Re: Re: Fluid dynamics

*To*: mathgroup at smc.vnet.net*Subject*: [mg44475] Re: [mg44454] Re: Fluid dynamics*From*: Anton Antonov <antonov at wolfram.com>*Date*: Wed, 12 Nov 2003 08:01:25 -0500 (EST)*References*: <boif5j$oau$1@smc.vnet.net> <200311110055.TAA25144@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

Paul Abbott 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. >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 >>> >>> >>> > > >

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

**Re: Numerical Optimization of**

**Re: Re: Fluid dynamics**

**Re: Fluid dynamics**

**Re: Re: Fluid dynamics**