Consideration of Non-Locality for Gene Expression Programming: Modeling the Transition to Turbulence in the Boundary Layer

Abstract The consideration of the inherently non-local characteristics of turbulence is an open challenge and subject to many investigations. Recent approaches rely on the utilization of spatially configured Neural Networks such as e.g. Convolutional Neural Networks to account for non-local effects (Comput. Methods Appl. Mech. Eng. 384:113927, 2021). Nevertheless, approaches featuring Neural Networks are not easily available for Gene Expression Programming. An alternative option, to consider non-local effects, is the use of partial differential equations (PDE) like an additional convection-diffusion equation as is done for example in several transition models such as the $$\gamma$$ - model by Menter et al. (Flow Turbul. Combust. 583–619, 2015). Consequently, instead of only modeling a local correction factor directly using GEP, we equip the input quantities with an additional optional convection-diffusion equation of which we model the production term, diffusion constants and boundary type. The methodology is applied on a set of low pressure turbine testcases in order to find transition models. Resulting expressions are further analysed in terms of underlying mechnims and logical foundations.