Data-Driven Post-Processing Correction of Low-Order Discontinuous Galerkin Simulations

Abstract

Computational Fluid Dynamics (CFD) facilitates the analysis of fluid flows to harness the needs for next-generation industries such as aviation, while reducing the time for experimentation and prototyping. However, the increased computational effort required for high-fidelity simulations still remains a concern for further development. The datadriven approach seems as a promising alternative to reduce the evaluation time in such cases, where the bulk of the computational effort is concentrated only during the initial training phase. This work highlights the applicability of high-order accurate schemes like discontinuous Galerkin (DG). In addition, a comparative study with finite-volume method(FVM) test case is performed to illustrate relative performance. Further investigation is performed on a two-dimensional flow around RAE2822 airfoil at various transsonic conditions. In addition to this, the role of a truncation-error based mapping function in approximating solutions across different fidelity levels has been quantified. The objective of this thesis is to learn these truncation-based corrections with the help of data-driven strategies. Correspondingly, the use of ML as a post-processing tool for correcting less accurate low-order DG simulations is examined. DG-CFD computations with p-refinement are performed on low-order simulations with the help of p-staging. Training allows the model to learn the mapped approximation of high-order solutions on low-order in terms of corrections. Consequently, the trained model predicts corrections which can be added to the corresponding lower order solutions. Furthermore, for an efficient exploration of the design space, a sampling strategy is described with its implications. The result shows the effectiveness of the ML framework, in particular the Random Forest (RF) in learning the corrections to improve the low-order DG simulation, which then can be implemented to reconstruct an improved flow field. Furthermore, limitations of the model along with its potential causes are discussed concisely. Finally, further possible advances are suggested.