Hybrid Lagrangian/Eulerian for Probability Density Function Transport Models of Wall Bounded Turbulence

A large part of efforts to develop probability density function (PDF) approaches to turbulence modeling have focused on canonical applications and developing theory for Lagrangian viewpoints. Pure Lagrangian models require complex regression techniques in higher dimensions to find mean quantities. To simplify implementation in complex problems and mitigate some challengings due to sampling and regression, a hybrid Eulerian-Lagrangian RANS/PDF method is used for wall-bounded turbulent flows. The Eulerian transport equations in finite-volume form are used to time-advance mean quantities. Particle properties are used to close the Eulerian transport equations. Emphasis is placed on consistency between the finite-volume and particle representations. This method is applied to a turbulent channel flow, using an elliptic relaxation model. Additionally, inverse modeling based on direct numerical simulation data is used to guide the formulation of the elliptic relaxation model. The results are verified for against DNS data, and the impact of several modeling assumptions are discussed.