Engineering Notes Grid Convergence Study of Two Dimensional Euler Solutions
G RID CONVERGENCE study always plays a fundamental role in verifying the reliability of computational fluid dynamics (CFD) methods in predicting aerodynamic performance. Roy [1] reviewed the code and solution verification procedures and summarized the generalized Richardson extrapolation as one of the error evaluation approaches. Recently, a lot of such efforts [2 4] have been carried out on the accuracy study of either numerical schemes or physical models in the past decades. Vassberg and Jameson [5] investigated the grid convergence trends of two dimensional Euler solutions on flow around the NACA 0012 airfoil. Computation was run until the residual reached machine level zero. Three well known flow solvers, including FLO82, OVERFLOW, and CFL3D, were compared. In their paper,Vassberg and Jameson [5] listed two problems. First, the residual convergence was found to stall at values well above machine level zero when Roe's flux difference scheme (FDS) [6] was adopted for OVERFLOW and CFL3D. The authors had to switch to other schemes instead. Second, a so called hyperconvergence was observed for the drag prediction of transonic nonlifting case. Note that all three solvers showed first order accurate at the transonic lifting condition.When the angle of attack (AOA) was zero, the convergence trend of CFL3D raised to second order as in the subcritical cases. The solver FLO82 even surprisingly gave an accuracy as high as 2.631, or hyperconvergence, according to the authors. Motivated by the aforementioned problems, a grid convergence study based on an in house flow solver NSAWET with Roe's FDS flux is presented. The purpose is to check whether the numerical convergence stall and hyperconvergence will happen to other CFD codes and to seek the possible explanations. II. Numerical Methods