Artificial diffusion for convective and acoustic low Mach number flows I: Analysis of the modified equations, and application to Roe-type schemes Article Swipe
Joshua Hope-Collins
,
Luca di Mare
·
YOU?
·
· 2022
· Open Access
·
· DOI: https://doi.org/10.1016/j.jcp.2022.111858
YOU?
·
· 2022
· Open Access
·
· DOI: https://doi.org/10.1016/j.jcp.2022.111858
Three asymptotic limits exist for the Euler equations at low Mach number - purely convective, purely acoustic, and mixed convective-acoustic. Standard collocated density-based numerical schemes for compressible flow are known to fail at low Mach number due to the incorrect asymptotic scaling of the artificial diffusion. Previous studies of this class of schemes have shown a variety of behaviours across the different limits and proposed guidelines for the design of low-Mach schemes. However, these studies have primarily focused on specific discretisations and/or only the convective limit. In this paper, we review the low-Mach behaviour using the modified equations - the continuous Euler equations augmented with artificial diffusion terms - which are representative of a wide range of schemes in this class. By considering both convective and acoustic effects, we show that three diffusion scalings naturally arise. Single- and multiple-scale asymptotic analysis of these scalings shows that many of the important low-Mach features of this class of schemes can be reproduced in a straightforward manner in the continuous setting. As an example, we show that many existing low-Mach Roe-type finite-volume schemes match one of these three scalings. Our analysis corroborates previous analysis of these schemes, and we are able to refine previous guidelines on the design of low-Mach schemes by including both convective and acoustic effects. Discrete analysis and numerical examples demonstrate the behaviour of minimal Roe-type schemes with each of the three scalings for convective, acoustic, and mixed flows.
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- Type
- article
- Language
- en
- Landing Page
- https://doi.org/10.1016/j.jcp.2022.111858
- OA Status
- hybrid
- Cited By
- 8
- References
- 90
- Related Works
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- OpenAlex ID
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https://openalex.org/W4313593855Canonical identifier for this work in OpenAlex
- DOI
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https://doi.org/10.1016/j.jcp.2022.111858Digital Object Identifier
- Title
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Artificial diffusion for convective and acoustic low Mach number flows I: Analysis of the modified equations, and application to Roe-type schemesWork title
- Type
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articleOpenAlex work type
- Language
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enPrimary language
- Publication year
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2022Year of publication
- Publication date
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2022-12-16Full publication date if available
- Authors
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Joshua Hope-Collins, Luca di MareList of authors in order
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https://doi.org/10.1016/j.jcp.2022.111858Publisher landing page
- Open access
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YesWhether a free full text is available
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hybridOpen access status per OpenAlex
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https://doi.org/10.1016/j.jcp.2022.111858Direct OA link when available
- Concepts
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Mach number, Euler equations, Scaling, Euler's formula, Convection, Diffusion, Mathematics, Numerical diffusion, Asymptotic analysis, Compressible flow, Mechanics, Compressibility, Physics, Mathematical analysis, Geometry, ThermodynamicsTop concepts (fields/topics) attached by OpenAlex
- Cited by
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8Total citation count in OpenAlex
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2025: 5, 2024: 1, 2023: 2Per-year citation counts (last 5 years)
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90Number of works referenced by this work
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10Other works algorithmically related by OpenAlex
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