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A finite-element study of the onset of vortex shedding in flow past variously shaped bodies. (English) Zbl 0639.76041
This paper examines the onset of periodic behavior in two-dimensional laminar flow past bodies of various shapes. The steady equations of motion are transformed into a set of nonlinear algebraic equations by means of a finite element method. These nonlinear equations are solved by Newton-ta solutions are shown to exist for a time interval dependent of \(\lambda\), a parameter proportional to the ion acoustic speed. For such data, solutions of (Z) converge as \(\lambda\to \infty\) to a solution of the cubic nonlinear Schrödinger equation \(iE_ t+\Delta E+| E|^ 2E=0\). We consider both weak and strong solutions. For the case of strong solutions the results are analogous to previous results on the incompressible limit of compressible fluids.

MSC:
76D25 Wakes and jets
76E99 Hydrodynamic stability
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