CABARET scheme with conservation-flux asynchronous time-stepping for nonlinear aeroacoustics problems

Explicit time stepping renders many high-resolution computational schemes to become less efficient when dealing with non-uniform grids typical of many aeroacoustic applications. Asynchronous time stepping, i.e., updating the solution in different cell sizes according to their local rates, is known to be a promising way to improve the efficiency of explicit time-stepping methods without compromise in accuracy. In the present paper, a new asynchronous time-stepping algorithm is developed for the Compact Accurately Boundary-Adjusting high-REsolution Technique (CABARET) Euler method. This allows to significantly speedup the original single-step CABARET method with non-uniform grids and improves its accuracy at the same time. Numerical examples are provided and issues associated with the method performance on various grid resolutions are discussed.