Comparison of upwind and symmetric WENO schemes in large eddy simulation of basic turbulent flows

The properties of modern WENO schemes are examined as applied to large eddy simulation (LES). The WENO-ZM5 scheme with modified smoothness indicators (“upwind”) and the WEN-O-SYMBOO6 scheme on a symmetric stencil (“symmetric WENO scheme”) are chosen. The schemes are compared on one-dimensional test problems (advection, Hopf, and Burgers equations) with both smooth and discontinuous solutions. The decay of isotropic turbulence is modeled within LES and the results are discussed. The solutions produced by the new schemes are compared with those based on the central difference scheme, the classical WENO5 scheme, and a hybrid scheme. The level of dissipation of the schemes is compared by analyzing their energy spectra. A similar comparison is made between the LES computations of the temporal evolution of a mixing layer, where the profiles of mean velocity and Reynolds stresses are considered in addition to the energy spectrum.