Differential equation-based wall distance computation for DES and RANS

Abstract

Surprisingly expensive to compute wall distances are still used in a range of key turbulence and peripheral physics models. Potentially economical, accuracy improving differential equation-based distance algorithms are considered. These involve elliptic Poisson and a hyperbolic-natured Eikonal equation approaches. Numerical issues relating to non-orthogonal curvilinear grid solution of the latter are addressed. Eikonal extension to a Hamilton–Jacob equation is discussed. Use of this extension to improve turbulence model accuracy and, along with the Eikonal, enhance detached eddy simulation (DES) techniques is considered. Application of the distance approaches is studied for various geometries. These include a plane channel flow with a wire at the centre, a wing–flap system, and a supersonic double-delta configuration. Although less accurate than the Eikonal, Poisson method-based flow solutions are extremely close to those using a search procedure. For a moving grid case the Poisson method is found especially efficient. Results show that the Eikonal equation can be solved on highly stretched, non-orthogonal, and curvilinear grids. A key accuracy aspect is that metrics must be upwinded in the propagating front direction. The Hamilton–Jacobi equation is found to have qualitative turbulence model improving properties.