Page 56 - Process Modelling and Simulation With Finite Element Methods

FEMLAB and the Basics of Numerical Analysis 43

Pull down the Mesh menu and select the Parameters option to set up our single
element.

Mesh Mode
Set Max element size, general = 1
Select Remesh
0 OK
Now pull down the Solve menu and select the Parameters option. This pops
up the Solver Parameters dialog window.

Solver Parameters
0 Time-stepping tab: set output times 0:O. 1 : 10.
Jacobian: numeric
Solve
Cancel
Try plotting point plots of ul, u2, u3 and u4 for the whole range of times. How
good is the qualitative agreement with Figure 1.5? Does it agree numerically
with the fully resolved solution?

Exercises:

1.3 Find the value of y'(x=l) from the system of equations below. Plot y' for x
between 0 and 3.
y"+ y'+ y2 = 0

y (x = 0) = 1
y' (x = 0) = 0

1.4 Linear systems of ODEs result from first order reversible reaction systems
in a continuously stirred tank reactor. For instance, consider the
isomerization reactions

A++B++C
with forward reaction rates kl and k3, respectively, as written; reverse
reaction rates k2 and b, as written. First order kinetics leads to the
following system of ODEs: