Published April 2011
| Version Erratum + Submitted
Journal Article
Open
Discrete Lie Advection of Differential Forms
Creators
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1.
California Institute of Technology
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2.
Michigan State University
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3.
University of Southern California
Abstract
In this paper, we present a numerical technique for performing Lie advection of arbitrary differential forms. Leveraging advances in high-resolution finite-volume methods for scalar hyperbolic conservation laws, we first discretize the interior product (also called contraction) through integrals over Eulerian approximations of extrusions. This, along with Cartan's homotopy formula and a discrete exterior derivative, can then be used to derive a discrete Lie derivative. The usefulness of this operator is demonstrated through the numerical advection of scalar fields and 1-forms on regular grids.
Additional Information
© 2010 SFoCM. Published online: 08 September 2010. Received: 10/10/2008; Revised: 7/16/10; Accepted: 8/10/10. Communicated by Douglas Arnold and Peter Olver. This research was partially supported by NSF grants CCF-0811313/ 0811373/-0936830/1011944, CMMI-0757106/0757123/0757092, IIS-0953096, and DMS-0453145, and by the Center for the Mathematics of Information at Caltech.Attached Files
Submitted - 0912.1177v2.pdf
Erratum - art_3A10.1007_2Fs10208-011-9089-1.pdf
Files
0912.1177v2.pdf
Additional details
Identifiers
- Eprint ID
- 20234
- Resolver ID
- CaltechAUTHORS:20100930-091445735
Related works
- Describes
- http://arxiv.org/abs/0912.1177 (URL)
- 10.1007/s10208-011-9089-1 (DOI)
Funding
- NSF
- CCF-0811313
- NSF
- CCF-0811373
- NSF
- CCF-0936830
- NSF
- CCF-1011944
- NSF
- CMMI-0757106
- NSF
- CMMI-0757123
- NSF
- CMMI-0757092
- NSF
- IIS-0953096
- NSF
- DMS-0453145
- Caltech Center for the Mathematics of Information
Dates
- Created
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2010-10-01Created from EPrint's datestamp field
- Updated
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2023-06-01Created from EPrint's last_modified field