Resolving Confusion Over Third Order Accuracy of U-MUSCL Article Swipe
Emmett Padway
,
Hiroaki Nishikawa
·
YOU?
·
· 2021
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2104.01292
YOU?
·
· 2021
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2104.01292
In this paper, we discuss the U-MUSCL reconstruction scheme -- an unstructured-grid extension of Van Leer's kappa-scheme -- proposed by Burg for the edge-based discretization [AIAA Paper 2005-4999]. This technique has been widely used in practical unstructured-grid fluid-dynamics solvers but with confusions: e.g., third-order accuracy with kappa=1/2 or kappa=1/3. This paper clarifies some of these confusions: e.g., the U-MUSCL scheme can be third-order accurate in the point-valued solution with kappa=1/3 on regular grids for linear equations in all dimensions, it can be third-order accurate with kappa=1/2 as the QUICK scheme in one dimension. It is shown that the U-MUSCL scheme cannot be third-order accurate for nonlinear equations, except a very special case of kappa=1/2 on regular simplex-element grids, but it can be an accurate low-dissipation second-order scheme. It is also shown that U-MUSCL extrapolates a quadratic function exactly with kappa=1/2 on arbitrary grids provided the gradient is computed by a quadratic least-squares method. Two techniques are discussed, which transform the U-MUSCL scheme into being genuinely third-order accurate on a regular grid: an efficient flux-reconstruction method and a special source term quadrature formula for kappa=1/2.
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Metadata
- Type
- preprint
- Language
- en
- Landing Page
- http://arxiv.org/abs/2104.01292
- https://arxiv.org/pdf/2104.01292
- OA Status
- green
- Cited By
- 1
- References
- 26
- Related Works
- 20
- OpenAlex ID
- https://openalex.org/W3141609744
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- OpenAlex ID
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https://openalex.org/W3141609744Canonical identifier for this work in OpenAlex
- DOI
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https://doi.org/10.48550/arxiv.2104.01292Digital Object Identifier
- Title
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Resolving Confusion Over Third Order Accuracy of U-MUSCLWork title
- Type
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preprintOpenAlex work type
- Language
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enPrimary language
- Publication year
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2021Year of publication
- Publication date
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2021-04-03Full publication date if available
- Authors
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Emmett Padway, Hiroaki NishikawaList of authors in order
- Landing page
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https://arxiv.org/abs/2104.01292Publisher landing page
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https://arxiv.org/pdf/2104.01292Direct link to full text PDF
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YesWhether a free full text is available
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greenOpen access status per OpenAlex
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https://arxiv.org/pdf/2104.01292Direct OA link when available
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Mathematics, Applied mathematics, Quadratic equation, Discretization, Grid, Third order, Calculus (dental), Mathematical analysis, Geometry, Philosophy, Theology, Medicine, DentistryTop concepts (fields/topics) attached by OpenAlex
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1Total citation count in OpenAlex
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2021: 1Per-year citation counts (last 5 years)
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26Number of works referenced by this work
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20Other works algorithmically related by OpenAlex
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| abstract_inverted_index.paper, | 2 |
| abstract_inverted_index.scheme | 8, 59, 89, 99, 161 |
| abstract_inverted_index.source | 178 |
| abstract_inverted_index.widely | 32 |
| abstract_inverted_index.U-MUSCL | 6, 58, 98, 132, 160 |
| abstract_inverted_index.discuss | 4 |
| abstract_inverted_index.exactly | 137 |
| abstract_inverted_index.formula | 181 |
| abstract_inverted_index.method. | 152 |
| abstract_inverted_index.regular | 71, 115, 169 |
| abstract_inverted_index.scheme. | 126 |
| abstract_inverted_index.solvers | 38 |
| abstract_inverted_index.special | 110, 177 |
| abstract_inverted_index.accuracy | 44 |
| abstract_inverted_index.accurate | 63, 83, 103, 123, 166 |
| abstract_inverted_index.computed | 147 |
| abstract_inverted_index.function | 136 |
| abstract_inverted_index.gradient | 145 |
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| abstract_inverted_index.provided | 143 |
| abstract_inverted_index.solution | 67 |
| abstract_inverted_index.arbitrary | 141 |
| abstract_inverted_index.clarifies | 51 |
| abstract_inverted_index.efficient | 172 |
| abstract_inverted_index.equations | 75 |
| abstract_inverted_index.extension | 12 |
| abstract_inverted_index.genuinely | 164 |
| abstract_inverted_index.kappa=1/2 | 46, 85, 113, 139 |
| abstract_inverted_index.kappa=1/3 | 69 |
| abstract_inverted_index.nonlinear | 105 |
| abstract_inverted_index.practical | 35 |
| abstract_inverted_index.quadratic | 135, 150 |
| abstract_inverted_index.technique | 29 |
| abstract_inverted_index.transform | 158 |
| abstract_inverted_index.dimension. | 92 |
| abstract_inverted_index.discussed, | 156 |
| abstract_inverted_index.edge-based | 23 |
| abstract_inverted_index.equations, | 106 |
| abstract_inverted_index.kappa=1/2. | 183 |
| abstract_inverted_index.kappa=1/3. | 48 |
| abstract_inverted_index.quadrature | 180 |
| abstract_inverted_index.techniques | 154 |
| abstract_inverted_index.2005-4999]. | 27 |
| abstract_inverted_index.confusions: | 41, 55 |
| abstract_inverted_index.dimensions, | 78 |
| abstract_inverted_index.third-order | 43, 62, 82, 102, 165 |
| abstract_inverted_index.extrapolates | 133 |
| abstract_inverted_index.kappa-scheme | 16 |
| abstract_inverted_index.point-valued | 66 |
| abstract_inverted_index.second-order | 125 |
| abstract_inverted_index.least-squares | 151 |
| abstract_inverted_index.discretization | 24 |
| abstract_inverted_index.fluid-dynamics | 37 |
| abstract_inverted_index.reconstruction | 7 |
| abstract_inverted_index.low-dissipation | 124 |
| abstract_inverted_index.simplex-element | 116 |
| abstract_inverted_index.unstructured-grid | 11, 36 |
| abstract_inverted_index.flux-reconstruction | 173 |
| cited_by_percentile_year.max | 93 |
| cited_by_percentile_year.min | 89 |
| countries_distinct_count | 1 |
| institutions_distinct_count | 2 |
| sustainable_development_goals[0].id | https://metadata.un.org/sdg/11 |
| sustainable_development_goals[0].score | 0.5699999928474426 |
| sustainable_development_goals[0].display_name | Sustainable cities and communities |
| citation_normalized_percentile.value | 0.44416064 |
| citation_normalized_percentile.is_in_top_1_percent | False |
| citation_normalized_percentile.is_in_top_10_percent | False |