Fictitious versus nonfictitious formulation of backward step flow

In this article we discuss the numerical results obtained by two methods to solve the incompressible viscous flow modelled by the Navier–Stokes equations for a backward step flow for Reynold’s number R e = 50 . In the first method we have used a nonfictitious formulation of the problem and compared the result with the alternating direction method obtained by Glowinski. In the second method we have considered the fictitious formulation of the same problem based on the distributed Lagrange multiplier method. Our goal is to observe its behavior at the nonsmooth points, both with matching and nonmatching boundary points. In the fictitious formulation the step is treated as a nonmoving obstacle present in a channel by extending the flow region to a simplified rectangular domain. In this study, we find that our results compare very well for this stationary problem with nonsmooth boundary. Our solution method combines the finite element method and the operator splitting scheme of the Marchuk–Yanenko type.