Iterative Errors in Unsteady Flow Simulations - Are they Really Negligible?

The numerical solution of a statistically steady flow problem is typically obtained in an iterative process. For a given mathematical model, including boundary conditions, the accuracy of the solution is governed by spatial resolution of the grid, spatial discretisation schemes and the convergence tolerance, which says when the solution is considered to have reached a steady state. Next to hardware quality (round-off error), the discretisation error and the iterative error determine the quality of the solution. For unsteady flow problems matters are more complicated. Temporal and spatial resolution have to be chosen carefully in proper balance. Moreover, in high Reynolds number (turbulent) flows, time integration is usually performed with implicit schemes, which require the solution of a non-linear system of equations at each time step. Again a convergence tolerance is needed to decide on when having solved this nonlinear system well enough. Any iterative error propagates to the next time step. How does one guarantee reliability of the results? A Workshop dedicated to Iterative Errors in Unsteady Flow Simulations was held at the ASME V&V Symposium of 2017. The main goals of this Workshop were to create awareness to the problem and to check if different flow solvers exhbited the same trends in the solution of a laminar, two-dimensional flow of an incompressible fluid around a circular cylinder. Five groups submitted results using respectively ANSYS Fluent, ANSYS CFX, OpenFoam, ReFRESCO and SATURNE. A significant influence of the convergence criteria applied at each time step on the numerical accuracy of the solution was experienced by all participants. This paper summarizes the main results of this first Workshop on Iterative Errors in Unsteady Flow Simulations. It presents a brief description of the proposed test case and the selected quantities of interest and an overview of some of the submitted data, which are available at Workshop (2017). The paper is also meant as an encouragement for participants of the NUTTS symposium to take part in the second edition of the Workshop that will take place at the ASME V&V Symposium of 2018.