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An Entropic Kinetic Scheme with Compactly Supported Velocities

Roy, SS and Raghurama Rao, SV (2024) An Entropic Kinetic Scheme with Compactly Supported Velocities. [Book Chapter]

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Official URL: https://doi.org/10.1007/978-3-031-55264-9_37

Abstract

We introduce a new kinetic model where the equilibrium distribution function has a range of velocities centered about two velocities (±λ) in 1D. In 2D, the equilibrium distribution comprises of a range of velocities about four velocities, one in each quadrant. This essential feature of a range of velocities (λ ± Δλ) offers a significant advantage to obtain both an exact shock capturing as well as an entropic scheme. The range of velocities (2Δλ) serves the purpose of augmenting the stability of the model. Δλ is used to provide additional diffusion in expansion regions. The average velocity λ is fixed to exactly capture grid-aligned steady discontinuities, by enforcing Rankine-Hugoniot jump conditions in the discretization process. Further, a novel kinetic relative entropy, appropriate to our kinetic model, is introduced. Along with an additional criterion, this kinetic relative entropy is used to identify expansions. Some standard 1D and 2D benchmark test cases are solved using this scheme. The Author(s), under exclusive license to Springer Nature Switzerland AG 2024.

Item Type: Book Chapter
Publication: SEMA SIMAI Springer Series
Series.: SEMA SIMAI Springer Series
Publisher: Springer Science and Business Media Deutschland GmbH
Additional Information: The copyright for this article belongs to Springer Science and Business Media Deutschland GmbH.
Department/Centre: Division of Mechanical Sciences > Aerospace Engineering(Formerly Aeronautical Engineering)
Date Deposited: 23 Dec 2024 09:32
Last Modified: 24 Dec 2024 05:11
URI: http://eprints.iisc.ac.in/id/eprint/85867

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