· · · Institutional Repository

In this report, transport problems are solved with a particle method that takes into account the Eulerian background flow field. Dispersion and other transport problems can be solved applying this model, as long as the corresponding transport process is formulated with a flux gradient relation, i.e., the advection-diffusion equation. The particle method has been made consistent with such a transport process. Since many 3D flow models are formulated in general coordinates, the 3D particle displacements are also given with respect to such a coordinate system. Analytical and numerical aspects of this particle method have been studied. The effectiveness of the method has been demonstrated with two academic test cases including streamlines in a recirculation zone and grid dependency in a discharge problem.

To gain insight into the physical behaviour of 2D hydraulic models (mathematically formulated as a system of partial differential equations), the method of characteristics is used to analyse the propagation of physical meaningful disturbances. These disturbances propagate as wave fronts along bicharacteristics (rays) into the physical solution domain, while carrying the information from initial and boundary conditions. The method is applied to 2DH models for flow on a fixed and a 2DH two-layer model for turbidity currents in a reservoir. Introducing a point disturbance, circular shaped wave fronts develop related to water movement, and a star-shaped wave front related to disturbances in the mobile bed. A transversal wave front, related to vorticity, is formed in all models. An essential difference is shown in the propagation of the wave fronts for subcritical and supercritical flows. The characteristics have been used to define rules for imposing boundary conditions, and to find a stability condition for the two-layer 2D flow. The theory presented in this report is also applicable to other twodimensional engineering problems, and is important for imposing boundary conditions and for using the 2D numerical solution methods.

Simulated Moving Bed (SMB) chromatography is a unit operation in bio(chemical) process industry that is gaining more and more popularity. Possible reasons for the increasing popularity are the continuous operation, high selectivity and considerable savings in the consumption of solvents and resin. The aim of this project was to apply gradient solvent operation to the SMB technology. This decreases the solvent and resin consumption even more, and reduces the costs even more. In addition, less dilution of the product is achieved. Possible drawbacks of the technology are the complicated construction, laborous set-up, and mathematical modeling to get the initial process parameters. The project was financed by the Norwegian company Alpharma, AS, based in Oslo.

To resolve the flooding problems of Ho Chi Minh City, the possibilities for a large barrier downstream of the city are under study. In the final design stage a detailed 1-or 2-dimensional mathematical model is necessary to describe water levels and flow in the branches of the estuary system. The authors plea for the use of simple, first-order models, additional to a detailed model. The use of such models is shown as a tool in the preliminary stages of such a project but also as a reflection tool to get a better understanding of the system. The authors strongly argue that such tools are indispensible since the design process is never smooth and is never a linear sequence of theoretically logical steps. Several examples are being given.