Improved Menter's one-equation turbulence model

Compatible modifications to original Menter model (OMM) are incorporated using an elliptic relaxation approach to accurately accounting non-local characteristics accompanied by near-wall turbulence. Coefficients/functions of improved Menter model (IMM) are parameterized with the elliptic relaxation function to imitate the combined effects of near-wall turbulence and non-equilibrium. The characteristic length scale involved in the elliptic relaxation scheme is constructed in terms of viscous and turbulent length scales in conjunction with a non-singular strain-rate invariant. Non-local effects are consequently reinforced by the mean flow and turbulent variables. A non-linear eddy-viscosity damping function is invoked to relax the viscous length-scale coefficient pertaining to the elliptic relaxation model. Comparisons indicate that the IMM substantially improves the accuracy of flow simulations compared to the OMM and widely used Spalart-Allmaras (SA) model. A good consensus is obtained between IMM and DNS (direct numerical simulation)/measured data.