A Hybrid CFD Discretization Error Estimation Method and Its Application

A hybrid error estimation method integrating adjoint theory and Richardson extrapolation is proposed to address the discretization error estimation issue in computational fluid dynamics (CFD). Conventional Richardson extrapolation relies on multiple consistently refined grids, which is costly and struggles to capture local error effects. While the adjoint method enables local error estimation, its accuracy is constrained by approximate solutions on an embedded fine grid. The present approach identifies flow-sensitive regions through adjoint-based error estimation, guides adaptive mesh refinement to automatically generate a series of grids, and subsequently employs Richardson extrapolation to obtain a grid-independent solution, thereby achieving quantitative assessment of discretization errors. Applied to a transonic case of the CHN-T1 transport aircraft, coarse, medium, and fine grids are generated via two adaptive refinement steps. The extrapolated results show good agreement with official reference data and high-resolution grid solutions, with a drag coefficient error within 2 counts. This method reduces the manual cost of grid generation and enables efficient, automated error estimation, providing an effective tool for the verification and validation of CFD simulations for complex geometries.