896 research outputs found
Master-modes in 3D turbulent channel flow
Turbulent flow fields can be expanded into a series in a set of basic
functions. The terms of such series are often called modes. A master- (or
determining) mode set is a subset of these modes, the time history of which
uniquely determines the time history of the entire turbulent flow provided that
this flow is developed. In the present work the existence of the
master-mode-set is demonstrated numerically for turbulent channel flow. The
minimal size of a master-mode set and the rate of the process of the recovery
of the entire flow from the master-mode set history are estimated. The velocity
field corresponding to the minimal master-mode set is found to be a good
approximation for mean velocity in the entire flow field. Mean characteristics
involving velocity derivatives deviate in a very close vicinity to the wall,
while master-mode two-point correlations exhibit unrealistic oscillations. This
can be improved by using a larger than minimal master-mode set. The near-wall
streaks are found to be contained in the velocity field corresponding to the
minimal master-mode set, and the same is true at least for the large-scale part
of the longitudinal vorticity structure. A database containing the time history
of a master-mode set is demonstrated to be an efficient tool for investigating
rare events in turbulent flows. In particular, a travelling-wave-like object
was identified on the basis of the analysis of the database. Two
master-mode-set databases of the time history of a turbulent channel flow are
made available online at http://www.dnsdata.afm.ses.soton.ac.uk/. The services
provided include the facility for the code uploaded by a user to be run on the
server with an access to the data
Computation of the magnetostatic interaction between linearly magnetized polyhedrons
In this paper we present a method to accurately compute the energy of the
magnetostatic interaction between linearly (or uniformly, as a special case)
magnetized polyhedrons. The method has applications in finite element
micromagnetics, or more generally in computing the magnetostatic interaction
when the magnetization is represented using the finite element method (FEM).
The magnetostatic energy is described by a six-fold integral that is singular
when the interaction regions overlap, making direct numerical evaluation
problematic. To resolve the singularity, we evaluate four of the six iterated
integrals analytically resulting in a 2d integral over the surface of a
polyhedron, which is nonsingular and can be integrated numerically. This
provides a more accurate and efficient way of computing the magnetostatic
energy integral compared to existing approaches.
The method was developed to facilitate the evaluation of the demagnetizing
interaction between neighouring elements in finite-element micromagnetics and
provides a possibility to compute the demagnetizing field using efficient fast
multipole or tree code algorithms
Computing the demagnetizing tensor for finite difference micromagnetic simulations via numerical integration
In the finite difference method which is commonly used in computational
micromagnetics, the demagnetizing field is usually computed as a convolution of
the magnetization vector field with the demagnetizing tensor that describes the
magnetostatic field of a cuboidal cell with constant magnetization. An
analytical expression for the demagnetizing tensor is available, however at
distances far from the cuboidal cell, the numerical evaluation of the
analytical expression can be very inaccurate.
Due to this large-distance inaccuracy numerical packages such as OOMMF
compute the demagnetizing tensor using the explicit formula at distances close
to the originating cell, but at distances far from the originating cell a
formula based on an asymptotic expansion has to be used. In this work, we
describe a method to calculate the demagnetizing field by numerical evaluation
of the multidimensional integral in the demagnetization tensor terms using a
sparse grid integration scheme. This method improves the accuracy of
computation at intermediate distances from the origin.
We compute and report the accuracy of (i) the numerical evaluation of the
exact tensor expression which is best for short distances, (ii) the asymptotic
expansion best suited for large distances, and (iii) the new method based on
numerical integration, which is superior to methods (i) and (ii) for
intermediate distances. For all three methods, we show the measurements of
accuracy and execution time as a function of distance, for calculations using
single precision (4-byte) and double precision (8-byte) floating point
arithmetic. We make recommendations for the choice of scheme order and
integrating coefficients for the numerical integration method (iii)
An adaptive octree finite element method for PDEs posed on surfaces
The paper develops a finite element method for partial differential equations
posed on hypersurfaces in , . The method uses traces of
bulk finite element functions on a surface embedded in a volumetric domain. The
bulk finite element space is defined on an octree grid which is locally refined
or coarsened depending on error indicators and estimated values of the surface
curvatures. The cartesian structure of the bulk mesh leads to easy and
efficient adaptation process, while the trace finite element method makes
fitting the mesh to the surface unnecessary. The number of degrees of freedom
involved in computations is consistent with the two-dimension nature of surface
PDEs. No parametrization of the surface is required; it can be given implicitly
by a level set function. In practice, a variant of the marching cubes method is
used to recover the surface with the second order accuracy. We prove the
optimal order of accuracy for the trace finite element method in and
surface norms for a problem with smooth solution and quasi-uniform mesh
refinement. Experiments with less regular problems demonstrate optimal
convergence with respect to the number of degrees of freedom, if grid
adaptation is based on an appropriate error indicator. The paper shows results
of numerical experiments for a variety of geometries and problems, including
advection-diffusion equations on surfaces. Analysis and numerical results of
the paper suggest that combination of cartesian adaptive meshes and the
unfitted (trace) finite elements provide simple, efficient, and reliable tool
for numerical treatment of PDEs posed on surfaces
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