A turbulence model: Model, analysis, and algorithm

The standard eddy viscosity model is commonly used to simulate turbulence, but there exist difficulties in simulating the backscatter of the non-statistical equilibrium turbulence. In this work, we construct a novel modified eddy viscosity model based on a simplified Cebeci–Smith equation, which is applied to the non-equilibrium turbulence. Moreover, we analyze some properties of the model and propose a fully discrete scheme, which is proven to be stable and convergent. Finally, some numerical examples are presented to test the theoretical prediction of the proposed scheme, and intermittent backscatter is captured and observed by simulating the established model.