Adaptive multilevel method for the air bearing problem in hard disk drives

An adaptive grid-generating algorithm is constructed and integrated with the multigrid method to form a numerical scheme that suits slider air-bearing simulation of hard disk drives. The relative truncation error, a by-product of the multigrid method, is used in grid adaptation criteria. Finer meshes are constructed over nodes of the current finest grid where the relative truncation error exceeds a predetermined tolerance. The union of these finer meshes forms a new level of grid, which may not cover the entire domain of the coarse grid underneath. The final grid system thus constructed is composed of levels of uniform grids with decreasing mesh sizes. This composite grid structure incorporates with numerical resolution as needed and efficiency of computation. A shaped rail, negative pressure slider is used to demonstrate the effectiveness of this numerical scheme. Compared with the traditional multigrid method, the proposed adaptive multilevel method can significantly reduce the computation work for achieving the same level of accuracy.