Abstract
In this paper a staggered scheme for partitioned solution of a coupled three-dimensional solidification problem is presented. Coupling is considered between several thermal and mechanical phenomena that take place in a mould and in a casting solidifying in the mould cavity. Numerical solution is based on the finite element method in space and the finite difference method in time. Two independently developed solvers are used for transient solution of non-linear heat and stress problems, respectively. Each solver solves its problem in the entire computational domain, which covers the casting and the mould, and is coupled with the other solver. The solvers can advance with different time steps and the coupling data is exchanged at selected times. Effects of weak and strong coupling of solvers are investigated. Numerical results show great influence of bidirectional coupling on the results when compared to the results of unidirectionally coupled run of the two solvers. In the weak case the solution scheme is explicit. The partial results of one solver are communicated to the other solver every selected number of time steps to be used in some further steps. Strong coupling makes the scheme implicit as it involves interfield iteration until convergence of results given by the two solvers is reached. This improves accuracy but increases computation time. Comparison of accuracy gain thanks to strong coupling to the improvement obtained by simply reducing time step size is also included in the paper.