Shape Sensitivity and Design for Fluids with Shocks |
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Authors: | Olivier Pironneau |
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Affiliation: | 1. pironneau@ann.jussieu.fr |
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Abstract: | For many problems of compressible fluid dynamics it is desirable to find the sensitivity of the shock position with respect to the shape of the domain occupied by the fluid. One application is for the minimization of the sonic boom of airplanes; another is for the stability of the stream in fast-flowing rivers or canals. Classical calculus of variation is not valid for these cases because of the presence of Dirac functions appearing when a discontinuous function is differentiated, but we show here on the compressible potential flow equation how to find the equations of the derivatives and what are the linearized problems. Some numerical test cases are given for illustration. |
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Keywords: | Partial differential equations Nozzle flow Sensitivity Transonic equation Shallow water equations Optimal shape design |
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