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Effective preconditioning methods for the euler equations

Effective preconditioning methods for the euler equations

引用

Fluids 2000 Conference and Exhibit

作者： Zaccanti, M. Cinnella, P. MSU/NSF Engineering Reseaich Center for Computational Field Simulation MS 39762 United States

This study is concerned with improving the robustness of preconditioning methods for the Euler equations, particularly when computing flows involving a stagnation region. Specifically, a technique first proposed by Darmofal and Schmid in order to ensure a valid set of eigenvectors in the preconditioning method by Turkel is reinterpreted by means of a more general approach that takes into consideration symmetrizability of the preconditioned equations and the need for limiting the preconditioned acoustic eigenvalues in the stagnation region. The result is an increased level of robustness of the Turkel scheme in computing realistic flow cases. Following this idea, a general investigation of sparse preconditioners with the same properties is pursued, which allows to identify the Turkel matrix and its transpose as the simplest preconditioners satisfying the proposed robustness criterion. When considering sub- optimal sets of eigenvalues, even the matrix by Choi and Merkle can be made robust enough to overcome the problem of the stagnation-point instability, if the same approach is followed. For an effective preconditioning procedure over the entire Mach range, a hybrid scheme is proposed that uses one of the above methods in low subsonic flow together with the preconditioner by van Leer-Lee-Roe in transonic and supersonic *** conclusions of this investigation are supported by some preliminary test cases involving the relaxation of a point disturbance in a uniform flow and the computation of an isolated stagnation point, as well as by the more realistic computation of a flow past a NACA0012 airfoil with an especially refined grid in the nose region. The newly proposed modification of the Turkel scheme that takes into consideration symmetrizability of the equations is shown to provide an effective preconditioning method over the entire Mach regime when the van Leer-Lee-Roe preconditioner is used in the transonic and supersonic parts of the flow field. © 2000 by the Am

关键词： Euler equations

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The biological basis of the immune system as a model for intelligent agents 13th

引用

13th International Parallel Processing Symposium, IPPS 1999 Held in Conjunction with the 10th Symposium on Parallel and Distributed Processing, SPDP 1999

作者： King, Roger L. Lambert, Aric B. Russ, Samuel H. Reese, Donna S. MSU/NSF Engineering Research Center for Computational Field Simulation Box 9627 MS39762-9627 United States

ISBN: (纸本)3540658319

This paper describes the human immune system and its functionalities from a computational viewpoint. The objective of this paper is to provide the biological basis for an artificial immune system. This paper will also serve to illustrate how a biological system can be studied and how inferences can be drawn from its operation that can be exploited in intelligent agents. Functionalities of the biological immune system (e.g., content addressable memory, adaptation, etc.) are identified for use in intelligent agents. Specifically, in this paper, an intelligent agent will be described for task allocation in a heterogeneous computing environment. This research is not intended to develop an explicit model of the human immune system, but to exploit some of its functionalities in designing agent-based parallel and distributed control systems. © Springer-Verlag Berlin Heidelberg 1999.

关键词： Intelligent agents

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Analysis of preconditioning methods for the Euler equations 14th

Analysis of preconditioning methods for the Euler equations

引用

14th computational Fluid Dynamics Conference, 1999

作者： Zaccanti, M. Cinnella, P. MSU/NSF Engineering Research Center for Computational Field Simulation Mississippi StateMS39762 United States Aerospace Engineering Dept. United States

This study attempts a systematic discussion of local preconditioning methods for the two-dimensional Euler equations, including an assessment of some of the large body of work already completed in this area. The methods by Van Leer-Lee-Roe, D. Lee, and Turkel are presented and analyzed in. detail, and their possible drawbacks are investigated. The study focuses on establishing a list of criteria for the design of a ‘good’ preconditioning method, extending and clarifying the original work by D. Lee. An. exhaustive exploration of sparse preconditioning is attempted, in an effort to find a matrix able to overcome all of the known difficulties in Euler preconditioning. It is shown that a sparse preconditioning matrix will be .unable to avoid all of the problems, which means that the full form will have to be investigated. Some preliiinary steps of this analysis are presented here. The implementation of a preconditioned method using the Roe scheme based on one" Riemann problem normal to the cell interface is proposed, and its advantages over the two-Riemamrproblem approach commonly found in the preconditioning literature are demonstrated. © 1999 The American Institute of Aeronautics and Astronautics Inc. All rights reserved.

关键词： Euler equations

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