An adaptive mesh refinement using a-posteriori finite element error estimation

An a-posteriori adaptive estimator is presented and employed for solving vi scous incompressible flow problems. In an effort to detect local flow featu res and resolve flow details, an error estimation that is based on velocity angle is investigated, analyzed and benchmarked by an exact solution which is known as Kovasznay flow. It is found that the estimator is sensitive to the variations of the derivative of the velocity direction field, and it c an capture the region and refine grids where the velocity direction has abr upt changes. Unstructured grids are adapted by employing local cell divisio n as well as unrefinement of transition cells. The adaptive scheme is appli ed to flow over a cavity, flow past a backward-facing step, and flow past a n obstacle at different Reynolds numbers. The pressure oscillation which us ually occurs in advection-dominated flow cases is suppressed by adding more nodes at the most appropriate regions by using the velocity angle estimato r, The results exhibit good accuracy and justify the applicability of the a lgorithm.