12,205 research outputs found
A Parallel Mesh-Adaptive Framework for Hyperbolic Conservation Laws
We report on the development of a computational framework for the parallel,
mesh-adaptive solution of systems of hyperbolic conservation laws like the
time-dependent Euler equations in compressible gas dynamics or
Magneto-Hydrodynamics (MHD) and similar models in plasma physics. Local mesh
refinement is realized by the recursive bisection of grid blocks along each
spatial dimension, implemented numerical schemes include standard
finite-differences as well as shock-capturing central schemes, both in
connection with Runge-Kutta type integrators. Parallel execution is achieved
through a configurable hybrid of POSIX-multi-threading and MPI-distribution
with dynamic load balancing. One- two- and three-dimensional test computations
for the Euler equations have been carried out and show good parallel scaling
behavior. The Racoon framework is currently used to study the formation of
singularities in plasmas and fluids.Comment: late submissio
Algorithms and data structures for adaptive multigrid elliptic solvers
Adaptive refinement and the complicated data structures required to support it are discussed. These data structures must be carefully tuned, especially in three dimensions where the time and storage requirements of algorithms are crucial. Another major issue is grid generation. The options available seem to be curvilinear fitted grids, constructed on iterative graphics systems, and unfitted Cartesian grids, which can be constructed automatically. On several grounds, including storage requirements, the second option seems preferrable for the well behaved scalar elliptic problems considered here. A variety of techniques for treatment of boundary conditions on such grids are reviewed. A new approach, which may overcome some of the difficulties encountered with previous approaches, is also presented
Vectorization and Parallelization of the Adaptive Mesh Refinement N-body Code
In this paper, we describe our vectorized and parallelized adaptive mesh
refinement (AMR) N-body code with shared time steps, and report its performance
on a Fujitsu VPP5000 vector-parallel supercomputer. Our AMR N-body code puts
hierarchical meshes recursively where higher resolution is required and the
time step of all particles are the same. The parts which are the most difficult
to vectorize are loops that access the mesh data and particle data. We
vectorized such parts by changing the loop structure, so that the innermost
loop steps through the cells instead of the particles in each cell, in other
words, by changing the loop order from the depth-first order to the
breadth-first order. Mass assignment is also vectorizable using this loop order
exchange and splitting the loop into loops, if the cloud-in-cell
scheme is adopted. Here, is the number of dimension. These
vectorization schemes which eliminate the unvectorized loops are applicable to
parallelization of loops for shared-memory multiprocessors. We also
parallelized our code for distributed memory machines. The important part of
parallelization is data decomposition. We sorted the hierarchical mesh data by
the Morton order, or the recursive N-shaped order, level by level and split and
allocated the mesh data to the processors. Particles are allocated to the
processor to which the finest refined cells including the particles are also
assigned. Our timing analysis using the -dominated cold dark matter
simulations shows that our parallel code speeds up almost ideally up to 32
processors, the largest number of processors in our test.Comment: 21pages, 16 figures, to be published in PASJ (Vol. 57, No. 5, Oct.
2005
Large scale optimization of transonic axial compressor rotor blades
[First Paragraphs]
In the present work the Multipoint Approximation Method (MAM) by Toropov et al. (1993) has been applied to
the shape optimization of an existing transonic compressor rotor (NASA rotor 37) as a benchmark case.
Simulations were performed using the Rolls-Royce plc. PADRAM-HYDRA system (Shahpar and Lapworth 2003,
Lapworth and Shahpar 2004) that includes the parameterization of the blade shape, meshing, CFD analysis, postprocessing,
and objective/constraints evaluation. The parameterization approach adopted in this system is very
flexible but can result in a large scale optimization problem.
For this pilot study, a relatively coarse mesh has been used including around 470,000 nodes. The
parameterization was done using 5 engineering blade parameters like axial movement of sections along the engine
axis in mm (XCEN), circumferential movements of sections in degrees (DELT), solid body rotation of sections in
degrees (SKEW), and leading/trailing edge recambering (LEM0/TEMO) in degrees. The design variables were
specified using 6 control points at 0 % (hub), 20%, 40%, 60%, 80%, and 100% (tip) along the span. Thus the total
number of independent design variables N was 30. B-spline interpolation was used through the control points to
generate smooth design perturbations in the radial direction
Adaptive Mesh Refinement for Hyperbolic Systems based on Third-Order Compact WENO Reconstruction
In this paper we generalize to non-uniform grids of quad-tree type the
Compact WENO reconstruction of Levy, Puppo and Russo (SIAM J. Sci. Comput.,
2001), thus obtaining a truly two-dimensional non-oscillatory third order
reconstruction with a very compact stencil and that does not involve
mesh-dependent coefficients. This latter characteristic is quite valuable for
its use in h-adaptive numerical schemes, since in such schemes the coefficients
that depend on the disposition and sizes of the neighboring cells (and that are
present in many existing WENO-like reconstructions) would need to be recomputed
after every mesh adaption.
In the second part of the paper we propose a third order h-adaptive scheme
with the above-mentioned reconstruction, an explicit third order TVD
Runge-Kutta scheme and the entropy production error indicator proposed by Puppo
and Semplice (Commun. Comput. Phys., 2011). After devising some heuristics on
the choice of the parameters controlling the mesh adaption, we demonstrate with
many numerical tests that the scheme can compute numerical solution whose error
decays as , where is the average
number of cells used during the computation, even in the presence of shock
waves, by making a very effective use of h-adaptivity and the proposed third
order reconstruction.Comment: many updates to text and figure
An adaptive Cartesian embedded boundary approach for fluid simulations of two- and three-dimensional low temperature plasma filaments in complex geometries
We review a scalable two- and three-dimensional computer code for
low-temperature plasma simulations in multi-material complex geometries. Our
approach is based on embedded boundary (EB) finite volume discretizations of
the minimal fluid-plasma model on adaptive Cartesian grids, extended to also
account for charging of insulating surfaces. We discuss the spatial and
temporal discretization methods, and show that the resulting overall method is
second order convergent, monotone, and conservative (for smooth solutions).
Weak scalability with parallel efficiencies over 70\% are demonstrated up to
8192 cores and more than one billion cells. We then demonstrate the use of
adaptive mesh refinement in multiple two- and three-dimensional simulation
examples at modest cores counts. The examples include two-dimensional
simulations of surface streamers along insulators with surface roughness; fully
three-dimensional simulations of filaments in experimentally realizable
pin-plane geometries, and three-dimensional simulations of positive plasma
discharges in multi-material complex geometries. The largest computational
example uses up to million mesh cells with billions of unknowns on
computing cores. Our use of computer-aided design (CAD) and constructive solid
geometry (CSG) combined with capabilities for parallel computing offers
possibilities for performing three-dimensional transient plasma-fluid
simulations, also in multi-material complex geometries at moderate pressures
and comparatively large scale.Comment: 40 pages, 21 figure
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