Residual-based Methods for Controlling Discretization Error in CFD.

摘要

Computational Fluid Dynamics (CFD) has enormous potential to impact the analysis, design, and optimization of U.S. Air Force flight systems. The objective of our work is to develop and demonstrate methods for the reliable and automatic control of discretization error in CFD. Our approach will provide designers and analysts with techniques to quantify and reduce discretization error in CFD predictions without the overhead of creating, and solving on, multiple meshes. Our work will lead to significant improvements in the accuracy and efficiency of CFD predictions of aerodynamic loads. We will investigate the following residual-based discretization error estimation techniques unified within the PI's generalized truncation error estimation framework: discretization error transport equations, defect correction methods, and adjoint methods. We will also develop mesh adaptation techniques wherein the mesh is automatically adapted to reduce discretization error in the solution or solution functionals (i.e., aerodynamic loads). The adaptation will be driven by the residuals/truncation errors, which serve as the local source of discretization error, rather than ad hoc solution features (e.g., gradients, shock waves).