Theory for Wall Distance
The Eikonal Equation
Turbulence models often use the distance to the closest wall to approximate the mixing length or for regularization purposes. One way to compute the wall distance is to solve the eikonal equation:
(16-16)
with D = 0 on solid walls and ∇D · n = 0 on other boundaries. The eikonal equation can be tricky to solve, and produces the exact distance to the closest wall. The modified equation described below is less computationally expensive to solve. It also uses a reference length to put more emphasis on solid objects larger than the reference length and to reduce the emphasis on smaller objects. The introduction of a reference length produces a more relevant wall distance in the following instances:
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In convex regions of small dimensions, the wall distance is reduced to reflect the close proximity of several walls.
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When a small object, such as a thin wire, is present in free flow, the wall distance is affected only in a very small region around it.