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On the Numerical Calculation of Nonlinear Residual Equations

In recent years, nonlinear ‘residual’ forms of the Navier-Stokes equations have been proposed for theoretical and computational analysis of unsteady flow and noise. In this approach, the flow variables are split into a user-specified base flow and the remaining residual flow. The ‘residual’ equations that govern the nonlinear evolution of the residual flow are obtained by removing the chosen base flow from the unsteady Navier-Stokes equations. Because there is no restriction on the choice of the base flow, the time-averaged mean flow is composed of contributions from the base and the residual flow components. In this work, the zero-average form of the residual equations is presented, in which the time-averaged mean flow is the base flow and the residual flow must have a zero mean. A new Zero-average Source Term (ZEST) strategy for numerically converging the residual flow to a zero mean is demonstrated.