Vorticity–velocity formulation of the 3D Navier–Stokes equations in cylindrical co‐ordinates |
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Authors: | Martin O L Hansen Jens Nrkr Srensen Wen Zhong Shen |
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Institution: | Martin O. L. Hansen,Jens Nørkær Sørensen,Wen Zhong Shen |
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Abstract: | A finite difference method is presented for solving the 3D Navier–Stokes equations in vorticity–velocity form. The method involves solving the vorticity transport equations in ‘curl‐form’ along with a set of Cauchy–Riemann type equations for the velocity. The equations are formulated in cylindrical co‐ordinates and discretized using a staggered grid arrangement. The discretized Cauchy–Riemann type equations are overdetermined and their solution is accomplished by employing a conjugate gradient method on the normal equations. The vorticity transport equations are solved in time using a semi‐implicit Crank–Nicolson/Adams–Bashforth scheme combined with a second‐order accurate spatial discretization scheme. Special emphasis is put on the treatment of the polar singularity. Numerical results of axisymmetric as well as non‐axisymmetric flows in a pipe and in a closed cylinder are presented. Comparison with measurements are carried out for the axisymmetric flow cases. Copyright © 2003 John Wiley & Sons, Ltd. |
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Keywords: | vorticity– velocity formulation Cauchy– Riemann equations treatment of polar singularity in cylindrical co‐ordinates |
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