Navier-Stokes solver using Green's functions II: spectral integration of channel flow and plane Couette flow

The Kleiser-Schumann algorithm has been widely used for the direct numerical simulation of turbulence in rectangular geometries. At the heart of the algorithm is the solution of linear systems which are tridiagonal except for one row. This note shows how to solve the Kleiser-Schumann problem using perfectly triangular matrices. An advantage is the ability to use functions in the LAPACK library. The method is used to simulate turbulence in channel flow at $Re=80,000$ (and $Re_{\tau}=2400$) using $10^{9}$ grid points. An assessment of the length of time necessary to eliminate transient effects in the initial state is included

An incremental development of the Mondex system in Event-B

A development of the Mondex system was undertaken using Event-B and its associated proof tools. An incremental approach was used whereby the refinement between the abstract specification of the system and its detailed design was verified through a series of refinements. The consequence of this incremental approach was that we achieved a very high degree of automatic proof. The essential features of our development are outlined. We also present some modelling and proof guidelines that we found helped us gain a deep understanding of the system and achieve the high degree of automatic proo