A Modified Upwind Scheme for Convective Transport Equations and the Use of a Conjugate Gradient Method for the Solution of Non-Symmetric Systems of Equations

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Abstract
A modified upwind scheme for convective-diffusion equations, which combines the advantages of being stable and of second order is considered. Comparisons are made with the central difference and the usual upwind schemes as well as with a scheme proposed by Il'in (1969) and Barrett (1974). Some methods for the solution of the arising non-symmetric systems of equations are also studied. Modified incomplete factorization algorithms combined with a minimum residual conjugate gradient method have turned out to need only a slight increase in the computational complexity in comparison with a corresponding symmetric problem.