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

摘要

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.