A p-Poisson wall distance approach for turbulence modeling Nathan A. Wukie ∗ and Paul D. Orkwis † University of Cincinnati, Cincinnati, Ohio, 45221 Distance fields are an important component of turbulence modeling approaches for com- putational fluid dynamics. Common approaches for obtaining distance fields include direct search methods as well as methods based on solving a partial differential equation(PDE) for an approximate distance field. An approach based on solving a p-Poisson equation was previously developed in the context of computer graphics and is introduced here for application to turbulence modeling for computational fluid dynamics. The p-Poisson ap- proach is more accurate than a simpler approach based on a Poisson equation and the p-Poisson approach is more readily implemented than methods based on solving Eikonal or Hamilton-Jacobi equations. The p-Poisson equation is implemented in a discontinu- ous Galerkin discretization to evaluate its effectiveness at providing approximate distance fields and also to evaluate its utility for informing turbulence models in Reynolds-Average Navier-Stokes(RANS) simulations. Simple geometries are investigated to characterize the behavior of the governing equation and several turbulent flow calculations are investigated to evaluate the ability of the approach to inform turbulent computational fluid dynamics analyses. Results obtained for the turbulent flow analyses compare well with analytical or reference data for the problems, indicating that the p-Poisson approach is useful for turbulent flow applications. Nomenclature Q Solution variable ψ Legendre basis polynomial  F Flux vector S Source function p p-Poisson parameter d Distance field ˜ d Normalized approximate distance field u Approximate distance field u Fluid velocity µ Viscosity coefficient λ Second coefficient of viscosity k Thermal conductivity I Identity tensor I. Introduction W all distance fields, defined here as the distance of a point in space to the nearest solid wall, are used in many approaches for turbulence modeling in computational fluid dynamics. The Spalart-Allmaras(SA) 1 and Shear-Stress Transport(SST) 2 turbulence models are two examples where the distance field is used in their formulation. Obtaining wall distance fields in support of these efforts for turbulence modeling remains * PhD Student, Dept. of Aerospace Engineering, ML 70, Cincinnati, Ohio 45221, AIAA Student Member. † Bradley Jones Professor, Dept. of Aerospace Engineering, ML 70, Cincinnati, Ohio 45221, AIAA Associate Fellow. 1 of 13 American Institute of Aeronautics and Astronautics