ABSTRACT
This chapter describes the fundamentals of the SIMPLE method based on non-orthogonal grids and also introduce the transformed volume of fluid (VOF) method for free surface tracking in the body-fitted coordinate system. Algorithms based on the body-fitted coordinate system using non-orthogonal grids have been developed to overcome the limitations and increasingly applied to model fluid flow problems. The SIMPLE algorithm coupled with the VOF method based on the body-fitted coordinate system has been developed for modelling the mould filling process for thin-walled and curved-shape castings. In fluid flow modelling based on the body-fitted coordinate system, the use of non-staggered or collocated grids for velocity components becomes more popular than the use of staggered grids. In order to apply the body-fitted coordinate system to the SIMPLE method, the transformation of the integral form of transport equation also needs to be carried out corresponding to the transformation of a physical domain to a computational domain.
