
If one has an AT (Algebraic Topology) model of a system of fields and operations in Riemannian geometry, there is a natural way to construct derived models at each scale of resolution. In addition there are transition mappings between these derived models at different scales.The process of constructing derived models is based on the key idea of AT: chain homotopy equivalences between chain complexes. If a nonlinear PDE among the original system of fields and operations can be reformulated in the derived models, one can obtain a system of finite energy or finite scale models which are correlated by structure mappings. Incompressible Navier Stokes evolution in 3D can be described by the differential algebra of differential forms, the Hodge star operator and the projections of the Hodge decomposition. These objects are naturally interpreted in AT. The lecture will discuss this AT approach to deriving computational fluid models.

