John von Neumann and computational fluid dynamics (memorandum)

NOTICE

• DO NOT TRUST THE FOLLOWING

HISTORY

• (added) "Recent theories of turbulence" (von Neumann 1949), esp. chap. VI
• argument on analogy of "ultraviolet catastrophe" appears in chap. II
• (added) See Ryder and Mattsson's slide: CFD before CFD

POINTS

• In the wide spectrum of John von Neumann's works, relation between early computational fluid dynamics (including explosives, atomic bomb and weather forecast studies), continuum geometry and other fundamental contributions to logic and quantum mechanics does not seem well explained
• continuum geometry is unclear to me, so I would consider later
• any real fluid (except superfluid helium) is somewhat compressible and have certain viscosity
• regarding fluid as quantum multi-body system, interaction matters
• Artificial viscosity, as convergence parameter in CFD computations, is one of JvN's inventions and he should have been aware of manipulation of AV is a form of ultraviolet cutoff
• Mathematical intuitionism (of Brouwer and Weyl) mandates "UV cutoff" to any mathematical objects (no such thing like non-measurable and null set of continuum cardinality might be permitted to appear in intuitionist reasoning): Intuitionist continuum is "viscous"
• Some efforts on Banach-Tarski paradox and two-dimensional analogues, topological/amenable(at first it was called "measurable") groups and regular rings preceding the huge theory of operator rings seems to be focused on defining "intuitionistically valid" objects in classical mathematics

TODO

• settle continuum geometry in above account
• examine Navier and Stokes' reasonings of FD