Development of numerical analysis method based on staggered grid for arbitrary 3-dimensional mesh shape for two-phase three-field model

Abstract

Paper presented at the 9th International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics, Malta, 16-18 July, 2012.Numerical analysis method for an unstructured staggered grid system for 3-field two-phase flow model was developed. Because of the complex definition of staggered volume and corresponding variables, commercial computational fluid dynamics codes usually adopt a collocated grid system for the analysis of complicated domain. In the conventional staggered grid system the staggered cell takes the halves of the neighboring two scalar cells. However, this study takes the whole of the two neighboring cells for the definition of the staggered cell. Finite volume method over this staggered grid system was implemented with some creative vector algebra and calculus. Time advancement was based on the semi-implicit method. This numerical treatment was successfully applied and the numerical tests show the effectiveness of this approach. This approach decreases the interpolation calculation to obtain not-solved-variables at cell or face. Only the diffusion terms require the interpolation, which is thought to be of minor importance.