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

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10.1098/rspa.2023.0080Licence: CC BY

Cite this

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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.",

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AU - Vasil, Geoffrey M.

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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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DO - 10.1098/rspa.2023.0080

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M1 - 479

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

Abstract

Data Availability Statement

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