Efficiency Improvements of RANS-Based Analysis and Optimization using Implicit and Adjoint Methods on Unstructured Grids

Abstract

The efficiency of an unstructured grid finite volume RANS solver is signicantly improved using two implicit methods based on diering philosophies. The LU-SGS multigrid method aims to improve performance, while maintaining the low memory requirements and robustness of an explicit scheme. The First-Order Krylov Implicit (FOKI) method sacrices these to some extent, in order to achieve high convergence rates and also avoid the use of a multigrid method, whilst care is taken that the method remains practical for large 3d cases. The speeds of the two schemes are compared with that of an existing, highly-tuned Runge-Kutta multigrid method, and it is seen that a factor of two speed-up can be obtained with no additional memory overhead using LU-SGS, and a factor of ten with FOKI. Attention is then turned to the efficiency of aerodynamic design optimization using gradient-based methods. Use of the Jacobian from the implicit methods allows construction of the adjoint of the flow solver. This adjoint is exact in the sense of being based on the full linearization of all terms in the solver, including all turbulence model contributions. From this starting point various approximations to the adjoint are derived with the intention of simplifying the development and reducing the memory requirements of the method. The effect of these approximations on the accuracy of the resulting design gradients, and the convergence and final solution of optimization problems is studied. The result is a tool for extremely rapid sensitivity evaluations.