Discretization Error Estimation by the Error Transport Equation on Unstructured Meshes - Applications to Viscous Flows

摘要

In this study, we apply the error transport equation (ETE) to steady viscous problems, including the Navier-Stokes equations in 2D, on general unstructured meshes, as an extension to the methodology for simpler model problems. The ETE is an auxiliary partial differential equation (PDE) derived from the primal one. We compare the accuracy of the resulting discretization error estimate from the linearized ETE and nonlinear ETE to solving the higher order primal problem, and results are consistent with simpler models from previous studies. Here we also investigate the efficiency of the approaches for a given level of error. It is found that for certain choices of discretization orders, the linearized ETE can be more efficient in terms of computation time than both the nonlinear ETE and the higher order primal problem in the best case by about a factor of two, when tested on problems with exact solutions or using manufactured solutions. The method was also applied to a NACA 0012 airfoil and efficiency was compared for some output quantities. Furthermore, the linearized ETE has the robustness properties of the lower order scheme, which is heuristically more robust than the nonlinear ETE or a higher order scheme, as several cases demonstrate.