Flow Control by H. T. Banks, R. C. Smith (auth.), Max D. Gunzburger (eds.) PDF

Nonfiction 8

By H. T. Banks, R. C. Smith (auth.), Max D. Gunzburger (eds.)

The articles during this quantity disguise fresh paintings within the zone of stream keep watch over from the perspective of either engineers and mathematicians. those writings are in particular well timed, as they coincide with the emergence of the position of arithmetic and systematic engineering research in circulate keep an eye on and optimization. lately this function has considerably extended to the purpose the place now subtle mathematical and computational instruments are being more and more utilized to the keep an eye on and optimization of fluid flows. those articles rfile a few very important paintings that has long past directly to impression the sensible, daily layout of flows; additionally, they symbolize the state-of-the-art within the formula, research, and computation of movement keep an eye on difficulties. This quantity might be of curiosity to either utilized mathematicians and to engineers.

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4 below. 2. The first 3 iterations used the Enquist-Osher method and then switched to the Godunov method for the remaining 12 iterations. 4. Comments. Shape optimization problems for systems with shocks can produce unexpected results. We illustrated one of these features by studying a particular Euler flow using a model1-D steady state duct problem. Numerical approximations of the cost functional coupled with discontinuous solutions (shocks) arising from the Euler equations, produced artificial local minima in the approximate cost functional, as we expected.

In this section, we present optimization results using a "black box" method [5]. 2 with a BFGS based quasi-Newton minimization algorithm using finite difference approximations to evaluate the gradient [3]. 15). T. 6 FIG. 4. 00000 b; This "black box" method is used to try to find the Bezier parameter which uniquely describes the cross-sectional area A* E B. We will compare the convergence of minimization schemes when the cost functional :145 is computed using numerical solutions 5 obtained using both the Godunov and the Enquist-Osher methods.

This problem is described in detail in papers by Huddleston [6] and Borggaard, Burns, Cliff and Gunzburger [1]. Fluid flow systems which are modeled by Euler equations are interesting since they are of mixed type, which can lead to discontinuities (or shocks) in their flow solutions. The existence of shocks produces some interesting difficulties in the resulting optimization problem, which is primarily caused by the choice of a numerical approximation. To understand this behavior, we study a simple model which displays the same features as the optimal FBS design problem.

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