Page 303 - Process Modelling and Simulation With Finite Element Methods

290 Process Modelling and Simulation with Finite Element Methods

Summary
This chapter has a plumbed the depths of coupling variables of all three varieties
to solve an array of inverse and integral equations. We encountered several
features of FEMLAB not previously explored - coupling to optimization tools
through MATLAB, extended meshes, using the time-dependent solver as an
iterative tool for stationary nonlinear models, and the ability to selectively
activate/deactivate multiphysics modes in coupled models. The latter is
particularly useful if there is only one-way coupling (as in the hydrodynamics
around the catalyst supported on the pellet in Chapter 3). In the case of the
integral equations treated here, a fictitious dependent variable on an auxiliary
domain is set up. The domain is used by coupling variables for various
operations, but the dependent variable is never needed itself. So deactivating it
results in better conditioning the FEM approximation to the integral equation.
Although we implemented this procedure only with the convolution integral in
our last model of the PBE, this is a generically useful technique for all the
integral equations posed here.
My contacts at COMSOL have led me to believe that coupling variables and
extended multiphysics were an addition to FEMLAB 2.2 “because they could”
without necessarily a vision of how they might prove to be practically useful.
With the wide survey of applications shown here, and earlier in Chapter 4, my
impression is that coupling variables and extended multiphysics are the features
of FEMLAB most likely to lead to rapid growth in its usage. Complex system
modeling and simulations that are envisaged for the biological systems,
micromachines (MEMs), and generic networked systems are readily modeled by
these features of FEMLAB. Process simulation packages such as HYSYS and
Aspen have long had the capability of simulating networks of coupled units
comprising ODES and nonlinear, algebraic constraints. Computational fluid
dynamics packages such as FLUENT and FIDAP and finite element solvers like
ANSYS contain the elements of PDE solver engines. FEMLAB, through
extended multiphysics and coupling variables, have made the combination
appear seamless to the user.

References

1. RA Gingold and JJ Monaghan, “Smooth particle hydrodynamics: theory
and application to nonspherical stars,” Mon. Not. Roy. Astr. SOC. 18 1 :375-
289, 1977.
2. AV Potapov, ML Hunt, and CS Campbell, “Solid-liquid flows using
smoothed particle hydrodynamics and the discrete element method.”
Powder Technology 116:204-213,2001.