Nodes strictly inner

In this paragraph the wall function concept is outlined. The wall functions are empirical parameterizations of the mean flow variable profiles within the inner part of the wall boundary layers, bridging the fully developed turbulent log-law flow quantities with the wall through the viscous and buffer sublayers where the two-equation turbulence model is strictly not valid. These empirical parameterizations thus allow the numerical flow simulation to be carried out with a finite resolution within the wall boundary layers, and one avoids accounting for viscous effects in the model equations. Therefore, in the numerical implementation of the k-e model one anticipates that the boundary layer flow is not fully resolved by the model resolution. The first grid point or node used at a wall boundary is thus placed within the fully turbulent log-law sub-layer, rather than on the wall itself [95]. In effect, the wall functions amount to a synthetic boundary condition for the k-e model. In addition, the limited boundary layer resolution required also provides savings on computer time and storage. 

Because of the rectangular form of the initial domain, the operators Ai and A2 are self-adjoint, positive and commutative. It is straightforward to verify the relations A1A2 A2A1 and A1A2 / = A2A1J/ = the inner nodes of the grid. In view of this, the strict inequality A A2 > 0 is simple to follow. From the form (24) it seems clear that... 

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