Modelling error and constitutive relations in simulation of flow and transport

SUMMARY The main theme of this paper is the modelling error associated with the choice of constitutive equations and associated parameter sensitivity. These key concepts arerst discussed in a general way and explored in detail subsequently for threeow application problems which share certain similarities not only in thenite element formulation but also in the nature of the non-linear constitutive laws that are investigated. The specicow problems involve: density drivenow in porous media, the Powell- Eyring model for generalized Newtonianows, and the related Glen'sow type of constitutive relations for glacier modelling. Copyright ? 2004 John Wiley & Sons, Ltd. Continuing advances in high-speed computing permit more complex non-linear problems to be simulated. Non-linearities can arise in several common ways, perhaps the most important being non-linear couplings such as the advective term inow and transport processes, through various non-linear reaction terms and through non-linearities associated with the applicable constitutive models. The focus of the present work is on mathematical and numerical issues associated with the constitutive model assumptions and the resulting model errors. We also study the sensitivity of models to model parameters.

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