Discrete lie derivative

Abstract

Convection is an important transport mechanism in physics. Especially, in fluid dynamics at high Reynolds numbers this term dominates. Modern mimetic discretization methods consider physical variables as differential k-forms and their discrete analogues as k-cochains. Convection, in this parlance, is represented by the Lie derivative,ℒX. In this paper we design reduction operators, R from differential forms to cochains and define a discrete Lie derivative, ℒX which acts on cochains such that the commutation relation RℒX = ℒXR holds.