388 research outputs found
Uncertain Data in Initial Boundary Value Problems: Impact on Short and Long Time Predictions
We investigate the influence of uncertain data on solutions to initial
boundary value problems. Uncertainty in the forcing function, initial
conditions and boundary conditions are considered and we quantify their
relative influence for short and long time calculations. It is shown that
dissipative boundary conditions leading to energy bounds play a crucial role.
For short time calculations, uncertainty in the initial data dominate. As time
grows, the influence of initial data vanish exponentially fast. For longer time
calculations, the uncertainty in the forcing function and boundary data
dominate, as they grow in time. Errors due to the forcing function grows faster
(linearly in time) than the ones due to the boundary data (grows as the square
root of time). Roughly speaking, the results indicate that for short time
calculations, the initial conditions are the most important, but for longer
time calculations, focus should be on modelling efforts and boundary
conditions. Our findings have impact on predictions where similar mathematical
and numerical techniques are used for both short and long times as for example
in regional weather and climate predictions
Implementation of Non-Reflecting Boundary Conditions in a Finite Volume Unstructured Solver for the Study of Turbine Cascades
The analysis of component interaction in the turbomachinery field is nowadays of growing importance. This leads to the combination of different approaches, such as Large Eddy Simulation for combustors and Unsteady Reynolds-Averaged Navier-Stokes equations for turbines, and is responsible for the increase of both computational effort and required accuracy of the numerical tools. To guarantee accurate results and efficient convergence rates, numerical schemes must handle the spurious reflecting waves coming from the boundaries of truncated domains. This can be achieved by means of Non-Reflecting Boundary Conditions. The research activity described in the present paper is aimed at implementing the method of Non-Reflecting Boundary Conditions for the Linearized Euler Equations proposed by Giles in an in-house finite volume implicit time-marching solver. The methodology is validated using the available experimental data obtained at the von Karman Institute for Fluid Dynamics on the LS89 High-Pressure Turbine vane for both subsonic and transonic working condition. The implemented approach demonstrates its importance for the correct evaluation of the pressure distribution both on the vane surface and in the pitchwise direction when the computational domain is truncated at the experimental probe's position
Glimmers of a Quantum KAM Theorem: Insights from Quantum Quenches in One Dimensional Bose Gases
Real-time dynamics in a quantum many-body system are inherently complicated
and hence difficult to predict. There are, however, a special set of systems
where these dynamics are theoretically tractable: integrable models. Such
models possess non-trivial conserved quantities beyond energy and momentum.
These quantities are believed to control dynamics and thermalization in low
dimensional atomic gases as well as in quantum spin chains. But what happens
when the special symmetries leading to the existence of the extra conserved
quantities are broken? Is there any memory of the quantities if the breaking is
weak? Here, in the presence of weak integrability breaking, we show that it is
possible to construct residual quasi-conserved quantities, so providing a
quantum analog to the KAM theorem and its attendant Nekhoreshev estimates. We
demonstrate this construction explicitly in the context of quantum quenches in
one-dimensional Bose gases and argue that these quasi-conserved quantities can
be probed experimentally.Comment: 21 pages with appendices; 13 figures; version accepted by PR
Estimating long term behavior of flows without trajectory integration: the infinitesimal generator approach
The long-term distributions of trajectories of a flow are described by
invariant densities, i.e. fixed points of an associated transfer operator. In
addition, global slowly mixing structures, such as almost-invariant sets, which
partition phase space into regions that are almost dynamically disconnected,
can also be identified by certain eigenfunctions of this operator. Indeed,
these structures are often hard to obtain by brute-force trajectory-based
analyses. In a wide variety of applications, transfer operators have proven to
be very efficient tools for an analysis of the global behavior of a dynamical
system.
The computationally most expensive step in the construction of an approximate
transfer operator is the numerical integration of many short term trajectories.
In this paper, we propose to directly work with the infinitesimal generator
instead of the operator, completely avoiding trajectory integration. We propose
two different discretization schemes; a cell based discretization and a
spectral collocation approach. Convergence can be shown in certain
circumstances. We demonstrate numerically that our approach is much more
efficient than the operator approach, sometimes by several orders of magnitude
Cumulative reports and publications through December 31, 1990
This document contains a complete list of ICASE reports. Since ICASE reports are intended to be preprints of articles that will appear in journals or conference proceedings, the published reference is included when it is available
Cumulative reports and publications
A complete list of Institute for Computer Applications in Science and Engineering (ICASE) reports are listed. Since ICASE reports are intended to be preprints of articles that will appear in journals or conference proceedings, the published reference is included when it is available. The major categories of the current ICASE research program are: applied and numerical mathematics, including numerical analysis and algorithm development; theoretical and computational research in fluid mechanics in selected areas of interest to LaRC, including acoustics and combustion; experimental research in transition and turbulence and aerodynamics involving LaRC facilities and scientists; and computer science
Research conducted at the Institute for Computer Applications in Science and Engineering in applied mathematics, numerical analysis and computer science
This report summarizes research conducted at the Institute for Computer Applications in Science and Engineering in applied mathematics, numerical analysis, and computer science during the period April l, 1988 through September 30, 1988
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