Grid-Convergence of Reynolds-Averaged Navier–Stokes Solutions for Benchmark Flows in Two Dimensions

Abstract

A detailed grid-convergence study has been conducted to establish reference solutions corresponding to the oneequation linear eddy-viscosity Spalart-Allmaras turbulence model for two-dimensional turbulent flows around the NACA 0012 airfoil and a flat plate. The study involved the three widely used codes CFL3D (NASA), FUN3D (NASA), and TAU (DLR, The German Aerospace Center), as well as families of uniformly refined structured grids that differed in the grid density patterns. Solutions computed by different codes on different grid families appeared to converge to the same continuous limit but exhibited strikingly different convergence characteristics. The grid resolution in the vicinity of geometric singularities, such as a sharp trailing edge, was found to be the major factor affecting accuracy and convergence of discrete solutions; the effects of this local grid resolution were more prominent than differences in discretization schemes and/or grid elements. The results reported for these relatively simple turbulent flows demonstrated that CFL3D, FUN3D, and TAU solutions were very similar on the finest grids used in the study, but even those grids were not sufficient to conclusively establish an asymptotic convergence order.

Grid Convergence for Three Dimensional Benchmark Turbulent Flows

“…CFL3D is a structured-grid, multiblock, cell-centered, finite-volume code widely applied for analysis of complex flows. It has been used for computing benchmark solutions in many recent workshops involving complex turbulent flows 12,[50][51][52][53] and at the TMR website. It uses second-order, upwind-biased spatial differencing scheme (a MUSCL scheme with the MUSCL coefficient κ = 1/3) that provides third-order accuracy in one dimension for the convection and pressure terms.…”

Unstructured Grid Adaptation and Solver Technology for Turbulent Flows

“…To identify and address the issues preventing grid convergence, a series of special sessions has been organized for the Evaluation of RANS Solvers on Benchmark Aerodynamic Flows [4]. This evaluation includes 2D test cases [5] and 3D test cases [6]. This effort uses a set of 3D test cases described on the Turbulence Modeling Resource (TMR) Website [7] as 3D Hemisphere Cylinder (new) and 3D ONERA M6 Wing with the Spalart-Allmaras (SA) turbulence model [8].…”

Numerical Simulation and Uncertainty Analysis of an Axial-Flow Waterjet Pump

“…It was shown that the differences between numerical and experimental results stemmed from modeling errors instead of numerical ones. Diskin et al [19] conducted a grid-convergence study of RANS simulations for the NACA 0012 airfoil and a flat plate by using three in-house codes and concluded that establishing an asymptotic converge order was more difficult than expected even with very fine grids. The authors also found that the grid resolution in the vicinity of geometric singularities, such as pointed leading/trailing edge, was essential to improve the accuracy and convergence property of CFD simulation.…”