The energy balance of a fixed bed system can be modelled by a Ist or 2
nd order evolutionary differential equation. In the first order case,
the equation exhibits shock behaviour. Standard numerical techniques f
ail to resolve the shock adequately without a large number of finely s
paced points in the spatial dimension. This leads to the use of adapti
ve grid methods to attempt to reduce the computational requirements fo
r fixed bed system simulation. This paper describes an adaptive grid a
lgorithm and the derivation of the nonuniform numerical approximations
for the derivative terms in the model equation and the boundary condi
tions. Two time stepping algorithms are compared: an implicit scheme b
ased on the Crank-Nicholson approximation coupled with a Newton-type s
olver and the explicit Runge-Kutte-Gill 4th order method. Results are
presented for the fixed bed system with appropriate initial and bounda
ry value conditions. A discussion of the effects of the interpolation
method used (required for generation of new grids adaptively) is prese
nted, indicating the most suitable choice for a problem of this type.
(C) 1998 Published by Elsevier Science Ltd: All rights reserved.