A coupled finite volume method for the computational modelling of mould filling in very complex geometries

Simulation of shape casting processes involves the simultaneous capture of the rapidly developing metal–air free surface and the liquid–solid moving boundary in the metal phase. Although a wide range of techniques have been developed to address this problem, there are occasions where existing techniques are limited, especially in very complex geometries where the mesh quality may inevitably be relatively poor at some key locations. Cell-centred finite volume methods, typical of most commercial CFD tools, are computationally efficient, but can lead to convergence problems on meshes that feature cells with highly non-orthogonal shapes. The control volume–finite element method uses a vertex-based approach and handles distorted meshes with relative ease, but is computationally expensive. A combined vertex-based–cell-centre technique, described in this paper, solves the flow field at the cell or element vertex, and all other variables are solved at the cell centre (as in conventional CFD tools). This flow solver strategy is much more tolerant of meshes with poor quality elements, allowing solutions on distorted meshes where purely cell-centred solutions procedures fail. The combined method enables the solution of simultaneous free surface flows coupled with solidification in very complex meshes, thus enabling the capture of such behavior in arbitrarily complex geometrical structures. It is relatively straightforward to embed within generic CC based CFD tools allowing it to be employed in a wide variety of processing applications.