Positivity-preserving CE/SE schemes for solving the compressible Euler and Navier–Stokes equations on hybrid unstructured meshes

Hua Shen; Matteo Parsani

doi:10.1016/j.cpc.2018.05.011

Positivity-preserving CE/SE schemes for solving the compressible Euler and Navier–Stokes equations on hybrid unstructured meshes

Hua Shen, Matteo Parsani

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

9 Scopus citations

Abstract

We construct positivity-preserving space–time conservation element and solution element (CE/SE) schemes for solving the compressible Euler and Navier–Stokes equations on hybrid unstructured meshes consisting of triangular and rectangular elements. The schemes use an a posteriori limiter to prevent negative densities and pressures based on the premise of preserving optimal accuracy. The limiter enforces a constraint for spatial derivatives and does not change the conservative property of CE/SE schemes. Several numerical examples suggest that the proposed schemes preserve accuracy for smooth flows and strictly preserve positivity of densities and pressures for the problems involving near vacuum and very strong discontinuities.

Original language	English (US)
Pages (from-to)	165-176
Number of pages	12
Journal	Computer Physics Communications
Volume	232
DOIs	https://doi.org/10.1016/j.cpc.2018.05.011
State	Published - May 28 2018

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledgements: We are grateful to Dr. David Ketcheson for his valuable help on improving the manuscript, and would also like to acknowledge the computer time provided by the Extreme Computing Research Center at King Abdullah University of Science & Technology (KAUST) in Thuwal, Saudi Arabia.

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10.1016/j.cpc.2018.05.011

https://repository.kaust.edu.sa/bitstream/10754/627991/1/1-s2.0-S0010465518301747-main.pdf

Cite this

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title = "Positivity-preserving CE/SE schemes for solving the compressible Euler and Navier–Stokes equations on hybrid unstructured meshes",

abstract = "We construct positivity-preserving space–time conservation element and solution element (CE/SE) schemes for solving the compressible Euler and Navier–Stokes equations on hybrid unstructured meshes consisting of triangular and rectangular elements. The schemes use an a posteriori limiter to prevent negative densities and pressures based on the premise of preserving optimal accuracy. The limiter enforces a constraint for spatial derivatives and does not change the conservative property of CE/SE schemes. Several numerical examples suggest that the proposed schemes preserve accuracy for smooth flows and strictly preserve positivity of densities and pressures for the problems involving near vacuum and very strong discontinuities.",

author = "Hua Shen and Matteo Parsani",

note = "KAUST Repository Item: Exported on 2020-10-01 Acknowledgements: We are grateful to Dr. David Ketcheson for his valuable help on improving the manuscript, and would also like to acknowledge the computer time provided by the Extreme Computing Research Center at King Abdullah University of Science & Technology (KAUST) in Thuwal, Saudi Arabia.",

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doi = "10.1016/j.cpc.2018.05.011",

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AU - Shen, Hua

AU - Parsani, Matteo

N1 - KAUST Repository Item: Exported on 2020-10-01 Acknowledgements: We are grateful to Dr. David Ketcheson for his valuable help on improving the manuscript, and would also like to acknowledge the computer time provided by the Extreme Computing Research Center at King Abdullah University of Science & Technology (KAUST) in Thuwal, Saudi Arabia.

PY - 2018/5/28

Y1 - 2018/5/28

N2 - We construct positivity-preserving space–time conservation element and solution element (CE/SE) schemes for solving the compressible Euler and Navier–Stokes equations on hybrid unstructured meshes consisting of triangular and rectangular elements. The schemes use an a posteriori limiter to prevent negative densities and pressures based on the premise of preserving optimal accuracy. The limiter enforces a constraint for spatial derivatives and does not change the conservative property of CE/SE schemes. Several numerical examples suggest that the proposed schemes preserve accuracy for smooth flows and strictly preserve positivity of densities and pressures for the problems involving near vacuum and very strong discontinuities.

AB - We construct positivity-preserving space–time conservation element and solution element (CE/SE) schemes for solving the compressible Euler and Navier–Stokes equations on hybrid unstructured meshes consisting of triangular and rectangular elements. The schemes use an a posteriori limiter to prevent negative densities and pressures based on the premise of preserving optimal accuracy. The limiter enforces a constraint for spatial derivatives and does not change the conservative property of CE/SE schemes. Several numerical examples suggest that the proposed schemes preserve accuracy for smooth flows and strictly preserve positivity of densities and pressures for the problems involving near vacuum and very strong discontinuities.

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UR - http://www.scopus.com/inward/record.url?scp=85048125471&partnerID=8YFLogxK

U2 - 10.1016/j.cpc.2018.05.011

DO - 10.1016/j.cpc.2018.05.011

M3 - Article

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SP - 165

EP - 176

JO - Computer Physics Communications

JF - Computer Physics Communications

ER -

Positivity-preserving CE/SE schemes for solving the compressible Euler and Navier–Stokes equations on hybrid unstructured meshes

Abstract

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