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Published April 2011 | Erratum + Submitted
Journal Article Open

Discrete Lie Advection of Differential Forms

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.

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Submitted - 0912.1177v2.pdf

Erratum - art_3A10.1007_2Fs10208-011-9089-1.pdf

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August 22, 2023
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