Introduction

To solve governing equation of motions, we need to resolve all the excited length and time scales. However, even to solve flow past a flat plate, if one takes uniform grid to accommodate the smallest energy carrying length scales, one would be forced to take too many grid points. Numerical solution of the Euler and Navier–Stokes equations for external flow problems requires an outer boundary far away, where some asymptotic boundary conditions apply. This also adds larger requirement on the grid points. Such large problems are poorly convergent and hence, not within the range of the available resources of prevalent high performance computing platforms. This is circumvented by using non-uniform grids. For example, we may decide to take finer grids inside the shear layer (or within the inner layer of a turbulent boundary layer), and take fewer points in the inviscid part of the flow. With nonuniform grids in the physical plane, we usually transform the governing equation in the computational plane, where the spacing is uniform. This also makes writing a code much easier, because of the uniform grid in transformed plane. One needs to write a single code for the transformed plane problem, and for flow past different geometries, one uses the same code provided one can generate a grid mapping from the physical to the transformed plane. Thus, the main solver is grid-independent, and all one needs to do is to generate an appropriate grid transformation either analytically or numerically.