Construction of explicit and implicit dynamic finite difference schemes and application to the large-eddy simulation of the Taylor–Green vortex

A general class of explicit and implicit dynamic finite difference schemes for large-eddy simulation is constructed, by combining Taylor series expansions on two different grid resolutions. After calibration for Re → ∞ , the dynamic finite difference schemes allow to minimize the dispersion errors during the calculation through the real-time adaption of a dynamic coefficient. In case of DNS resolution, these dynamic schemes reduce to Taylor-based finite difference schemes with formal asymptotic order of accuracy, whereas for LES resolution, the schemes adapt to Dispersion-Relation Preserving schemes. Both the explicit and implicit dynamic finite difference schemes are tested for the large-eddy simulation of the Taylor–Green vortex flow and numerical errors are investigated as well as their interaction with the dynamic Smagorinsky model and the multiscale Smagorinsky model. Very good results are obtained.