Orthogonal signed-distance coordinates and vector calculus near evolving curves and surfaces

Autor:	Hester, Eric W., Vasil, Geoffrey M.
Rok vydání:	2023
Předmět:	Mathematical Physics Condensed Matter - Materials Science Mathematics - Differential Geometry Physics - Fluid Dynamics 26B10 26B12 53Z05 53Z30 58J37
Zdroj:	Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 479, no. 2277 (2023): 20230080
Druh dokumentu:	Working Paper
DOI:	10.1098/rspa.2023.0080
Popis:	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. Comment: 24 pages, 3 figures, Mathematica code available at https://github.com/ericwhester/signed-distance-code
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2302.02891 Zobrazit plný text záznamu View this record from Arxiv