Investigation of low-dissipation low-dispersion schemes for incompressible and compressible flows in scale-resolving simulations

Abstract

A comprehensive study is conducted on a second-order low-dissipation low-dispersion (LD2) scheme in scale-resolving simulations of both incompressible and compressible flows, using a node-based unstructured CFD solver. The scheme deploys a higher order central reconstruction of the face values (up to fourth-order on structured meshes) and a matrix dissipation formulation to reduce the dispersive and dissipative numerical errors. The LD2 scheme is examined for compressible flow cases involving shock discontinuities, LD2-Compressible (LD2C), and is verified in a classical shock-tube problem. The scheme is then further verified in Large-Eddy Simulations (LES) of decaying isotropic turbulence (DIT) in comparison with available experimental data. It is shown that in scale-resolving simulations, the LD2C scheme is able to significantly improve the prediction as compared to a conventional second-order central scheme. The scheme is then further assessed and verified in hybrid Reynolds-Averaged Navier–Stokes (RANS)-LES computations for the subsonic and supersonic turbulent channel flow, where excellent agreement with reference DNS and correlations are observed. Moreover, a supersonic base flow is simulated using hybrid RANS-LES, where improved predictions are observed. The LD2C scheme exploits a shock sensor incorporating vorticity and is shown to improve the prediction of the resolved shear stress in the shear layer of compression.