Progress and challenges in the application of artificial intelligence to computational fluid dynamics

Andrews, Alison E.

doi:10.2514/3.9848

Cited by 22 publications

(4 citation statements)

References 8 publications

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“…Hybrid grids combine features of structural and nonstructural grids and are applied mostly to numeri cally solve boundary problems in regions of compli cated form [44].…”

Section: Optimization Using Simulation Modelsmentioning

confidence: 99%

Pattern recognition methods as applied to optimize systems represented by simulation models

Antonova

2012

Pattern Recognit. Image Anal.

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This overview lecture discusses four topics and describes the method of approximate optimization of dynamic stochastic systems known as the optimization simulation method. The grid method of uniform probing of the space of parameters called LP τ search with averaging allows estimating the efficiency region as the region in the space of parameters where the system quality indices are better than in other regions. Ensuring better quality of processing the results of simulation experiments, pattern recognition methods allow speeding up the evaluation of efficiency regions.

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“…Hybrid grids combine features of structural and nonstructural grids and are applied mostly to numeri cally solve boundary problems in regions of compli cated form [44].…”

Section: Optimization Using Simulation Modelsmentioning

confidence: 99%

Pattern recognition methods as applied to optimize systems represented by simulation models

Antonova

2012

Pattern Recognit. Image Anal.

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“…This paper also describes the current domain decomposition techniques developed by Shaw and Weatherill (1992), Stewart (1992), Dannenhoffer (1995), Wulf and Akrag (1995), Schonfeld, Weinerfelt, and Jenssen (1995), and Kim and Eberhardt (1995). The first attempts to overcome the problem of domain decomposition were discussed by Andrews (1988), Georgala and Shaw (1989), Allwright (1989), and Vogel (1990).…”

Section: Comprehensive Codesmentioning

confidence: 99%

A Computational Differential Geometry Approach to Grid Generation

Liseikin¹

2007

Scientific Computation

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“…Using the terminology adopted in differential geometry [5], the integral (1.9) is the total energy associated with the mapping r(s(q)):Q n -*S rn between the manifolds S rn and Q n having the local coordinates s and q and the metric tensors g. 1 ? for S rn and δ!…”

Section: Properties and Interpretations Of Grid Smoothnessmentioning

confidence: 99%

On some interpretations of a smoothness functional used in constructing regular and adaptive grids

Liseikin¹

1993

Russian Journal of Numerical Analysis and Mathematical Modelling

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Some properties are analysed and geometric interpretations are given of a smoothness functional and Euler-Lagrange equations, which are used in constructing adaptive grids in the projections method. Examples of adaptive grids are given.Methods based on the solution of elliptic equations and variational problems have found wide use in constructing structural grids in space domains and on their boundaries. Inverted Poisson's equations, suggested first in [7], are used in elliptic methods, while variational methods make use of various regularity and adaptation functionals [2,3,15,18,20]. Using these methods, we can construct difference grids in fairly complicated domains and on surfaces that arise in analysing multidimensional problems. However, as present and future applications are mainly based on a standard solution of increasingly involved mathematical problems, a demand grows for reliable and efficient algorithms for constructing grids that would be of high quality, adaptive, unified and simple to use as well as economical.Now that multiblock grids are widely used in solving problems with complex geometry, two main trends have emerged in research aimed at suiting the above requirements [1,12] The first trend is associated with the automation of those elements of grid construction programs which involve a lot of manual labour. These elements are: (1) the decomposition of a domain into blocks, which is consistent with the distinctive features of the domain geometry, with qualitative features of a physical medium and the sought-for solution, and with a computer architecture; (2) numbering the set of blocks, their faces and edges and setting the order in which grids are constructed in the blocks; (3) choosing the grid topology and the requirements placed on qualitative and quantitative characteristics of internal grids and on their communications between the blocks; (4) selecting appropriate methods that would allow the above requirements to be met; and (5) designing the structure of grid construction programs. The second trend deals with developing new, more reliable and elaborate methods for constructing the grid in a unified manner, regardless of the geometry and qualitative and quantitative characteristics the grid should possess [12,16].In this paper, we develop the second trend on the basis of a unified method [13] for constructing quasi-uniform grids on arbitrary «-dimensional surfaces S rn situated in the (n + &)-dimensional space R n+k . Using this method of constructing hypersurface grids, we can construct adaptive and regular grids in a unified manner both in the domain and on its boundary. In this approach, an adaptive grid is obtained as a projection of a quasi-uniform grid from an 'adaptive' surface defined by some quantities depending on the solution, its components, derivatives, or some other functions that would allow for the problem structure necessary in calculations.

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Progress and challenges in the application of artificial intelligence to computational fluid dynamics

Cited by 22 publications

References 8 publications

Pattern recognition methods as applied to optimize systems represented by simulation models

Pattern recognition methods as applied to optimize systems represented by simulation models

A Computational Differential Geometry Approach to Grid Generation

On some interpretations of a smoothness functional used in constructing regular and adaptive grids

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