A new approximate factorization method suitable for structured and unstructured grids

Abstract

Further modification of a novel numerical method named as the "Alternating Cell Directions Implicit" (ACDI) was made using an ADI type approximate factorization method for the space-time integration. The original ACDI method was similar to the classical the Line Gauss-Seidel (LGS) method. In this method, designated alternating directions are not along curvilinear coordinates as in the classical ADI method, but rather along a series, or a chain of contiguous cells, ie. 'cell directions' that is amenable to unstructured grids as well as the structured grids. In this study, a cell-centered finite volume formulation of the ACDI method utilizing the ADI methodology is presented for potential flows simulating heat diffusion between two parallel plates. Present results demonstrate the implementation of the ADI algorithm for the structured grids. Further work is necessary to prove its suitability for both the structured and unstructured grids in terms of convergence, accuracy and run times.