Lid driven flow field statistics: A non-conforming finite element Simulation

• Published in: Physica A 2019-08, Vol.528, p.121198, Article 121198
• Main Authors: Mahmood, R., Kousar, N., Rehman, Khalil Ur, Mohasan, M.
• Format: Article
• Language: English
• Subjects: Driven-cavity; Finite element method; Non-conforming finite element; UMFPACK
• ISSN: 0378-4371; 1873-2119
• DOI: 10.1016/j.physa.2019.121198

In this paper, we implement the non-conforming finite elements for the simulation of two dimensional incompressible Newtonian fluid flows. The classical driven cavity benchmark problem is simulated on a very fine uniform grid. In order to discretize the governing partial differential equations (PDEs) we employ the rotated bilinearQ˜1element for velocity and piecewise constant Q0element for the pressure on the general quadrilateral meshes. In L2-norm this pair is 2ndorder accurate for velocity and provides 1st order accuracy for pressure approximations. For the solution of non-linear systems arising from the discretization, Newton’s method is used as an outer nonlinear iteration and for the inner linear sub problems, the direct solver UMFPACK is utilized. The results have been compared with the reference data present in the literature and a good agreement is found. •An incompressible Navier–Stokes equations are simulated for a square cavity.•The non-conforming finite element method is adopted to report the solution.•The rotated bilinear element is carried for velocity approximation.•The UMFPACK directory is chosen to solve the associated linearized sub-problems.•Kinetic energy in the cavity at various Reynolds number is evaluated.