A family of dynamic finite difference schemes for large-eddy simulation

A family of dynamic low-dispersive finite difference schemes for large-eddy simulation is developed. The dynamic schemes are constructed by combining Taylor series expansions on two different grid resolutions. The schemes are optimized dynamically during the simulation according to the flow physics and dispersion errors are minimized through the real-time adaption of the dynamic coefficient. In case of DNS-resolution, the dynamic schemes reduce to the standard Taylor-based finite difference schemes with formal asymptotic order of accuracy. When going to LES-resolution, the schemes seamlessly adapt to dispersion-relation preserving schemes. The schemes are tested for large-eddy simulation of Burgers’ equation and numerical errors are investigated as well as their interaction with the subgrid model. Very good results are obtained.