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Overview of the 2018 Workshop on Iterative Errors in Unsteady Flow Simulations

Two Workshops were held at the ASME V&V Symposiums of 2017 and 2018 dedicated to Iterative Errors in Unsteady Flow Simulations. The focus was on the effect of iterative errors on numerical simulations performed with implicit time integration, which require the solution of a non-linear set of equations at each time step. The main goal of these Workshops was to create
awareness to the problem and to confirm that different flow solvers exhibited the same trends. The test case was a simple two-dimensional, laminar flow of a single-phase, incompressible, Newtonian fluid around a circular cylinder at the Reynolds number of 100. A set of geometrically similar multi-block structured grids was available and boundary conditions to perform the simulations were proposed to the participants. Results from seven flow solvers were submitted, but not all of them followed exactly the proposed conditions. One set of results was obtained with adaptive grid and time refinement using triangular elements (CADYF) and another used a compressible flow solver with a dual time stepping technique and a Mach number of 0.2 (DLR-Tau). The remaining five submissions were obtained with five different incompressible flow solvers (ANSYS CFX 14.5, pimpleFoam, ReFRESCO, SATURNE, STAR CCM+ v12.06.010-R8) using implicit time integration in the proposed grids. The results obtained in this simple test case showed that iterative errors may have a significant impact on the numerical accuracy of unsteady flow simulations performed with implicit
time integration. Iterative errors can be significantly larger (one to two orders of magnitude) than the residuals and/or solution changes used as convergence criteria at each time step. The Courant number affected the magnitude of the iterative errors obtained in the proposed exercise.
For the same iterative convergence criteria at each time step, increasing the Courant number tends to increase the iterative error.