3,173 research outputs found
Adaptive mesh refinement with spectral accuracy for magnetohydrodynamics in two space dimensions
We examine the effect of accuracy of high-order spectral element methods,
with or without adaptive mesh refinement (AMR), in the context of a classical
configuration of magnetic reconnection in two space dimensions, the so-called
Orszag-Tang vortex made up of a magnetic X-point centered on a stagnation point
of the velocity. A recently developed spectral-element adaptive refinement
incompressible magnetohydrodynamic (MHD) code is applied to simulate this
problem. The MHD solver is explicit, and uses the Elsasser formulation on
high-order elements. It automatically takes advantage of the adaptive grid
mechanics that have been described elsewhere in the fluid context [Rosenberg,
Fournier, Fischer, Pouquet, J. Comp. Phys. 215, 59-80 (2006)]; the code allows
both statically refined and dynamically refined grids. Tests of the algorithm
using analytic solutions are described, and comparisons of the Orszag-Tang
solutions with pseudo-spectral computations are performed. We demonstrate for
moderate Reynolds numbers that the algorithms using both static and refined
grids reproduce the pseudo--spectral solutions quite well. We show that
low-order truncation--even with a comparable number of global degrees of
freedom--fails to correctly model some strong (sup--norm) quantities in this
problem, even though it satisfies adequately the weak (integrated) balance
diagnostics.Comment: 19 pages, 10 figures, 1 table. Submitted to New Journal of Physic
Lagrangian and geometric analysis of finite-time Euler singularities
We present a numerical method of analyzing possibly singular incompressible
3D Euler flows using massively parallel high-resolution adaptively refined
numerical simulations up to 8192^3 mesh points. Geometrical properties of
Lagrangian vortex line segments are used in combination with analytical
non-blowup criteria by Deng et al [Commun. PDE 31 (2006)] to reliably
distinguish between singular and near-singular flow evolution. We then apply
the presented technique to a class of high-symmetry initial conditions and
present numerical evidence against the formation of a finite-time singularity
in this case.Comment: arXiv admin note: text overlap with arXiv:1210.253
An efficient parallel immersed boundary algorithm using a pseudo-compressible fluid solver
We propose an efficient algorithm for the immersed boundary method on
distributed-memory architectures, with the computational complexity of a
completely explicit method and excellent parallel scaling. The algorithm
utilizes the pseudo-compressibility method recently proposed by Guermond and
Minev [Comptes Rendus Mathematique, 348:581-585, 2010] that uses a directional
splitting strategy to discretize the incompressible Navier-Stokes equations,
thereby reducing the linear systems to a series of one-dimensional tridiagonal
systems. We perform numerical simulations of several fluid-structure
interaction problems in two and three dimensions and study the accuracy and
convergence rates of the proposed algorithm. For these problems, we compare the
proposed algorithm against other second-order projection-based fluid solvers.
Lastly, the strong and weak scaling properties of the proposed algorithm are
investigated
LES of an Inclined Jet into a Supersonic Turbulent Crossflow
This short article describes flow parameters, numerical method, and
animations of the fluid dynamics video "LES of an Inclined Jet into a
Supersonic Turbulent Crossflow"
(http://ecommons.library.cornell.edu/bitstream/1813/14073/3/GFM-2009.mpg
[high-resolution] and
http://ecommons.library.cornell.edu/bitstream/1813/14073/2/GFM-2009-web.m1v
[low-resolution] video). We performed large-eddy simulation with the sub-grid
scale (LES-SGS) stretched-vortex model of momentum and scalar transport to
study the gas-dynamics interactions of a helium inclined round jet into a
supersonic () turbulent (\Reth) air flow over a flat
surface. The video shows the temporal development of Mach-number and magnitude
of density-gradient in the mid-span plane, and isosurface of helium
mass-fraction and \lam_2 (vortical structures). The identified vortical
structures are sheets, tilted tubes, and discontinuous rings. The vortical
structures are shown to be well correlated in space and time with helium
mass-fraction isosurface ().Comment: 7 pages, 1 figure, 1 table, article describing fluid dynamics video
submitted to Gallery of Fluid Motion, APS-DFD 200
A partition of unity approach to fluid mechanics and fluid-structure interaction
For problems involving large deformations of thin structures, simulating
fluid-structure interaction (FSI) remains challenging largely due to the need
to balance computational feasibility, efficiency, and solution accuracy.
Overlapping domain techniques have been introduced as a way to combine the
fluid-solid mesh conformity, seen in moving-mesh methods, without the need for
mesh smoothing or re-meshing, which is a core characteristic of fixed mesh
approaches. In this work, we introduce a novel overlapping domain method based
on a partition of unity approach. Unified function spaces are defined as a
weighted sum of fields given on two overlapping meshes. The method is shown to
achieve optimal convergence rates and to be stable for steady-state Stokes,
Navier-Stokes, and ALE Navier-Stokes problems. Finally, we present results for
FSI in the case of a 2D mock aortic valve simulation. These initial results
point to the potential applicability of the method to a wide range of FSI
applications, enabling boundary layer refinement and large deformations without
the need for re-meshing or user-defined stabilization.Comment: 34 pages, 15 figur
A fast immersed boundary method for external incompressible viscous flows using lattice Green's functions
A new parallel, computationally efficient immersed boundary method for
solving three-dimensional, viscous, incompressible flows on unbounded domains
is presented. Immersed surfaces with prescribed motions are generated using the
interpolation and regularization operators obtained from the discrete delta
function approach of the original (Peskin's) immersed boundary method. Unlike
Peskin's method, boundary forces are regarded as Lagrange multipliers that are
used to satisfy the no-slip condition. The incompressible Navier-Stokes
equations are discretized on an unbounded staggered Cartesian grid and are
solved in a finite number of operations using lattice Green's function
techniques. These techniques are used to automatically enforce the natural
free-space boundary conditions and to implement a novel block-wise adaptive
grid that significantly reduces the run-time cost of solutions by limiting
operations to grid cells in the immediate vicinity and near-wake region of the
immersed surface. These techniques also enable the construction of practical
discrete viscous integrating factors that are used in combination with
specialized half-explicit Runge-Kutta schemes to accurately and efficiently
solve the differential algebraic equations describing the discrete momentum
equation, incompressibility constraint, and no-slip constraint. Linear systems
of equations resulting from the time integration scheme are efficiently solved
using an approximation-free nested projection technique. The algebraic
properties of the discrete operators are used to reduce projection steps to
simple discrete elliptic problems, e.g. discrete Poisson problems, that are
compatible with recent parallel fast multipole methods for difference
equations. Numerical experiments on low-aspect-ratio flat plates and spheres at
Reynolds numbers up to 3,700 are used to verify the accuracy and physical
fidelity of the formulation.Comment: 32 pages, 9 figures; preprint submitted to Journal of Computational
Physic
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