Accurate, Robust Simulations of Aerodynamics Flows, Especially Wakes and Shocks

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My research area is the development of more accurate, efficient, and robust algorithms for computational fluid dynamics (CFD) and mesh generation. My medium term research goal for my group is to bring together our work in algorithms for flow solution, mesh generation and adaptation, error analysis, and numerical stability to more consistently produce reliable simulation results for analysis and design in external aerodynamics. The technical challenge here is not just to obtain a numerical solution for a particular flow problem, but to reduce as much as possible the need for a human user to intervene and iterate during this process, while at the same time providing tight quantitative bounds on the error in output quantities of engineering interest, including for example forces and heat fluxes. These advances will improve the CFD analysis tools engineers use to design quieter, more fuel efficient aircraft and land transportation vehicles. Our strategic objectives during the term of the proposed Discovery Grant are: 1. Meshing. While adaptive meshing is poised to take over CFD, there is still a need in computational aerodynamics for better non-adaptive meshing, especially for complex configurations like high-lift systems. We will continue our current work on a fully anisotropic 3D mesh generator which maximizes internal structure throughout the mesh. 2. Highly-Accurate Flow Solvers. The Reynolds-averaged Navier-Stokes equations are a sometimes maligned model for turbulent flow, but remain the only feasible alternative for large-scale aerodynamic simulations. Even though the model is not an exact representation of the flow physics, simulations should not compound that problem with numerical error. We will complete work on our fourth-order accurate unstructured mesh finite-volume RANS flow solver, and demonstrate its usefulness, accuracy, and efficiency for aircraft in cruise and high-lift configurations. 3. Numerical Treatment of Shock Waves. Modern numerical methods in CFD rely for accuracy on the assumption of smooth solutions, which breaks down for transonic and supersonic flows with shock waves. Shock fitting is a paradigm that treats such flows explicitly as discontinuous. We are developing meshing tools for shock fitting for 3D flows, including complex shock-shock and shock-boundary interaction. We will also begin work in-house on developing a high-order shock-fitting scheme. 4. Steady-State Convergence. Most commercial CFD software requires hundreds or thousands of iterations to reach full convergence to steady state. We will leverage what we have learned about eigensystems and convergence for unstructured mesh flow solvers in our stability work to improve convergence rates by an order of magnitude. Taken together, these capabilities will have a significant impact on the reliability and robustness of CFD simulations, which in turn will open their use to a wider range of industrial analysis and design applications.