Discrete Lie Advection of Differential Forms
This work provides a novel method for simulating advection of differential forms, which is important for computational physics and geometry processing, but the results are limited to regular grids and simple cases.
The paper presents a numerical technique for Lie advection of differential forms using discrete exterior calculus and finite volume methods, demonstrating accurate advection of scalar fields and 1-forms on regular grids.
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.