Adaptative remeshing for viscous incompressible flows

This paper presents an adaptive finite element procedure for solving viscous incompressible flows. The methodology is based on adaptive remeshing for steady-state problems. The Navier-Stokes equations for an incompressible fluid are solved in primitive variables by an Uzawa algorithm using a highly accurate element. The efficiency and convergence rate of the adaptive strategy are evaluated by solving problems with known analytical solutions. Finally, the methodology is applied to the flow over a backward-facing step and predictions are compared with experimental measurements. The use of the proposed adaptive procedure is shown to lead to improved accuracy of the finite element predictions. Nomenclature C = a constant e - error in the solution h - element size /(•) = dissipation energy n = number of elements in the mesh p = pressure 5 - step and fence height U = velocity vector u, v = velocity components x, y = coordinates V = gradient operator 6 = element size predicted by adaptation module e = strain rate tensor = 1A( V U + V UT) a = stress tensor = 2/*e £ = similarity variable in a boundary layer t - relative error on a mesh H = absolute viscosity of the fluid v - kinematic viscosity of the fluid