Erik Boström: Investigation of Outflow Boundary Conditions for Convection-Dominated Incompressible Fluid Flows in a Spectral Element Framework

In this thesis we implement and study the effects of different convective outflow boundary conditions for the high order spectral element solver Nek5000 in the context of solving highly convective fluid flow problems. By numerical testing we show that the convective boundary conditions preserve the spatial, and temporal convergence rates of the solver. We also study convective-dominant test cases such as a single vortex propagating through the outflow boundary, and the typical Kármán vortex shedding problem to analyze the accuracy and stability. A detailed comparison with the natural boundary condition that corresponds to the variational form of the incompressible Navier–Stokes equations (the Nek5000 “O” condition), and a stabilized version of it (by Dong et al. (2014)), are also presented. Our results show a major advantage of using the convective boundary conditions over the natural analog in solving convective problems, both in case of stability and accuracy. Analytic and numerical results show that the natural condition has big problems with stability for high Reynolds numbers, which make the use of stabilization methods or damping regions crucial. However, a stabilized natural condition gives stable results, but does not yield good accuracy. The convective conditions have very good accuracy if the convection speed is approximated accurately, and that the dissipation of the flow is negligible. Reflections follows from the accuracy of the boundary conditions. The magnitude of reflections significantly depends on the amplitude of the disturbances that move through the boundary. The convective boundary condition can handle large disturbances without producing significant reflections, while the natural one or a stabilized version of it in general cannot