Adaptively switched time stepping scheme for direct aeroacoustic computations

The physical variables involved in a flow field are of very different scales to those of the aeroacoustic field within the flow. Thus, direct aeroacoustic computations (DACs) require extremely small time steps to capture the fluctuations in the aeroacoustic field and stabilize the numerical scheme. As a result, the computation time for DACs can be very long. This paper describes an implicit Adaptively Switched Time Stepping (ASTS) scheme that enables the use of larger time steps when solving DAC problems. ASTS is based on the adaptive selection of the time stepping scheme according to the value of the residual. Early in the iteration process, an artificial time term is used to afford larger time steps while ensuring that the numerical scheme remains stable. Once the residual is less than some preset reference value, the artificial time term is removed, thus eliminating the Newton linearization error. Simulation results show that ASTS can reduce the computational cost of DACs by a factor of more than eight while maintaining the required level of accuracy.