Nonuniform-time-step explicit Runge–Kutta scheme for high-order finite difference method.

Explicit Runge–Kutta method has been widely used for time-accurate simulations in aeroacoustics and aerodynamics, partly because of its strong stability properties. However, when dealing with problems involving irregular geometries or multi-scale phenomena where the grid is often refined in localized regions, a single global time step size dictated by the smallest grid size based on the explicit stability condition would inevitably result in excessive computational consumption. A local time stepping strategy that adopts time step size to the local stability requirement in different grid blocks is an effective way to reduce the cost of time integration and to increase the overall computational efficiency. In the present paper, a non-uniform time step (NUTS) explicit Runge–Kutta scheme, previously introduced in the framework of discontinuous Galerkin method, which makes the local time stepping strategy applicable to the explicit Runge–Kutta family without any interpolation and extrapolation in time, is further extended to high-order finite difference methods. The stability of non-uniform time step (NUTS) scheme in combination with high order difference schemes is studied. Numerical experiments are carried out using 1D and 2D acoustic problems for validation of the proposed approach. Computational cost reduction by the proposed algorithm is also discussed. [ABSTRACT FROM AUTHOR]