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A model is developed, and a difference scheme is constructed for obtaining the vertical turbulence coefficient. The scheme is based on a mathematical analysis of the 'b-δ' turbulence model and a suitable choice of input parameters.

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C e n t r u m v o o r W i s k u n d e e n I n f o r m a t i c a MAS Modelling, Analysis and Simulation Modelling, Analysis and SimulationDifference schemes for the class of singularly pertubed boundary value problems I. Rafatov, S.N. Sklyar Difference schemes for the class of singularly perturbed boundary value problems ABSTRACT This work deals with the construction of difference schemes for the numerical solution of singularly perturbed boundary value problems, which appear while solving heat transfer equations with spherical symmetry. The projective version of integral interpolation (PVIIM) method is used. Derived schemes allow to approximate the solution of the problem and the derivatives of the solution at the same time. Moreover, they allow to approximate the boundary conditions of general form in the framework of the same method. New schemes are tested in order to compare them with well known difference schemes. Estimates for rates of classical and uniform convergence are carried out. This work deals with the construction of difference schemes for the numerical solution of singularly perturbed boundary value problems, which appear while solving heat transfer equations with spherical symmetry. The projective version of integral interpolation (PVIIM) method is used. Derived schemes allow to approximate the solution of the problem and the derivatives of the solution at the same time. Moreover, they allow to approximate the boundary conditions of general form in the framework of the same method. New schemes are tested in order to compare them with well known difference schemes. Estimates for rates of classical and uniform convergence are carried out. REPORT MAS-R0310 SEPTEMBER 2003