Numerical study of laminar flow past one and two circular cylinders.

*(English)*Zbl 0721.76049Summary: A finite element program was developed in order to simulate the vortex shedding behind one or two circular cylinders. The velocity-pressure formulation was used to solve the unsteady, two-dimensional, incompressible Navier-Stokes equations. The characteristics of the time integration schemes (implicit-Euler and Crank-Nicolson) were studied. Using the Crank-Nicolson scheme, the classical von Kármán vortex street was found in the solution of the Navier-Stokes equations. The drag lift coefficients as well as the Strouhal number calculated from our numerical data for Re\(\leq 500\) were compared both with experimental and numerical results and good agreement was observed. The critical Reynolds number \(Re_ c\) found in the present study was well within the range of experimental measurements. Flow past two circular cylinders arranged behind one another at different intervals was also studied for \(Re=100\). The pressure distributions around the upstream and downstream cylinders together with their vortex shedding frequencies as a function of cylinder interval were determined and compared with the experimental values. Discontinuity changes in the flow pattern, the Strouhal number and the pressure distribution were detected.

##### MSC:

76M10 | Finite element methods applied to problems in fluid mechanics |

76D10 | Boundary-layer theory, separation and reattachment, higher-order effects |

##### Keywords:

finite element program; unsteady, two-dimensional, incompressible Navier- Stokes equations; time integration schemes; Crank-Nicolson scheme; classical von Kármán vortex street
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\textit{J. Li} et al., Comput. Fluids 19, No. 2, 155--170 (1991; Zbl 0721.76049)

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