FINITE-DIFFERENCE APPROXIMATIONS OF THE VORTICITY OF LAMINAR FLOWS AT SOLID SURFACES,
Abstract
Finite-difference methods for solving the Navier-Stokes equations by means of the stream function-vorticity formulation require the computation of the vorticity on solid surfaces with the aid of one-sided difference schemes. Several such schemes of second-order accuracy in the vorticity are derived for asixymmetric flows in orthogonal coordinate systems. Their accuracies are examined by comparing the appropriate solutions with the exact values of flows past oblate spheroids for vanishing Reynolds numbers (Oberbeck solution). It is found that if exact values of the solution are used at the inner points, the various approximations of the surface vorticity differ considerably from each other, and that the main source of error is the use of numerical derivatives. However, if the various methods of computing the surface vorticity are incorporated in an overall numerical scheme, the distinctions among them are reduced considerably. Errors in the drag coefficients computed by the various methods are an order of magnitude smaller than those of the surface vorticity. Experiments with numerical stability reveal that the diffusion process near the solid surface dominates the numerical stability properties of the scheme used. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Apr 01, 1970
- Accession Number
- AD0706328
Entities
People
- Hans J. Lugt
- Yermiyahu Rimon