  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.

Computational Physics