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

Eric Hester; Geoffrey M. Vasil

doi:10.1098/rspa.2023.0080

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

Eric Hester, Geoffrey M. Vasil

Department of Mathematical Sciences

University of Edinburgh

Research output: Contribution to journal › Article › peer-review

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 to arbitrary order for boundary layer asymptotics in a wide range of physical systems.

Original language	English
Article number	479
Journal	Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Early online date	27 Sept 2023
DOIs	https://doi.org/10.1098/rspa.2023.0080
Publication status	Published - 27 Sept 2023

Data Availability Statement

Code is provided in the ESM. The data are provided in the electronic supplementary material

Funding

No funding has been received for this article.

Access to Document

10.1098/rspa.2023.0080Licence: CC BY

Cite this

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AB - 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 to arbitrary order for boundary layer asymptotics in a wide range of physical systems.

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

Abstract

Data Availability Statement

Funding

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Cite this