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Uniform flow past a closed body at low Reynolds number employing a novel matching in a boundary element formulation. (English) Zbl 1464.76083

Summary: Consider a two dimensional steady low Reynolds number flow past a circular cylinder. A boundary integral representation that matches an outer Oseen flow and inner Stokes flow is given, and the matching error is shown to be smallest when the outer domain is as close as possible to the body. Also, it is shown that as the Greenâs function is approached, the oseenlet becomes the stokeslet to leading order and has the same order of magnitude error as the matching error. This means a novel boundary integral representation in terms of oseenlets is possible. To test this, a corresponding boundary element code is developed which uses point collocation weighting functions, linear shape functions, two-point Gaussian quadrature with analytic removal of the Greenâs function singularity for the integrations. The method is compared against various methods for the benchmark problem of flow past a circular cylinder. In particular, the drag coefficient is used for the comparison. The advantage of this method over existing ones is demonstrated and discussed particularly in the Reynolds number range \(\operatorname{Re}=1\sim 4\).

MSC:

76M15 Boundary element methods applied to problems in fluid mechanics
65N38 Boundary element methods for boundary value problems involving PDEs
76D25 Wakes and jets
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References:

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