Re: Fluid dynamics

*To*: mathgroup at smc.vnet.net*Subject*: [mg44532] Re: Fluid dynamics*From*: Paul Abbott <paul at physics.uwa.edu.au>*Date*: Thu, 13 Nov 2003 05:57:50 -0500 (EST)*Organization*: The University of Western Australia*References*: <boif5j$oau$1@smc.vnet.net> <200311110055.TAA25144@smc.vnet.net> <botblj$cdu$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

In article <botblj$cdu$1 at smc.vnet.net>, Anton Antonov <antonov at wolfram.com> wrote: >In article <boif5j$oau$1 at smc.vnet.net>, > Nathan Moore <nmoore at physics.umn.edu> wrote: > >Cellular automa has always looked like a discretization of continuous >differential equations (ever looked closely at the Runge-Kutta DEQ >solver? A cursory glance shows that any x(i+1) comes from x(i) and >maybe also x(i-1) with statistical weights coming from taylor >expansions. This means that any differential equation can be >discretized and expressed as a "cellular automa system" > >There's nothing new and fabulous about that - its the standard approach >in Numerical methods. >> >> > I was doing research in large scale air pollutioning for some time. In > this area are usually considered 5 different physical processes with > very different time scales. From the mathematical modeling one gets, > say, 30-70 equations. The system cannot be treated directly with > classical PDE or ODE methods. These methods are used together with a > procedure called "splitting". E.g. one simulates separately first the > advection, then the chemistry; then again the advection, then the > chemistry, and so on. Now I find the idea to use the cellular automata > to skip the splitting as fabulous and exciting, :) but probably I like > mathematics too much. And at least in this researh area cellular > automata are not standard Numerical methods. And this _is_ the point of NKS! At the NKS conference I had an interesting conversation with Brian Vick <bvick at vt.edu> on this very topic. Paul Abbott wrote: > >But this is _not_ the point of A New Kind of Science (NKS): Of course > >you can discretize the Navier-Stokes equations but, instead of starting > >with a differential equation and discretizing, why not _start_ with a > >cellular automata, modeling the microscopic behavior of fluid molecules, > >having properties directly related to the physics at hand (by satisfying > >a set of simple collsion rules). See NKS pp 376-382 and 996-997. > > > >Cheers, > >Paul > > > > > >>On Friday, November 7, 2003, at 04:16 AM, martinro at carleton.edu wrote: > >> > >> > >> > >>>Hi, > >>>A partner and I are working on a project that describes fluid dynamic > >>>behavior in systems such as hurricanes and galaxy formation, for a > >>>college > >>>cellular automata physics seminar. It seems that research about the > >>>models > >>>to create these simulations are extremely hard to find, has anyone done > >>>this type of research on Mathematica or would know the form to write > >>>the > >>>programs? I know that the galaxy formation has been done on Fortran, > >>>but > >>>hurricanes and similar systems yield almost no results on a literature > >>>search. Dr. Wolfram says in his book A New Kind of Science that these > >>>type > >>>of weather related systems can be described by cellular automata in a > >>>similar manner to fluid dynamics, but gives no examples of the > >>>programs, > >>>can anyone help us? > >>> > >>>Thanks > >>>Ross Martin > >>>Carleton College > >>> > >>> > >>> > > > > > > > > -- Paul Abbott Phone: +61 8 9380 2734 School of Physics, M013 Fax: +61 8 9380 1014 The University of Western Australia (CRICOS Provider No 00126G) 35 Stirling Highway Crawley WA 6009 mailto:paul at physics.uwa.edu.au AUSTRALIA http://physics.uwa.edu.au/~paul

**References**:**Re: Fluid dynamics***From:*Paul Abbott <paul@physics.uwa.edu.au>