Robust Eddy Viscosity Turbulence Modeling with Elliptic Relaxation and Compound Wall Treatment

This paper presents a holistic Reynolds-averaged Navier-Stokes (RANS) turbulence modeling framework for the computational fluid dynamics (CFD) simulations of complex wall-bounded turbulent flows. Based on the elliptic relaxation idea, the deployed eddy viscosity turbulence model reconstructs the near-wall stress anisotropy and nonviscous effects. The appropriate selection of the turbulent quantities that are being solved for, together with the zero value wall boundary condition for the related turbulent quantities, renders the model less sensitive to the near-wall grid nonuniformities and resolution. The unified near-wall velocity profile, obtained based on the boundary layer theory, is used to devise the compound near-wall treatment that ensures the robustness of the numerical simulation. The proposed turbulence modeling framework is implemented into the general-purpose open-source CFD code and validated against the generic test cases with satisfactory agreement.