A family of low dispersive and low dissipative explicit schemes for flow and noise computations

Explicit numerical methods for spatial derivation, filtering and time integration are proposed. They are developed with the aim of computing flow and noise with high accuracy and fidelity. All the methods are constructed in the same way by minimizing the dispersion and the dissipation errors in the wavenumber space up to kΔx=π/2 corresponding to four points per wavelength. They are shown to be more accurate, and also more efficient numerically, than most of the standard explicit high-order methods, for uniform and slowly non-uniform grids. Two problems involving long-range sound propagation are resolved to illustrate their respective precisions. Remarks about their practical applications are then made, especially about the connection with the boundary conditions. Finally, their relevance for the simulation of turbulent flows is emphasized.