Research Projects

Traditional Computational Fluid Dynamics (CFD) solvers primarily rely on second-order Finite Volume Methods to solve the governing flow equations. While effective in many scenarios, these methods face limitations when applied to flows requiring extremely high accuracy, such as vortex-dominated or separated turbulent flows. Achieving such accuracy often necessitates computationally expensive mesh resolutions, making these methods impractical for certain applications. To address these challenges, high-order finite element methods, particularly the Discontinuous Galerkin (DG) approach, have gained significant attention within the research community. In DG methods, the solution within each mesh element is represented as a polynomial of a specified degree. This approach offers numerous advantages, including, arbitrary order of accuracy on unstructured meshes, and flexibility in mesh and polynomial degree adaptation (hp-adaptation) to resolve the flow features efficiently. These features enable highly accurate solutions at a moderate computational cost, even for complex geometries. Discontinuous Galerkin methods are also well suited for the state-of-the-art heterogeneous computing architectures with GPU acceleration due to the high arithmetic intensity inherent to the methods. Although theoretically there are many advantages with the DG methods, there remains work to be done to improve the robustness of the DG solver for scale resolving turbulent simulations, and also to develop appropriate algorithms for hp-adaptive simulations. Towards this, the present proposal aims to develop a robust 3D high-order Discontinuous Galerkin flow solver utilizing modern heterogeneous computer architectures and to perform hp-adaptive scale-resolving turbulent flow simulations. The proposed DG-based solver with adaptivity features will enable simulations of turbulent flows around geometrically complex configurations that were previously computationally infeasible. Moreover, the high-fidelity data generated from the DG simulations can be used to improve lower-fidelity models, such as RANS, using data-driven methods, thus bridging the gap between scale-resolving research and practical engineering design. In summary, this project addresses a significant technological gap at the intersection of high-order methods, LES, adaptivity, and state-of-the-art HPC infrastructure, and will play a significant role in advancing capabilities for high-fidelity aerospace simulations.