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

*(English)*Zbl 1349.76530Summary: 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.

##### MSC:

76M20 | Finite difference methods applied to problems in fluid mechanics |

76F65 | Direct numerical and large eddy simulation of turbulence |

65M06 | Finite difference methods for initial value and initial-boundary value problems involving PDEs |

76Q05 | Hydro- and aero-acoustics |

##### Software:

Turbulence Modeling
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\textit{V. A. Semiletov} and \textit{S. A. Karabasov}, J. Comput. Phys. 253, 157--165 (2013; Zbl 1349.76530)

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##### References:

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