Accelerating CFD solver computation time with reduced-order modeling in a multigrid environment

Abstract

Reduced-order models (ROMs) are more and more considered for use in aerodynamic applications. Benefits of these methods can be expected for optimization problems or predicting aerodynamic loads for the entire flight envelope. For these applications it is often possible to perform computations for various parameter combinations before any ROM evaluations are needed. The order reduction of the CFD solutions in this article is done using proper orthogonal decomposition. Coupled with an interpolation method predictions for unknown parameter combinations can be made. The CFD solutions are computed using a discontinuous Galerkin finite element method combined with a nonlinear multigrid scheme. The nonlinear multigrid solver algorithms depend on a good initial guess of the flow field to be computed. Typically, the initial guess on a fine mesh is obtained by solving the problem on a agglomerated mesh. Alternatively, an initial guess could be obtained from a ROM prediction, if available. The main objective is to identify the benefits of using a ROM in a higher-order multigrid environment. Integral as well as distributed surface quantities of the ROM predictions originating from several multigrid levels will be compared with fully converged flow solutions on the top level of the multigrid algorithm. Furthermore, initializing the flow solver with predictions from several multigrid levels will be analyzed in comparison to full multigrid computations as well as to a scenario where already converged solutions for similar parameter combinations are used as initial flow solutions on the top multigrid Level.