SIMULATION OF A FIXED-BED SYSTEM USING A GEOMETRICALLY BASED ADAPTIVE-GRID METHOD

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.