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Projective Integration for Moment Models of the BGK Equation
In this paper, we apply the projective integration method to moment models of the Boltzmann-BGK equation and investigate the numerical properties of the resulting scheme. Projective integration is an explicit, asymptotic-preserving scheme that is tailored to problems with a large spectral gap betwee...
Autores principales: | , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
2020
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Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7304693/ http://dx.doi.org/10.1007/978-3-030-50433-5_25 |
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author | Koellermeier, Julian Samaey, Giovanni |
author_facet | Koellermeier, Julian Samaey, Giovanni |
author_sort | Koellermeier, Julian |
collection | PubMed |
description | In this paper, we apply the projective integration method to moment models of the Boltzmann-BGK equation and investigate the numerical properties of the resulting scheme. Projective integration is an explicit, asymptotic-preserving scheme that is tailored to problems with a large spectral gap between fast and slow eigenvalues of the model. A spectral analysis of the moment model shows a clear spectral gap and reveals the multi-scale nature of the model. The new scheme overcomes the severe time step constraint of standard explicit schemes like the forward Euler scheme by performing a number of inner iterations and then extrapolating the solution forward in time. The projective integration scheme is non-intrusive and yields fast and accurate solutions, as demonstrated using a 1D shock tube test case. These observations open up many possibilities for further use of the scheme for high-resolution discretizations and different collision models. |
format | Online Article Text |
id | pubmed-7304693 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2020 |
record_format | MEDLINE/PubMed |
spelling | pubmed-73046932020-06-22 Projective Integration for Moment Models of the BGK Equation Koellermeier, Julian Samaey, Giovanni Computational Science – ICCS 2020 Article In this paper, we apply the projective integration method to moment models of the Boltzmann-BGK equation and investigate the numerical properties of the resulting scheme. Projective integration is an explicit, asymptotic-preserving scheme that is tailored to problems with a large spectral gap between fast and slow eigenvalues of the model. A spectral analysis of the moment model shows a clear spectral gap and reveals the multi-scale nature of the model. The new scheme overcomes the severe time step constraint of standard explicit schemes like the forward Euler scheme by performing a number of inner iterations and then extrapolating the solution forward in time. The projective integration scheme is non-intrusive and yields fast and accurate solutions, as demonstrated using a 1D shock tube test case. These observations open up many possibilities for further use of the scheme for high-resolution discretizations and different collision models. 2020-05-25 /pmc/articles/PMC7304693/ http://dx.doi.org/10.1007/978-3-030-50433-5_25 Text en © Springer Nature Switzerland AG 2020 This article is made available via the PMC Open Access Subset for unrestricted research re-use and secondary analysis in any form or by any means with acknowledgement of the original source. These permissions are granted for the duration of the World Health Organization (WHO) declaration of COVID-19 as a global pandemic. |
spellingShingle | Article Koellermeier, Julian Samaey, Giovanni Projective Integration for Moment Models of the BGK Equation |
title | Projective Integration for Moment Models of the BGK Equation |
title_full | Projective Integration for Moment Models of the BGK Equation |
title_fullStr | Projective Integration for Moment Models of the BGK Equation |
title_full_unstemmed | Projective Integration for Moment Models of the BGK Equation |
title_short | Projective Integration for Moment Models of the BGK Equation |
title_sort | projective integration for moment models of the bgk equation |
topic | Article |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7304693/ http://dx.doi.org/10.1007/978-3-030-50433-5_25 |
work_keys_str_mv | AT koellermeierjulian projectiveintegrationformomentmodelsofthebgkequation AT samaeygiovanni projectiveintegrationformomentmodelsofthebgkequation |