Resolving non‐symmetry in flows via subdomain shifts

Abstract

In this study, non‐symmetric flow problems are modeled by selecting subdomains and shifting them in such a way that the symmetry is recovered. As a result, the domains are made of simple grid structures and re‐generation of mesh is avoided. Three test problems with various decomposition characteristics, namely, translation, rotation and deformation are selected, and they are analyzed in different flow regimes. To study the internal flow between eccentric cylinders, two cylindrical concentric subdomains are considered, one translated relative to the other. Hence, a simple polar‐coordinates mesh can be utilized instead of generating a mesh for the solution domain between the eccentric cylinders of the original problem. External flow around a curvature tube is studied shifting the subdomain around the object in rotation, relative to the outer domain thus avoiding a re‐generation of the mesh as the angle‐of‐attack changes. A third example involves deformation of an object exposed to natural convection, and the shifting of the domain facilitates the iteration process as the object deflects. Systems of nonlinear equations are solved within Newton‐Krylov framework using the matrix‐free approach. Geometrical and physical parameters are used to improve the solution process. Several results are provided to show the applicability of proposed method.

First published online: 09 Jun 2011

Keyword : Newton‐Krylov, matrix‐free, translation, rotation, deformation