Constructing a Mimetic Curl using Gauss’ Theorem

The common way to define a curl operator considers Stoke’s Theorem and the concept of circulation. Common numerical discretizations for this operator also use this approach. In this work, we revisit the construction of the curl operator using an extended form of Gauss’ Divergence Theorem instead. This new approach allows us to present a discretization framework that naturally inherits all the desirable properties of the mimetic differential operators. We present the mathematical justification for this new approach and we test the mimetic curl operator on 2D test cases. Physical applications concern the computational study of hurricanes.