Orthogonal signed-distance coordinates and vector calculus near evolving curves and surfaces
arXiv:2302.02891 · doi:10.1098/rspa.2023.0080
Abstract
We provide an elementary derivation of an orthogonal coordinate system for boundary layers around evolving smooth surfaces and curves based on the signed-distance function. We go beyond previous works on the signed-distance function and collate useful vector calculus identities for these coordinates. These results and provided code enable consistent accounting of geometric effects in the derivation of boundary layer asymptotics for a wide range of physical systems.
arXiv comment24 pages, 3 figures, Mathematica code available at https://github.com/ericwhester/signed-distance-code
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