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  • 1
    Digitale Medien
    Digitale Medien
    Cheap control of the time-invariant regulator (1975)
    Springer
    Applied mathematics & optimization 1 (1975), S. 337-354 
    Details
    ISSN: 1432-0606
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract The asymptotic solution of the linear quadratic state regulator problem is obtained as the cost of the control tends to zero. Matrix Riccati gains are obtained via singular perturbations theory and are used to asymptotically calculate the optimal control and the corresponding trajectories. Several cases are distinguished and applications are discussed.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01447957
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  • 2
    Digitale Medien
    Digitale Medien
    Aerodynamic design via control theory (1988)
    Springer
    Journal of scientific computing 3 (1988), S. 233-260 
    Details
    ISSN: 1573-7691
    Schlagwort(e): Computational aerodynamics ; transonic flow ; inverse problem ; wing design ; optimization
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Informatik
    Notizen: 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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01061285
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  • 3
    Digitale Medien
    Digitale Medien
    ANALYSIS AND IMPLEMENTATION OF THE GAS-KINETIC BGK SCHEME FOR COMPUTATIONAL GAS DYNAMICS (1997)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 25 (1997), S. 21-49 
    Details
    ISSN: 0271-2091
    Schlagwort(e): gas evolution model ; gas-kinetic BGK schemes ; entropy condition ; gas-kinetic Lax-Wendroff flux ; kinetic flux vector splitting ; local extremum diminishing ; advection equations ; non-linear hyperbolic systems ; Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Maschinenbau
    Notizen: Gas-kinetic schemes based on the BGK model are proposed as an alternative evolution model which can cure some of the limitations of current Riemann solvers. To analyse the schemes, simple advection equations are reconstructed and solved using the gas-kinetic BGK model. Results for gas-dynamic application are also presented. The final flux function derived in this model is a combination of a gas-kinetic Lax- Wendroff flux of viscous advection equations and kinetic flux vector splitting. These two basic schemes are coupled through a non-linear gas evolution process and it is found that this process always satisfies the entropy condition. Within the framework of the LED (local extremum diminishing) principle that local maxima should not increase and local minima should not decrease in interpolating physical quantities, several standard limiters are adopted to obtain initial interpolations so as to get higher-order BGK schemes. Comparisons for well-known test cases indicate that the gas-kinetic BGK scheme is a promising approach in the design of numerical schemes for hyperbolic conservation laws. © 1997 by John Wiley & Sons, Ltd.
    Zusätzliches Material: 27 Ill.
    Materialart: Digitale Medien
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  • 4
    Digitale Medien
    Digitale Medien
    Positive schemes and shock modelling for compressible flows (1995)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 20 (1995), S. 743-776 
    Details
    ISSN: 0271-2091
    Schlagwort(e): computational aerodynamics ; shock capturing ; positive schemes ; Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Maschinenbau
    Notizen: 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.
    Zusätzliches Material: 9 Ill.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/fld.1650200805
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  • 5
    Buch
    Buch
    Computational mathematics driven by industrial problems ; lectures given at the 1st session of the Centro Internazionale Matematico Estivo (C. I. M. E.) held in Martina Franca, Italy, June 21-27, 1999; 1739 (2000)
    Berlin u.a. :Springer,
    Details
    Titel: Computational mathematics driven by industrial problems ; lectures given at the 1st session of the Centro Internazionale Matematico Estivo (C. I. M. E.) held in Martina Franca, Italy, June 21-27, 1999; 1739
    Autor: Burkard, Rainer E.
    Beteiligte Person(en): Deuflhard, Peter , Jameson, Antony , Lions, Jacques-Louis , Strang, Gilbert , Capasso, Vincenzo , Periaux, Jacques , Engl, Heinz
    Verlag: Berlin u.a. :Springer,
    Erscheinungsjahr: 2000
    Seiten: 414 S.
    Serie: Lecture notes in mathematics 1739
    Materialart: Buch
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