Computation of Wall Distance Based on Differential Equations

The use of differential equations such as Eikonal, Hamilton-Jacobi, and Poisson for the economical calculation of the nearest (normal) wall distance d, which is needed by some turbulence models, is explored. Modifications that could palliate some turbulence-modeling anomalies are also discussed. Economy is of especial value for deforming/adaptive grid problems. For these, ideally, d is repeatedly computed. It is shown that the Eikonal and Hamilton-Jacobi equations can be easy to implement when written in implicit (or iterated) advection and advection-diffusion equation analogous forms, respectively. These, like the Poisson Laplacian term, are commonly occurring in computational-fluid-dynamics (CFD) solvers, allowing the reuse of efficient algorithms and code components. The use of the NASA CFL3D CFD program to solve the implicit Eikonal and Hamilton-Jacobi equations is explored. The reformulated d equations are easy to implement and are found to have robust convergence. For accurate Eikonal solutions, upwind metric differences are required. The Poisson approach is also found effective and easiest to implement. Hence this method is recommended. Modified distances are not found to affect global outputs such as lift and drag significantly, at least in common situations such as airfoil flows.[PUBLICATION ABSTRACT]