The interaction between the melt flow and the developing mushy zone during solidification is still an issue that is not yet completely understood, although it plays an important role in the formation of microstructures and many other associated casting defects like macrosegregation, shrinkage porosity, hot tearing, etc. This interaction can be extremely complicated. The flow can modify the dendrite morphology and arm spacings by affecting the coarsening law, alter the growth kinetics of the dendrite tips, change the thickness of the mushy zone, induce the macrosegregation, cause fragmentation (branches, detachment and fragmentation), transport phases, and lead to remelting and grain-destruction. In turn, the influences of the mushy zone on the melt flow include: (1) modify the flow pattern (laminar or turbulence behaviour), (2) reduce or enhance the turbulence. In this thesis, the volume-average multiphase solidification model, as developed by Wu and Ludwig, is used and extended to study the flow-solidification interaction. Following major extensions are made. 1) A novel three-phase volume-average-based solidification model is introduced to simulate the formation of the intermetallic phase (??Al5FeSi) during the unidirectional solidification of an AlSi7Fe1 alloy under rotating magnetic field (RMF). The blocking effect of the ??Al5FeSi is considered through a modified anisotropic permeability formulation. Dendrite coarsening is coupled and its effect on the final macrosegregation and microstructure was studied. 2) A new model to treat the melting and grain destruction during globular equiaxed grains solidification is proposed. Both nucleation and destruction of equiaxed grains are considered. The inoculants serve as heterogeneous nucleation sites for the equiaxed grains. One re-melted/disappeared equiaxed grain will turn into one inoculant, which is reserved for a future potential nucleation site. In order to investigate the flow-solidification interactions, both the originally developed and newly-extended models are implemented on the unidirectional solidification simulations of AlSi7 and AlSi7Fe1 alloys under nature convection and/or forced convection conditions. It is not possible to cover all aspects of the aforementioned interactions in one thesis. Only several sub-topics are involved: (1) the role of mush permeability in the solidifying mushy zone; (2) geometrical effect on macrosegregation and microstructure formation; (3) effect of intermetallic phase precipitation and dendrite coarsening on macrosegregation; (4) remelting and grain destruction phenomena during solidification. All these simulations are verified by experiments qualitatively or quantitatively. Model-aided visualization of the flow-solidification interaction phenomena is of ultimate importance for metallurgists to get deep understanding of solidification fundamentals, and thus to control the casting defects and improve the product quality. Furthermore, the extended numerical models can be implemented in different casting techniques, such as continuous casting, mould casting, unidirectional solidification, welding, and additive manufacture.