Study of differential operators in the context of the semi-analytical wall boundary conditions

In this paper the semi-analytical wall boundaryconditions by Ferrand et al. [1] are investigated theoreticallyby looking at the property of skew-adjointness in a continuoussetting. As stabilizing procedure a volume diffusion term [2] isused and a new interpretation for it is given in the Reynoldsaveraged context. Additonally, a correction term for externalforces is presented. The final theoretical contribution concernsarbitrary order Robin boundary conditions. The theoreticalconstructs are then investigated in various confined and free-surface flows. The issue of convergence is illustrated in the case ofPoiseuille flow, the external force correction terms in the volumediffusion term and the boundary conditions are demonstratedvia still water simulations. Finally, a standing wave and a dam-break over a wedge is simulated and quantitative comparisonsare given. The paper is concluded by highlighting the difficultiesassociated with the extension to three dimensions as well as givingan insight into the current developments.