A Novel Alternating Cell Directions Implicit Method for the Solution of Incompressible Navier Stokes Equations on Unstructured Grids

Abstract

In this paper, A Novel Alternating Cell Direction Implicit Method (ACDI) is researched which allows implementation of fast line implicit methods on quadrilateral unstructured meshes. In ACDI method, designated alternating cell directions are taken along a series of contiguous cells within the unstructured grid domain and used as implicit lines similar to Line Gauss Seidel Method (LGS). ACDI method applied earlier for the solution of potential flows is extended for the solution of the incompressible Navier-Stokes equations on unstructured grids. The system of equations is solved by using the Symmetric Line Gauss-Seidel (SGS) method along the alternating cell directions. Laminar flow fields over a single element NACA-0008 airfoil are computed by using structured and unstructured quadrilateral grids, and inviscid Euler flow solutions are given for the NACA-23012b multielement airfoil. The predictive capability of the method is validated against the data taken from the experimental or the other numerical studies and the efficiency of the ACDI method is compared with the implicit Point Gauss Seidel (PGS) method. In the selected validation cases, the results show that a reduction in total computation between 18% and 23% is achieved by the ACDI method over the PGS. In general, the results show that the ACDI method is a fast, efficient, robust and versatile method that can handle complicated unstructured grid cases with equal ease as with the structured grids.