Solidification Analysis by FVM on Irregular Grid

A method of numerical simulation of the solidification of castings, particularly of complicated shapes, is developed. The proposed method is based on the finite volume method (FVM) and uses an irregular grid system. The irregular grid system is obtained by the boundary fit method. The coordinates lines of the grid are formed to coincide with the complicated boundaries of the castings. Nodal points are placed inside the each cell of the grid. Using the local oblique Cartesian Coordinates which are formed by connecting neighboring nodal points, the energy balance equation is directly solved by the vector analysis technique in the generalized coordinates. Some calculation results of two-dimensional sections are shown and the accuracy of the method is checked. The proposed method has the following advantages : (1) The algorithm is simple and calculation time is short comparable to the conventional finite difference method (FDM), and (2) It can handle castings of complicated shapes which could not be handled by the conventional FDM.