Optimized prefactored compact schemes for wave propagation phenomena

A new family of prefactored cost-optimized schemes is developed to minimize the computational cost for a given level of error in linear wave propagation applications, such as aerodynamic sound propagation. This work extends the theory of Pirozzoli1 to the pref-actored compact high-order schemes of Hixon,2 which are MacCormack type schemes that use discrete Padé approximations. An explicit multi-step Runge-Kutta scheme advances the states in time. Theoretical predictions for spatial and temporal error bounds are used to drive the optimization process. Theoretical comparisons of the cost-optimized schemes with a classical benchmark scheme are made. Then, two numerical experiments assess the computational efficiency of the cost-optimised schemes for computational aeroacoustic applications. A polychromatic sinusoidal test-case verifies that the cost-optimized schemes perform according to the design high-order accuracy characteristics for this class of problems. For this test case, upwards of a 50% computational cost-saving at the design level of error is recorded. The final test case shows that the cost-optimized schemes can give substantial cost savings for problems where a fully broadband signal needs to be resolved.