Staggered grids for multidimensional multiscale modelling
For high accuracy and to improve simulated wave characteristics, this article extends the concept of staggered grids to novel multidimensional multiscale modelling enabling efficient computation on sparse patches. Computational schemes for wave-like systems with small dissipation are often inaccurat...
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| Published in: | Computers & fluids Vol. 271; p. 106167 |
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| Main Authors: | , , , , |
| Format: | Journal Article |
| Language: | English |
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15.03.2024
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| ISSN: | 0045-7930, 1879-0747 |
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| Abstract | For high accuracy and to improve simulated wave characteristics, this article extends the concept of staggered grids to novel multidimensional multiscale modelling enabling efficient computation on sparse patches. Computational schemes for wave-like systems with small dissipation are often inaccurate and unstable due to truncation errors and numerical roundoff errors. Hence simulations of wave-like systems lacking proper handling of these numerical issues often fail to represent the physical characteristics of wave phenomena. This challenge gets even more intricate for multiscale modelling, especially in multiple dimensions. But numerical schemes on staggered grids are significantly less dispersive, better model the group velocity, and preserve much of the wave characteristics. This article develops and exhaustively studies all 167040 possible 2D multiscale staggered grids. Our catalog (Divahar, 2023) interactively plots all of them. Only 120 multiscale staggered patch grids give stable and accurate multiscale schemes. Specifically, this article develops these 120 multiscale staggered grids and demonstrates their stability, accuracy, and wave-preserving characteristic for equation-free multiscale modelling of weakly damped linear waves. These characteristics of the developed multiscale staggered grids must also hold in general for multiscale modelling of many complex spatio-temporal physical phenomena such as the general computational fluid dynamics.
•We develop and comprehensively explore multidimensional multiscale staggered grids.•Among 167040 2D multiscale staggered grids, only 120 give stable and accurate schemes.•These 120 grids give highly accurate equation-free multiscale patch scheme for waves.•We show the accuracy for multiscale modelling of ideal and weakly damped linear waves.•This work provides an essential foundation to multiscale schemes for wave systems. |
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| AbstractList | For high accuracy and to improve simulated wave characteristics, this article extends the concept of staggered grids to novel multidimensional multiscale modelling enabling efficient computation on sparse patches. Computational schemes for wave-like systems with small dissipation are often inaccurate and unstable due to truncation errors and numerical roundoff errors. Hence simulations of wave-like systems lacking proper handling of these numerical issues often fail to represent the physical characteristics of wave phenomena. This challenge gets even more intricate for multiscale modelling, especially in multiple dimensions. But numerical schemes on staggered grids are significantly less dispersive, better model the group velocity, and preserve much of the wave characteristics. This article develops and exhaustively studies all 167040 possible 2D multiscale staggered grids. Our catalog (Divahar, 2023) interactively plots all of them. Only 120 multiscale staggered patch grids give stable and accurate multiscale schemes. Specifically, this article develops these 120 multiscale staggered grids and demonstrates their stability, accuracy, and wave-preserving characteristic for equation-free multiscale modelling of weakly damped linear waves. These characteristics of the developed multiscale staggered grids must also hold in general for multiscale modelling of many complex spatio-temporal physical phenomena such as the general computational fluid dynamics.
•We develop and comprehensively explore multidimensional multiscale staggered grids.•Among 167040 2D multiscale staggered grids, only 120 give stable and accurate schemes.•These 120 grids give highly accurate equation-free multiscale patch scheme for waves.•We show the accuracy for multiscale modelling of ideal and weakly damped linear waves.•This work provides an essential foundation to multiscale schemes for wave systems. |
| ArticleNumber | 106167 |
| Author | Kevrekidis, Ioannis G. Mattner, Trent W. Divahar, J. Bunder, J.E. Roberts, A.J. |
| Author_xml | – sequence: 1 givenname: J. orcidid: 0000-0002-9506-8846 surname: Divahar fullname: Divahar, J. email: jdivahar@outlook.com organization: School of Mathematical Sciences, University of Adelaide, Australia – sequence: 2 givenname: A.J. orcidid: 0000-0001-8930-1552 surname: Roberts fullname: Roberts, A.J. organization: School of Mathematical Sciences, University of Adelaide, Australia – sequence: 3 givenname: Trent W. orcidid: 0000-0002-5313-5887 surname: Mattner fullname: Mattner, Trent W. organization: School of Mathematical Sciences, University of Adelaide, Australia – sequence: 4 givenname: J.E. orcidid: 0000-0001-5355-2288 surname: Bunder fullname: Bunder, J.E. organization: UniSA STEM, University of South Australia, Mawson Lakes, SA, 5095, Australia – sequence: 5 givenname: Ioannis G. orcidid: 0000-0003-2220-3522 surname: Kevrekidis fullname: Kevrekidis, Ioannis G. organization: Departments of Chemical and Biomolecular Engineering & Applied Mathematics and Statistics, Johns Hopkins University, Baltimore, MD, USA |
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| Cites_doi | 10.1175/1520-0469(1986)043<1547:OTEOAS>2.0.CO;2 10.1109/MCSE.2005.57 10.1007/BF03024036 10.4310/CMS.2004.v2.n4.a2 10.1007/s11075-020-01027-z 10.1038/s41563-020-00913-0 10.21914/anziamj.v46i0.981 10.1137/0727052 10.1017/S0022112006008640 10.1017/S0962492921000015 10.1017/S0334270000005968 10.1016/0022-0396(88)90110-6 10.1016/0375-9601(88)90295-2 10.5334/jors.151 10.1093/imamat/hxv034 10.1016/j.cma.2023.116133 10.21914/anziamj.v54i0.6137 10.1063/1.1761178 10.1016/j.jcp.2017.02.004 10.1007/s10665-015-9817-7 10.1146/annurev.physchem.59.032607.093610 10.1137/S0036142998335881 10.1007/s00211-021-01232-5 10.1002/aic.10106 10.1051/m2an/2009026 10.1080/21664250.2018.1529265 10.1007/s00707-021-02962-1 10.1137/060654554 10.1016/0017-9310(72)90054-3 |
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| Keywords | Equation-free patch scheme Large-scale waves Staggered grids Computational fluid dynamics Multiscale modelling |
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| Title | Staggered grids for multidimensional multiscale modelling |
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