Development of Numerical Methods for Accurate and Efficient Scale-Resolving Simulations

Licentiate thesis, 2021

Hybrid RANS (Reynolds-Averaged Navier-Stokes)-LES (Large-Eddy Simulation) techniques are considered to be sufficiently accurate and computationally affordable for the aeronautical industry. Scale-resolving simulations is a powerful tool that can accurately predict complex unsteady compressible high-Reynolds-number turbulent flows, as often encountered aeronautical applications. However, since the turbulent scales are resolved instead of modeled, higher demand is placed on the underlying numerical methods used in the simulations.

This thesis explores and develops numerical methods suitable for hybrid RANS-LES. The methods are implemented in the Computational Fluid Dynamics (CFD) solver M-Edge, a compressible unstructured node-centered edge-based solver. A low-dissipative, low-dispersive numerical scheme was calibrated and verified in LES of turbulent channel flow and Decaying Homogeneous Isotropic Turbulent (DHIT). It was shown that numerical dissipation and dispersion needs to be carefully tuned, in order to accurately predict resolved turbulent stresses and the correct decay of turbulent kinetic energy. The reported results are in good agreement with reference DNS and experimental data.

The optimized numerical scheme was then applied to simulate developing hybrid RANS-LES turbulent channel flow. In order to mitigate the grey area region in the LES zone, a Synthetic Turbulence Generator (STG) was applied at the RANS-LES interface. It was shown that using upstream turbulent statistics from a precursor LES or RANS, the recovery length of the skin friction coefficient could be reduced to just a few boundary layer thicknesses.

A new implicit gradient reconstruction scheme suitable for node-centered solvers was proposed. It was shown that the reconstruction scheme achieves fourth-order scaling on regular grids and third-order scaling on irregular grid for an analytical academic case. The Navier-Stokes Characteristic Boundary Condition (NSCBC) was implemented and verified for transport of an analytical vortex. It was shown that special boundary treatment is needed for transporting turbulent structures through the boundary with minimal reflections.