fluid mechanics

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2 total messages Started by COMTET Sun, 13 Sep 1992 05:23

#512

Author: COMTET
Date: Sun, 13 Sep 1992 05:23

13 lines
717 bytes

Is there an algorithm using Finite Elements to simulate the evolution of

a dye with a given difusivity in an uncompressible fluid in two spatial

dimensions ? the equation adimensionned is :

dC/dt + v.gradC = (1/Re.Sc) Laplacian (C)

wher Re and Sc are the Reynolds and the Schmidt numbers.

Such an algorithm exists with finite centered differences and an implicit

scheme in time. (overelaxation method)

Re: fluid mechanics

#516

Author: Andreas Dunker
Date: Sun, 13 Sep 1992 11:49

28 lines
1789 bytes

In article <92257.012310COMTET@FRECP12.BITNET> <COMTET@FRECP12.BITNET> writes:
>Date: Sunday, 13 Sep 1992 01:23:10 EDT
>From: <COMTET@FRECP12.BITNET>
>Subject: fluid mechanics

>Is there an algorithm using Finite Elements to simulate the evolution of
>a dye with a given difusivity in an uncompressible fluid in two spatial
>dimensions ? the equation adimensionned is :
>dC/dt + v.gradC = (1/Re.Sc) Laplacian (C)
>wher Re and Sc are the Reynolds and the Schmidt numbers.
>Such an algorithm exists with finite centered differences and an implicit
>scheme in time. (overelaxation method)

You have to do a FEM-Discretisation in space only. Tho node-values are
now timedependent only and you've got a system of ODE's for this node-values.
Then you can do a difference method to solve this equations.
(Use Crank-Nicolson or implizit Euler-Method.)

By the way: This explained in a very good manner in:

Claes Johnson
numerical solution of partial differential equations by the
finite element method
Cambridge University Press, 1990
   ------------------------------------------------------------------------
   Andreas Dunker                                  andredu@hannover.by.byte
   In der Steinriede 7                           andreas@veeble.han.sub.org
   D-3000 Hannover 1

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