This thesis describes the development and implementation of a dynamic adaptive grid method for general two and three dimensional static and transient fluid flow problems solved over structured grids. The technique automatically manipulates the location of grid points within the domain of interest to concentrate cells in regions of high solution activity, thus aiming to improve the accuracy of the overall simulation for a given number of initial grid cells. To achieve this aim the Laplace Poisson Equidistribution equation is used. Furthermore, the work also covers different types and treatment of weight functions needed to represent areas of high solution activity and a range of techniques necessary to make the use of adaptive grids practical, including geometry modelling and grid quality control. The technique is implemented on simple functions and within the commercial CFD code PHOENICS, on fluid flow problems ranging from convection driven flows to shock capturing. The ability of the technique to be used for general grid manipulation is demonstrated by using it to couple PHOENICS with a stress code in the simulation of a deflecting beam in a uniform flow. In addition, a novel technique to adapt grids to solution phenomena using neural nets is demonstrated
