I gave a talk Efficient and Robust Time Integration with Automatic Step Size Control for Compressible Computational Fluid Dynamics at the 92nd annual meeting of the International Association of Applied Mathematics and Mechanics, on Friday, 2022-08-19, 10:10 CEST.
We report on the development of optimized time integration algorithms for computational fluid dynamics (CFD). These new methods are equipped with error estimators, allowing an automatic error-based step size control. The schemes are efficient and robust in both the accuracy-limited and stability-limited regime for CFD applications using discontinuous spectral element discretizations. The robusness and efficiency of these methods depends on the choice of adequate step size controllers. We present a data-driven approach combining analysis with data to obtain these in practice. We compare the common step size control based on the Courant-Friedrichs-Lewy (CFL) number with error-based controllers. We demonstrate that our new methods yield improved performance in challenging industrial CFD applications.