The Reynolds stress model (RSM)  [203],  [338],  [339] is the most elaborate type of RANS turbulence model that Ansys Fluent provides. Abandoning the isotropic eddy-viscosity hypothesis, the RSM closes the Reynolds-averaged Navier-Stokes equations by solving transport equations for the Reynolds stresses, together with an equation for the dissipation rate. This means that five additional transport equations are required in 2D flows, in comparison to seven additional transport equations solved in 3D.

Since the RSM accounts for the effects of streamline curvature, swirl, rotation, and rapid changes in strain rate in a more rigorous manner than one-equation and two-equation models, it has greater potential to give accurate predictions for complex flows. However, the fidelity of RSM predictions is still limited by the closure assumptions employed to model various terms in the exact transport equations for the Reynolds stresses. The modeling of the pressure-strain and dissipation-rate terms is particularly challenging, and often considered to be responsible for compromising the accuracy of RSM predictions.

In addition, even RSM rely on scale equations (- or - / BSL-) and inherit deficiencies resulting from the underlying assumptions in these equations. Ansys Fluent offers the following model combinations:

The default Reynolds stress model in Ansys Fluent is based on the -equation, and uses a linear model for the pressure-strain term. The second -based model allows the usage of a quadratic model for the pressure-strain term.

The two Reynolds stress models based on the -equation both use a linear model for the pressure-strain term, but differ with regard to the scale equation: the stress-omega model is based on the -equation, whereas the stress-BSL model solves the scale equation from the baseline (BSL) - model and thus removes the free-stream sensitivity observed with the stress-omega model.

The RSM might not always yield results that are clearly superior to the simpler models in all classes of flows to warrant the additional computational expense. However, use of the RSM is a must when the flow features of interest are the result of anisotropy in the Reynolds stresses. Among the examples are cyclone flows, highly swirling flows in combustors, rotating flow passages, and the stress-induced secondary flows in ducts.

The exact form of the Reynolds stress transport equations may be derived by taking moments of the exact momentum equation. This is a process wherein the exact momentum equations for the fluctuations are multiplied by the fluctuating velocities and averaged, the product then being Reynolds-averaged. Unfortunately, several of the terms in the exact equation are unknown and modeling assumptions are required in order to close the equations.