A dynamically optimized finite difference scheme for Large-Eddy Simulation

A low-dispersive dynamic finite difference scheme for Large-Eddy Simulation is developed. The dynamic scheme is constructed by combining Taylor series expansions on two different grid resolutions. The scheme is optimized dynamically through the real-time adaption of a dynamic coefficient according to the spectral content of the flow, such that the global dispersion error is minimal. In the case of DNS-resolution, the dynamic scheme reduces to the standard Taylor-based finite difference scheme with formal asymptotic order of accuracy. When going to LES-resolution, the dynamic scheme seamlessly adapts to a dispersion-relation preserving scheme. The scheme is tested for Large-Eddy Simulation of Burgers equation. Very good results are obtained.