A grid stretching technique for efficient capturing of the MHD boundary layers

The purpose of this paper is to present a technique for creating a stretched grid targeted for the simulation of internal MHD flows, using a custom algebraic stretching function. The advantages of the present stretching technique lie in the fact that the function can cluster near the walls in such way, so that a desired number of grid points is placed within the thin MHD boundary layers for efficient capturing of the steep velocity gradients, while having smaller overall grid size compared with other stretching functions. This was achieved by using a two-parameter stretching function and employing an estimation of the boundary layer thickness that is well suited for MHD flows. The efficiency of the present technique is demonstrated via a comparison with a stretching function available in the bibliography, in terms of the total grid size that is required to accurately capture the MHD boundary layers. The results show that the reduction of the total grid size can reach up to 93.6%, which minimizes the cross-sectional computational cost. The present technique can easily be adapted for flows with known boundary layers, especially in cases where the layers are thin and require a very fine mesh close to the boundaries of the domain.