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Article

Fluid Dynamics in Curvilinear Coordinates without Fictitious Forces

Physics Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831-6354, USA
This manuscript has been authored by UT-Battelle, LLC, under contract DE-AC05-00OR22725 with the US Department of Energy (DOE). The US government retains and the publisher, by accepting the article for publication, acknowledges that the US government retains a nonexclusive, paid-up, irrevocable, worldwide license to publish or reproduce the published form of this manuscript, or allow others to do so, for US government purposes. DOE will provide public access to these results of federally sponsored research in accordance with the DOE Public Access Plan (http://energy.gov/downloads/doe-public-access-plan).
Academic Editors: Laura A. Miller, Antonis Anastasiou, Amy Buchmann and Nicholas Battista
Fluids 2021, 6(10), 366; https://doi.org/10.3390/fluids6100366
Received: 13 September 2021 / Revised: 10 October 2021 / Accepted: 15 October 2021 / Published: 16 October 2021
(This article belongs to the Collection Feature Paper for Mathematical and Computational Fluid Mechanics)
The use of curvilinear coordinates is sometimes indicated by the inherent geometry of a fluid dynamics problem, but this introduces fictitious forces into the momentum equations that spoil the strict conservative form. If one is willing to work in three dimensions, these fictitious forces can be eliminated by solving for rectangular (Cartesian) momentum components on a curvilinear mesh. A thoroughly geometric approach to fluid dynamics on spacetime demonstrates this transparently, while also giving insight into a greater unity of the relativistic and nonrelativistic cases than is usually appreciated. View Full-Text
Keywords: curvilinear coordinates; spherical coordinates; cylindrical coordinates; fictitious forces; pseudo-forces; relativistic fluid dynamics; nonrelativistic fluid dynamics; conservation form curvilinear coordinates; spherical coordinates; cylindrical coordinates; fictitious forces; pseudo-forces; relativistic fluid dynamics; nonrelativistic fluid dynamics; conservation form
MDPI and ACS Style

Cardall, C.Y. Fluid Dynamics in Curvilinear Coordinates without Fictitious Forces. Fluids 2021, 6, 366. https://doi.org/10.3390/fluids6100366

AMA Style

Cardall CY. Fluid Dynamics in Curvilinear Coordinates without Fictitious Forces. Fluids. 2021; 6(10):366. https://doi.org/10.3390/fluids6100366

Chicago/Turabian Style

Cardall, Christian Y. 2021. "Fluid Dynamics in Curvilinear Coordinates without Fictitious Forces" Fluids 6, no. 10: 366. https://doi.org/10.3390/fluids6100366

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