A Parallel algorithm for thixoforming oriented computations

Abstract

Numerical simulation of complex phenomena such as semi-solid flow requires a high computational power. Due to the two phase nature of the material and time dependent properties the simulation requires repeated solution of various differential transport equations in a time stepping procedure. Particularly, owing to highly non-linear rheological properties of semi-solid material, a solution of the momentum conservation equation offers the best stability when using the direct solution of the pertinent equations. As the computational cost grows with the size of a simulation problem with a power of two or grater, this is a serious “bottleneck” particularly for a 3D problem in obtaining results with a satisfactory accuracy. Such intensive computation requires advanced computer techniques such as the parallel computing. In this work a new parallel algorithm is developed specially oriented for the thixoforming process simulation with the two-phase approach. The computational speedup for various mesh renumbering options is determined with up to eight CPUs. An experiment described thoroughly in the literature (1), was chosen here for the illustration of the computations with use of the own numerical model (2) modified here to account for some elastic properties.