Smooth Local Correlation-Based Transition Model for the Spalart–Allmaras Turbulence Model

Abstract

A smooth version of the local correlation-based transition model (LM2015) for the Spalart–Allmaras (SA) turbulence model is presented. The LM2015 model with helicity-based crossflow correlations is modified and coupled to the SA turbulence model, designated SA-LM2015. The LM2015 and SA-LM2015 transition models include source terms that contain stiff and nonsmooth functions. Approximations to these functions are introduced to eliminate discontinuities and improve the numerical behavior of the model, with the smooth model designated SA-sLM2015. Deep convergence is achieved using a fully coupled, implicit Newton–Krylov algorithm globalized using an efficient pseudotransient continuation strategy. Modifications to the Newton–Krylov algorithm are introduced, including a source-term time stepping strategy, to address the large sources introduced by the turbulence and transition model equations. Two- and three-dimensional transition test cases demonstrate that both models, SA-LM2015 and SA-sLM2015, are able to predict transition due to a variety of mechanisms accurately, with the smooth variant displaying significantly improved numerical behavior. Several of the strategies presented, including the smoothing techniques and source-term time stepping, could be useful in the context of other transition models as well.