Iterative solvers and inflow boundary conditions for plane sudden expansion flows

Incompressible laminar flow in a symmetric plane sudden expansion is studied numerically. The flow is known to exhibit a stable symmetric solution up to a critical Reynolds number above which symmetry-breaking bifurcation occurs. The aim of the present study is to investigate the effect of using different iterative solvers on the calculation of the bifurcation point. For this purpose, the governing equations for steady two-dimensional incompressible flow are written in terms of a stream function-vorticity formulation. A second order finite volume discretization is applied. Explicit and implicit solvers are used to solve the resulting system of algebraic equations. It is shown that the explicit solver recovers the stable asymmetric solution, while the implicit solver can recover both the unstable symmetric solution or the stable asymmetric solution, depending on whether the initial guess is symmetric or not. It is also found that the type of inflow velocity profile, whether uniform or parabolic, has a significant effect on the onset of bifurcation as uniform inflows tend to stabilize the symmetric solution by delaying the onset of bifurcation to a higher Reynolds number as compared to parabolic inflows.