A localized dynamic closure model for Euler turbulence

Abstract

In this work, we present a localized form of the dynamic eddy viscosity model for computationally efficient and accurate simulation of the turbulent flows governed by Euler equations. In our framework, we determine the dynamic model coefficient locally using the information from neighboring grid points through a test filtering process. We then develop an optimized Gaussian filtering kernel, using a consistent definition with respect to the test filtering ratio, which gives full attenuation at the grid cut-off wave number. A systematic a-posteriori analysis of our model is performed by solving two 3D test problems: (i) incompressible Taylor-Green vortex flow and (ii) compressible shear layer turbulence induced by Kelvin-Helmholtz instability to show the wide range of applicability of the proposed localized dynamic model. We demonstrate that the proposed dynamic model is robust and provides a better estimation of the inertial range turbulence dynamics than other numerical models tested in this study.