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A Numerical Method for the Incompressible Navier-Stokes Equations in Three-Dimensional Cylindrical Geometry.
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WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER
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The authors finite difference describe a method for solving the steady, three-dimensional, incompressible Navier-Stokes equations in cylindrical geometry. Also, they present results of computations in which this method is used determine the flow in fluid-filled cylinders undergoing spinning and coning motion. Second-order accurate central finite difference formulas are used to approximate derivatives in the radial and axial directions and a Fourier method is used to approximate the angular derivatives. Nonuniform grids are used to improve the resolution of the velocity and pressure near the cylinder walls. The system of difference equations are solved using an iterative method based on successive-over-relaxation. The method has been found to be very efficient in terms of both computer time and storage. Results of the numerical method applied to the flow in spinning and coning cylinders are presented for several cases for which experimental data are available. In addition, perturbation methods are used to study the data a t small coning speeds and small coning angles. Numerical results of this no-coning limit are compared with both the numerical data and experimental data at low coning conditions.
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