2019/11/28 by Aldaïr Petronilia, Petronilia, Aldaïr, Edward James Brambley +1
Earth and Planetary Sciences · Engineering · #Aerodynamics and Acoustics in Jet Flows #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Fluid Dynamics and Turbulent Flows #Meteorological Phenomena and Simulations #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.1911.12678
openalex publication_date 2019/11/28 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28
Finite differences and Runge-Kutta time stepping schemes used in\nComputational AeroAcoustics simulations are often optimized for low dispersion\nand dissipation (e.g. DRP or LDDRK schemes) when applied to linear problems in\norder to accurately simulate waves with the least computational cost. Here, the\nperformance of optimized Runge-Kutta time stepping schemes for linear\ntime-invariant problems with non-constant-amplitude oscillations is considered.\nThis is in part motivated by the recent suggestion that optimized spatial\nderivatives perform poorly for growing and decaying waves, as their\noptimization implicitly assumes real wavenumbers. To our knowledge, this is the\nfirst time the time-stepping of non-constant-amplitude oscillations has been\nconsidered. It is found that current optimized Runge-Kutta schemes perform\npoorly in comparison with their maximal order equivalents for\nnon-constant-amplitude oscillations. Moreover, significantly more accurate\nresults can be achieved for the same computation cost by replacing a two-step\nscheme such as LDDRK56 with a single step higher-order scheme with a longer\ntime step. Attempts are made at finding optimized schemes that perform well for\nnon-constant-amplitude oscillations, and three such examples are provided.\nHowever, the traditional maximal order Runge-Kutta time stepping schemes are\nstill found to be preferable for general problems with broadband excitation.\nThese theoretical predictions are illustrated using a realistic 1D\nwave-propagation example.\n