A general strategy for the optimization of RungeKutta schemes for wave propagation phenomena
We analyze optimized explicit RungeKutta schemes (RK) for computational aeroacoustics, and wave propagation phenomena in general. Exploiting the analysis developed in [S. Pirozzoli, Performance analysis and optimization of finite-difference schemes for wave propagation problems, J. Comput. Phys. 222 (2007) 809831], we rigorously evaluate the performance of several time integration schemes in terms of appropriate error and cost metrics, and provide a general strategy to design RungeKutta methods tailored for specific applications. We present families of optimized second- and third-order RungeKutta schemes with up to seven stages, and describe their implementation in the framework of Williamsons 2N 2 N -storage formulation [J.H. Williamson, Low-storage RungeKutta schemes, J. Comput. Phys. 35 (1980) 4856]. Numerical simulations of the 1D linear advection equation and of the 2D linearized Euler equations are performed to demonstrate the validity of the theory and to quantify the improvement provided by optimized schemes.
rungekutta schemes computational aeroacoustics optimized algorithms numerical dispersion numerical dissipation