependent on the jet's initial kinetic energy, and
a key requirement for spatially localized mass deposition is for the jet's
slowing-down time to be less than the time for the perturbed background
magnetic flux to relax due to magnetic reconnection. This work suggests that
more accurate treatment of reconnection is needed to fully model this problem.
Parameters for unmagnetized dense plasma jet injection are identified for
localized core deposition as well as edge localized mode (ELM) pacing
applications in ITER and NSTX-relevant regimes.Comment: 16 pages, 8 figures and 2 tables; accepted by Nuclear Fusion (May 11,
2011
High-Order Unstructured Lagrangian One-Step WENO Finite Volume Schemes for Non-Conservative Hyperbolic Systems: Applications to Compressible Multi-Phase Flows
In this article we present the first better than second order accurate
unstructured Lagrangian-type one-step WENO finite volume scheme for the
solution of hyperbolic partial differential equations with non-conservative
products. The method achieves high order of accuracy in space together with
essentially non-oscillatory behavior using a nonlinear WENO reconstruction
operator on unstructured triangular meshes. High order accuracy in time is
obtained via a local Lagrangian space-time Galerkin predictor method that
evolves the spatial reconstruction polynomials in time within each element. The
final one-step finite volume scheme is derived by integration over a moving
space-time control volume, where the non-conservative products are treated by a
path-conservative approach that defines the jump terms on the element
boundaries. The entire method is formulated as an Arbitrary-Lagrangian-Eulerian
(ALE) method, where the mesh velocity can be chosen independently of the fluid
velocity.
The new scheme is applied to the full seven-equation Baer-Nunziato model of
compressible multi-phase flows in two space dimensions. The use of a Lagrangian
approach allows an excellent resolution of the solid contact and the resolution
of jumps in the volume fraction. The high order of accuracy of the scheme in
space and time is confirmed via a numerical convergence study. Finally, the
proposed method is also applied to a reduced version of the compressible
Baer-Nunziato model for the simulation of free surface water waves in moving
domains. In particular, the phenomenon of sloshing is studied in a moving water
tank and comparisons with experimental data are provided
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