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Aerodynamic design via control theory (1988)

Jameson, Antony

Springer

Journal of scientific computing 3 (1988), S. 233-260

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ISSN: 1573-7691

Keywords: Computational aerodynamics ; transonic flow ; inverse problem ; wing design ; optimization

Source: Springer Online Journal Archives 1860-2000

Topics: Computer Science

Notes: Conclusion The purpose of the last three sections is to demonstrate by representative examples that control theory can be used to formulate computationally feasible procedures for aerodynamic design. The cost of each iteration is of the same order as two flow solutions, since the adjoint equation is of comparable complexity to the flow equation, and the remaining auxiliary equations could be solved quite inexpensively. Provided, therefore, that one can afford the cost of a moderate number of flow solutions, procedures of this type can be used to derive improved designs. The approach is quite general, not limited to particular choices of the coordinate transformation or cost function, which might in fact contain measures of other criteria of performance such as lift and drag. For the sake of simplicity certain complicating factors, such as the need to include a special term in the mapping function to generate a corner at the trailing edge, have been suppressed from the present analysis. Also it remains to explore the numerical implementation of the design procedures proposed in this paper.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/BF01061285

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Positive schemes and shock modelling for compressible flows (1995)

Jameson, Antony

Chichester : Wiley-Blackwell

International Journal for Numerical Methods in Fluids 20 (1995), S. 743-776

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ISSN: 0271-2091

Keywords: computational aerodynamics ; shock capturing ; positive schemes ; Engineering ; Engineering General

Source: Wiley InterScience Backfile Collection 1832-2000

Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics

Notes: A unified theory of non-oscillatory finite volume schemes for both structured and unstructured meshes is developed in two parts. In the first part, a theory of local extremum diminishing (LED) and essentially local extremum diminishing (ELED) schemes is developed for scalar conservation laws. This leads to symmetric and upstream limited positive (SLIP and USLIP) schemes which can be formulated on either structured or unstructured meshes. The second part examines the application of similar ideas to the treatment of systems of conservation laws. An analysis of discrete shock structure leads to conditions on the numerical flux such that stationary discrete shocks can contain a single interior point. The simplest formulation which meets these conditions is a convective upwind and split pressure (CUSP) scheme, in which the coefficient of the pressure differences is fully determined by the coefficient of convective diffusion. Numerical results are presented which confirm the properties of these schemes.

Additional Material: 9 Ill.