Discretising the linearised navier-stokes equations: A systems theory approach

The linearised Navier-Stokes equations form the basis of many models used in the design of feedback controllers for fluid flows. This set of coupled, partial differential algebraic equations (PDAEs) presents several numerical problems upon spatial discretisation, and whilst these problems are relatively well understood in the computational fluid dynamics (CFD) community, little attention has been paid to their system theoretic model analogies. This paper considers the problem known in the fluid dynamics community as the `checkerboard instability', and reconciles current understanding of this phenomenon from a systems' theory perspective, whereby frequency domain analysis elegantly explains the phenomenon. We report work in progress on deriving a discretised version of the linearised Navier-Stokes equations that avoids this problem.