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<< JRScience Home     Volume 15 No.3   December 2004     << Back to Volume Home


K. S. Syed1, G. E. Tupholme2 and A. S. Wood2

1CASPAM, Bahauddin Zakariya University, Multan, Pakistan.

2Department of Mathematics, University of Bradford, Richmond Road, Bradford, West Yorkshire  BD7 1DP.

Abstract: A difference-based numerical algorithm is developed to efficiently solve a class of elliptic boundary value problems up to any desired order of accuracy. Through multi-level discretization the algorithm uses the multigrid-concept of nested iterations to accelerate the convergence rate at higher discretization levels and exploits the advantages of extrapolation methods to achieve higher order accuracy with less computational work. The algorithm employs the SOR method to solve the discrete problem at each discretization level by using an estimated optimum value of the relaxation parameter. The advantages of the algorithm are shown through comparison with the simple discrete method for simulations of fluid flows in finned circular ducts.

Keywords: Fluid flow, finned tubes, multigrid-concept, relaxation parameters.