Heat transfer in multi-block grid during solidification: Performance of Finite Differences and Finite Volume methods

Abstract

A multi-block grid generated by bilinear interpolation is applied in combination with a generalized curvilinear coordinates system to a complex geometry in a casting solidification scenario. To model the phase change a simplified two-dimensional mathematical model was used based on the energy differential equation. Two discretization methods: finite differences and finite volume were applied in order to determine, by comparison with experimental measurements, which works better in these conditions. A good agreement between both discretization methods was obtained with a slight advantage for the finite volume method. This could be explained due to the use of more information by the finite volume method to compute each temperature value than the finite differences method. Conclusion can be drawn that the multi-block grid in combination with a generalized curvilinear coordinates system has considerably advantages such as: any physical feature of the cast part or mold can be straightforwardly defined and obtained in a specific zone of the domain, better capacity to describe the contours through a lesser number of elements, which considerably reduces the computational time. Moreover, the difficulty of the several virtual interfaces created by the geometry division are easily overcome by the continuity condition, and straightforwardly programming. This technique could also be an excellent choice for parallel computation, being each block or blocks affected to a physical processor.