16,951 research outputs found
A Comparison of Two Shallow Water Models with Non-Conforming Adaptive Grids: classical tests
In an effort to study the applicability of adaptive mesh refinement (AMR)
techniques to atmospheric models an interpolation-based spectral element
shallow water model on a cubed-sphere grid is compared to a block-structured
finite volume method in latitude-longitude geometry. Both models utilize a
non-conforming adaptation approach which doubles the resolution at fine-coarse
mesh interfaces. The underlying AMR libraries are quad-tree based and ensure
that neighboring regions can only differ by one refinement level.
The models are compared via selected test cases from a standard test suite
for the shallow water equations. They include the advection of a cosine bell, a
steady-state geostrophic flow, a flow over an idealized mountain and a
Rossby-Haurwitz wave. Both static and dynamics adaptations are evaluated which
reveal the strengths and weaknesses of the AMR techniques. Overall, the AMR
simulations show that both models successfully place static and dynamic
adaptations in local regions without requiring a fine grid in the global
domain. The adaptive grids reliably track features of interests without visible
distortions or noise at mesh interfaces. Simple threshold adaptation criteria
for the geopotential height and the relative vorticity are assessed.Comment: 25 pages, 11 figures, preprin
Construction and Application of an AMR Algorithm for Distributed Memory Computers
While the parallelization of blockstructured adaptive mesh refinement techniques is relatively straight-forward on shared memory architectures, appropriate distribution strategies for the emerging generation of distributed
memory machines are a topic of on-going research. In this paper, a locality-preserving domain decomposition is proposed that partitions the entire AMR hierarchy from the base level on. It is shown that the approach reduces the
communication costs and simplifies the implementation. Emphasis is put on the effective parallelization of the flux correction procedure at coarse-fine boundaries, which is indispensable for conservative finite volume schemes. An
easily reproducible standard benchmark and a highly resolved parallel AMR
simulation of a diffracting hydrogen-oxygen detonation demonstrate the proposed
strategy in practice
Analysis of the discontinuous Galerkin method for elliptic problems on surfaces
We extend the discontinuous Galerkin (DG) framework to a linear second-order
elliptic problem on a compact smooth connected and oriented surface. An
interior penalty (IP) method is introduced on a discrete surface and we derive
a-priori error estimates by relating the latter to the original surface via the
lift introduced in Dziuk (1988). The estimates suggest that the geometric error
terms arising from the surface discretisation do not affect the overall
convergence rate of the IP method when using linear ansatz functions. This is
then verified numerically for a number of test problems. An intricate issue is
the approximation of the surface conormal required in the IP formulation,
choices of which are investigated numerically. Furthermore, we present a
generic implementation of test problems on surfaces.Comment: 21 pages, 4 figures. IMA Journal of Numerical Analysis 2013, Link to
publication: http://imajna.oxfordjournals.org/cgi/content/abstract/drs033?
ijkey=45b23qZl5oJslZQ&keytype=re
Task-based adaptive multiresolution for time-space multi-scale reaction-diffusion systems on multi-core architectures
A new solver featuring time-space adaptation and error control has been
recently introduced to tackle the numerical solution of stiff
reaction-diffusion systems. Based on operator splitting, finite volume adaptive
multiresolution and high order time integrators with specific stability
properties for each operator, this strategy yields high computational
efficiency for large multidimensional computations on standard architectures
such as powerful workstations. However, the data structure of the original
implementation, based on trees of pointers, provides limited opportunities for
efficiency enhancements, while posing serious challenges in terms of parallel
programming and load balancing. The present contribution proposes a new
implementation of the whole set of numerical methods including Radau5 and
ROCK4, relying on a fully different data structure together with the use of a
specific library, TBB, for shared-memory, task-based parallelism with
work-stealing. The performance of our implementation is assessed in a series of
test-cases of increasing difficulty in two and three dimensions on multi-core
and many-core architectures, demonstrating high scalability
Numerical Structure Analysis of Regular Hydrogen-Oxygen Detonations
Large-scale numerical simulations have been carried out to analyze the internal
wave structure of a regular oscillating low-pressure H2 : O2 : Ar-Chapman-Jouguet
detonation in two and three space-dimensions. The chemical reaction is modeled
with a non-equilibrium mechanism that consists of 34 elementary reactions and uses
nine thermally perfect gaseous species. A high local resolution is achieved dynamically
at run-time by employing a block-oriented adaptive finite volume method that
has been parallelized efficiently for massively parallel machines. Based on a highly
resolved two-dimensional simulation we analyze the temporal development of the
ow field around a triple point during a detonation cell in great detail. In particular,
the influence of the reinitiation phase at the beginning of a detonation cell
is discussed. Further on, a successful simulation of the cellular structure in three
space-dimensions for the same configuration is presented. The calculation reproduces
the experimentally observed three-dimensional mode of propagation called
"rectangular-mode-in-phase" with zero phase shift between the transverse waves in
both space-directions perpendicular to the detonation front and shows the same
oscillation period as the two-dimensional case
Adaptive Multi-Rate Wavelet Method for Circuit Simulation
In this paper a new adaptive algorithm for multi-rate circuit simulation encountered in the design of RF circuits based on spline wavelets is presented. The ordinary circuit differential equations are first rewritten by a system of (multi-rate) partial differential equations (MPDEs) in order to decouple the different time scales. Second, a semi-discretization by Rothe's method of the MPDEs results in a system of differential algebraic equations DAEs with periodic boundary conditions. These boundary value problems are solved by a Galerkin discretization using spline functions. An adaptive spline grid is generated, using spline wavelets for non-uniform grids. Moreover the instantaneous frequency is chosen adaptively to guarantee a smooth envelope resulting in large time steps and therefore high run time efficiency. Numerical tests on circuits exhibiting multi-rate behavior including mixers and PLL conclude the paper
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