Numerical methods are utilised to reproduce the evolution of a system observed in natural phenomena. Within the area of materials science there is an increase of interest in modelling techniques that can accurately predict the microstructure of a material subject to various processing conditions. Recently, there is a requirement of techniques that have the ability to be applied to systems involving microstructural change in the presence of fluid flow. This presents a challenge since the forces governing these processes involve those predominately influenced by thermodynamics as well as those influenced by hydrodynamics. The phase-field method, a popular technique used in this area, has been shown to have the ability to cope with phase transformation dynamics such as solidification and solid-state phase transformations. However, its predictive capabilities mainly apply to a flow free environment where flow effects are minimal compared to other effects. Other techniques such as smoothed particle hydrodynamics exist that are more than capable of describing the mechanisms of flow demonstrating superiority in many complex flow problems. The thermodynamic quantities related to the evolution of a system to which this method is applied must then be consistent in order to be translated between models. This thesis develops the tools necessary to deal with phase growth and microstructural change within the presence of flow. This is done by developing phase-field models that can efficiently deal with displacive transformations in steels as well as diffusive, and SPH models with the ability to be coupled with thermodynamics. The phase-field models are developed to be applied to structure growth observed at relatively low temperatures within steels, namely martensite and bainite growth. The SPH method is analysed in order to assess and provide solutions for consistency when considered for coupling with models mainly dependent on thermodynamics.