An improved implicit finite‐difference scheme for boundary‐layer flows

The paper presents a modification to two well‐known non‐iterative implicit finite‐difference schemes for confined and unconfined boundary‐layer‐type flows. The modification aims at improving the accuracy of these schemes by reducing the adverse effect of linearization, which is inherent in both of them. Using the present improved scheme, the same level of accuracy of the results could be obtained with large mesh sizes in the flow direction (coarse grid). The modification is done by adding a local iterative procedure at each computational step in the flow (marching) direction. As an example, to demonstrate the proposed modification, the simple case of developing forced convection in the entry region of concentric annuli has been considered. The results are presented, which prove the applicability of the proposed modification and show its effect on the obtained accuracy and on the required computer time.