Orthogonal signed-distance coordinates and vector calculus near evolving curves and surfaces
Mathematical Physics
2023-10-27 v2 Materials Science
Differential Geometry
math.MP
Fluid Dynamics
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.
Keywords
Cite
@article{arxiv.2302.02891,
title = {Orthogonal signed-distance coordinates and vector calculus near evolving curves and surfaces},
author = {Eric W. Hester and Geoffrey M. Vasil},
journal= {arXiv preprint arXiv:2302.02891},
year = {2023}
}
Comments
24 pages, 3 figures, Mathematica code available at https://github.com/ericwhester/signed-distance-code