Discrete Lie Advection of Differential Forms

Details Discrete Lie Advection of Differential Forms Discrete Lie Advection of Differential Forms

2009-12-07

arxiv.org/abs/0912.1177v2

Mathematics

Numerical Analysis

Accepted version; to be published in J. FoCM

Scientific paper

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.

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