Optimization of body shape at small reynolds numbers
The problem of the optimization of the shape of a body in a stream of viscous liquid or gas was treated in [1–5]. The necessary conditions for a body to offer minimum resistance to the flow of a viscous gas past it were derived in , The necessary optimality conditions when the motion of the fluid is described by the approximate Stokes equations were derived in , The shape of a body of minimum resistance was found numerically in  in the Stokes approximation. The optimality conditions when the motion of the fluid is described by the Navier—Stokes equations were derived in [4, 5], and in  these conditions were extended to the case of a fluid whose motion is described in the boundary-layer approximation. The necessary optimality conditions when the motion of the fluid is described by the approximate Oseen equations were derived in  and an asymptotic analysis of the behavior of the optimum shape near the critical points was performed for arbitrary Reynolds numbers.
KeywordsMathematical Modeling Reynold Number Mechanical Engineer Optimality Condition Industrial Mathematic
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