High-accuracy large-step explicit Runge–Kutta (HALE-RK) schemes for computational aeroacoustics

In many realistic calculations, the computational grid spacing required to resolve the mean flow gradients is much smaller than the grid spacing required to resolve the unsteady propagating waves of interest. Because of this, the high temporal resolution provided by existing optimized time marching schemes can be excessive due to the small time step required for stability in regions of clustered grid. In this work, explicit fourth-order accurate Runge–Kutta time marching schemes are optimized to increase the inviscid stability limit rather than the accuracy at large time steps. Single and multiple-step optimized schemes are developed and analyzed. The resulting schemes are validated on several realistic benchmark problems.