Effect of Numerical Dissipation on Long Time Energy Dissipation Rate

When modeling fluids, accurately capturing the energy dissipation rate is vital to ensure the correct long time behavior of the simulation. Many popular turbulence models, e.g., eddy viscosity models, may overdissipate in the long time average, pushing flow to lower Reynolds number states. Other sources of dissipation, e.g., numerical dissipation can also contribute to incorrect behavior in simulations. Here, we examine the effect of numerical dissiaption on the long time energy dissipationr ate. A-stable timestepping methods, which are necessary for high Reynolds number simulations are known to be dissipative. We explore the effect of the time discretization on the energy dissipation rate for a simple numerical experiment for three dimensional flow.