Computations of wall distances by solving a transport equation

Computations of wall distances still play a key role in modern turbulence modeling. Motivated by the expense involved in the computation, an approach solving partial differential equations is considered. An Euler-like transport equation is proposed based on the Eikonal equation. Thus, the efficient algorithms and code components developed for solving transport equations such as Euler and Navier-Stokes equations can be reused. This article provides a detailed implementation of the transport equation in the Cartesian coordinates based on the code of computational fluid dynamics for missiles (MICFD) of Beihang University. The transport equation is robust and rapidly convergent by the implicit lower-upper symmetric Gauss-Seidel (LUSGS) time advancement and upwind spatial discretization. Geometric derivatives must also be upwind determined to ensure accuracy. Special treatments on initial and boundary conditions are discussed. This distance solving approach is successfully applied on several complex geometries with 1-1 blocking or overset grids.