A numerical technique for the prediction of fluid flow in three-dimensional domains is presented. The technique is based on local grid refinement and the current state of the mathematical framework as well as the numerical solution procedure based on the finite- volume methodology is reviewed. There follows an examination of various already existing formulations and techniques related to local grid refinement, and, thereafter desirable features of the proposed scheme are set out. The method is a finite-volume one employing the primitive variables and a collocated grid. It can be classed as a grid-embedding technique, but it is distinctive in that the coarse- and fine-grid domain are treated simultaneously over the whole computational domain. A computational molecule is selected which serves as an interface between regions of different grid-node density. Then, the discretisation procedure as well as the solution method for the linear equation system, arising from the discretisation, along with a novel approach to the treatment of the interfaces is presented. A user-friendly pre-processor has been developed to generate desired meshes with as many levels of refinement in any or all the co-ordinate directions. Access to the information required by the solution procedure is facilitated by a data structure especially arranged for this purpose. As far as the modelling of turbulence is concerned, a two equation model (k-e) is used. Example solutions are presented, illustrating the efficiency and stability of the method and verifying the fact that high levels of accuracy are obtainable using low-order discretisation schemes and without complex formulations. The proposed method is extendible to the prediction of two-phase flows and it will be particularly useful for the simulation of ambustión chambers where multiple burner arrangements and large variations in physical scale are common.