Fluid dynamics in curvilinear coordinates without fictitious forces

Christian Y. Cardall

doi:10.3390/fluids6100366

Fluid dynamics in curvilinear coordinates without fictitious forces

Christian Y. Cardall

Theoretical and Computational Physics

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

Abstract

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.

Original language	English
Article number	366
Journal	Fluids
Volume	6
Issue number	10
DOIs	https://doi.org/10.3390/fluids6100366
State	Published - Oct 2021

Funding

Funding: This work was supported by the U.S. Department of Energy, Office of Science, Office of Nuclear Physics, under contract number DE-AC05-00OR22725.

Keywords

Conservation form
Curvilinear coordinates
Cylindrical coordinates
Fictitious forces
Nonrelativistic fluid dynamics
Pseudo-forces
Relativistic fluid dynamics
Spherical coordinates

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10.3390/fluids6100366

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abstract = "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.",

keywords = "Conservation form, Curvilinear coordinates, Cylindrical coordinates, Fictitious forces, Nonrelativistic fluid dynamics, Pseudo-forces, Relativistic fluid dynamics, Spherical coordinates",

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AB - 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.

KW - Conservation form

KW - Curvilinear coordinates

KW - Cylindrical coordinates

KW - Fictitious forces

KW - Nonrelativistic fluid dynamics

KW - Pseudo-forces

KW - Relativistic fluid dynamics

KW - Spherical coordinates

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JF - Fluids

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ER -

Fluid dynamics in curvilinear coordinates without fictitious forces

Abstract

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Keywords

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