The continued increase in the storage density of hard disk drives requires corresponding reduction of the thickness of the air bearing between the slider and the disk surfaces that provides the needed lubrication. The current thickness of the gas layer is already only an order of magnitude larger than the diameter of gas molecules. At such small spacing, the physical models that describe the air bearing phenomenon well at much larger spacing can no longer give predictions close to reality. As a result, it is important to have an improved lubrication model that works under the extremely rarified condition and is free of pressure singularities caused in some existing models by the unavoidable contact between the slider and disk surface at such small spacing. The industry also needs an efficient design code to help design the air bearing surfaces, to ensure that the sliders with the read/write elements attached at their trailing edge fly at desirable attitudes with respect to the moving disk. This thesis focuses on these two topics.; Two new lubrication equations are derived first. They are based on slip velocity assumptions at the gas-solid interface. The new equations are free of contact pressure singularities that some other existing models contain. The causes of these unphysical singularities are also studied.; Next the problem of accurate solution of the lubrication equation is addressed. Unstructured adaptive triangular mesh generation techniques that suit the particular geometry of slider air bearing simulation of hard disk drives are implemented. Different refinement and adaptation techniques are used to generate several levels of good quality mesh over sliders with complex rail shapes. The overall mesh generation procedure offers great flexibility and control over the quality and distribution of the generated mesh, which makes it superior to its much simpler structured counterpart. An explicit vertex based finite volume method based on Patankar's scheme is first constructed. Then the explicit scheme is extended to a fully implicit one. Unconditional stability of the scheme is achieved. A non-nested full approximation storage (FAS) multi-grid algorithm is then used to significantly speed up the convergence rate of the implicit finite volume scheme. The steady state flying attitude of the slider is obtained by a Quasi-Newton iteration method.; To further improve the efficiency and accuracy of the code, three other different multi-grid numerical schemes are presented. The so called flux difference splitting, the multi-dimensional upwind residue distribution and the SUPG finite element techniques are used to discretize the governing equation. Improved results are obtained.; Finally, the intermolecular force effect on the flying attitude of new ultra-low flying slider designs is investigated numerically. It is found that the van der Waals force has significant influence on the flying height and has non-negligible effect on the pitch angle for both positive pressure sliders and negative pressure sliders, when the flying height is below 5 nm. When the flying height is below 0.5 nm, the repulsive portion of the intermolecular force becomes important and also has to be included.
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