Re: Fluid dynamics

*To*: mathgroup at smc.vnet.net*Subject*: [mg44488] Re: Fluid dynamics*From*: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>*Date*: Wed, 12 Nov 2003 08:01:36 -0500 (EST)*Organization*: Universitaet Leipzig*References*: <boif5j$oau$1@smc.vnet.net> <bopc55$olh$1@smc.vnet.net>*Reply-to*: kuska at informatik.uni-leipzig.de*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. > > 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 Hi, oh with "why not _start_ with a cellular automata, modeling the microscopic behavior of fluid molecules" you can also make a cow from the beef ? The Naver-Stokes equation is an approximation, a numerical model is an approximation to this approximation and a CA is an approximation to this approximation. And now tell me why the approximation, of the approximation, of a approximation is a good starting point to describe the *real* process without an approximation. Where is the source of all the information that is lost in during the various approximations if you start not with the original ? In a real collision the scattering take not place on a hexagonal grid, and the scattering directions are not bounded on a grid. The *only* reason to use a CA is, that a CA has excelent properties for massive parallel computing. And it is realy surprising that such a lausy model has still some (qualitative) features of the real process. However, in the most cases the quatitative computed features, like pressure differ significant from the measured ones or from the computed values obtained by a FE solution. Starting with a CA and use it for the real process is like to take the a photograph of an image of a painted apple and eat it. Regards Jens