Page 49 - Process Modelling and Simulation With Finite Element Methods

36 Process Modelling and Simulation with Finite Element Methods

dY
- z(x)
=
dx
dz
- r(x)- q(x)z(x)
=
dx
Each of these ODEs can be numerically integrated by time marching methods as
in (1.10) or (1.1 l), simultaneously. A simple example is
d 'u
-+u=o (1.13)
dt2

Reduction of order yields two first order ODEs:
du
1- u2
dt
(1.14)
du2
dt - u1
Taking the initial condition to be u,=l and u2=0, we can now set up a O-D spatial
system to integrate this coupled set of ODEs.
Start up FEMLAB and await the Model Navigator window. If you already have
a FEMLAB session started, save your workspace as a model MAT-file or the
commands as a model m-file, and the pull down the file menu and select New.

Model Navigator
Select l-D dimension
Select PDE modes + Coefficient+time dependent
Select 2 dependent variables
Element: Lagrange - linear
0 More>>
OK
0
This application mode gives us two dependent variables uI and u2 and one space
coordinate x. Next, set up the domain.
Pull down the Draw menu and select Specify Geometry.

Draw Mode
Name: interval
start: 0
stop: 1
ApplylOK