Physics – Computational Physics
Scientific paper
2003-08-04
Physics
Computational Physics
16 pages, 7 figures, 4 tables. New submission: corrected typos, formulas (14') and (15') have been added
Scientific paper
To study and develop wall-functions for low-Reynolds-number models, a model linear equation is introduced. This equation simulates major mathematical peculiarities of the low-Reynolds-number model including a near wall sub-layer and transition region. Dirichlet and Newman boundary-value problems are considered. The standard and analytical wall-functions are investigated on different properties including the mesh sensitivity of a solution. A Robin-type interpretation of wall functions as boundary conditions is suggested. It is shown that solution of a problem is mesh independent and more accurate in this case. General type analytical and numerical wall-functions are developed on the basis of a boundary condition transfer. An effective numerical method of decomposition is suggested. The method can be used in application to either high-Reynolds-number models with the numerical wall-functions or low-Reynolds-number models directly. Although a model equation is considered, the formulas, methods and conclusions are valid and can be directly used for real low-Reynolds-number equations.
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