AbstractsMathematics

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 convective-dominated 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 highly convective 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 counterpart in solving convective problems, both according to stability and accuracy. Analytic and numerical results show that the natural condition has big stability problems for high Reynolds numbers, which make the use of stabilization methods or damping regions crucial. But, the (Dong) stabilized natural condition does not improve accuracy, and damping regions are computationally expensive. The convective conditions show very good accuracy if its convection speed is approximated accurately, and our results indicate that it can be used without damping regions efficiently. Our results also show that 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 can not. ; I det här examensarbetet har vi implementerat och studerat effekterna av olika konvektiva randvillkor för spektralelement lösaren Nek5000 vid beräkningar av konvektivt dominanta flödesproblem. Med hjälp av numeriska tester bevisar vi att de nya implementationerna bevarar lösarens konvergens i både rum och tid. Vi studerar noggrannheten hos de konvektiva randvillkoren genom konvektivt dominanta testfall i form av en ensam virvel som propagerar genom utflödet, samt det klassiska Kármán-virvel-gata problemet. En detaljerad jämförelse med det naturliga randvillkoret tillhörande den svaga formuleringen av de inkompressibla Navier-Stokes ekvationerna (Nek5000 “O”) och en stabiliserad version av denna är också presenterade.   Våra resultat visar tydliga fördelar med att använda de konvektiva randvillkoren mot det naturliga vid lösningar av konvektiva problem, både stabilitetsmässigt och noggrannhetsmässigt. Analytiska och numeriska resultat visar att det naturliga randvillkoret har stora stabilitetsproblem vid höga Reynolds-tal, vilket medför att specifika stabilitetsversioner eller dämpningsregioner måste användas. Men stabiliserande naturliga randvillkor (Dong) förbättrar inte noggrannheten och dämpningsregioner är…