A robust high-order compact method for large eddy simulation

We present a high-order compact method for large eddy simulation (LES) of compressible turbulent flows. Numerical solution of Navier–Stokes equations with high-order compact methods has been limited by numerical instabilities caused by ill-resolved features of the flow. This problem is alleviated by a staggered arrangement of conserved variables. Simulations of decaying isotropic turbulence at high Reynolds numbers demonstrate the superiority of the present method over the collocated method. Furthermore, the present method is applicable to the conservative form of the governing equations, thereby allowing total energy conservation, a property usually sacrificed in LES with the collocated method. Boundary schemes that extend the present methodology to non-periodic domains are also presented.