1 

Multigrid schemes for timedependent incompressible NavierStokes equations

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2 

Formulae to describe porous flow
For the description of porous flow the Forchheimer equation is normally used. Several formulae have been proposed for the coefficients Cl and c2 from this equation. All these formulae are based on experiments. Those coefficients represent the friction and resistance caused by the porous medium. The Forchheimer equation is a somewhat semiempirical formula. The phenomena that appear in a porous flow are not really described and implemented in the formula. In this report the assumptions and approximations to derive the Forchheimer equation using the NavierStokes equation were mentioned. To describe the flow on a porous structure (e.g., a breakwater) and the internal flow with a numerical model, the NavierStokes equation need to be adapted for the internal flow. In this report the NavierStokes equation is adapted for porous flow. The approach to derive this equation gives the adapted NavierStokes equation and it shows how several parameters are present in the coefficients. Those coefficients are also present in the Forchheimer equation. So, it gives expressions for the coefficients for the Forchheimer equation as well. The derived formula can be used for a numerical model that describes the flow on a porous structure (with NavierStokes equations) and the flow in the structure. This formula is derived by regarding several contributions of the force on the grains. Each contribution is written as a result of one term from the NavierStokes equation. Sometimes rather rough assumptions and approximations were made to derive the adapted NavierStokes equation for porous flow; those were mentioned in earlier sections. The contributions to the total force on the grains that are included in this formula are called laminar friction, turbulence friction, added mass and resistance as a result of the convective term (shaperesistance). The assumption is made that the force on the grains can be described by a summation of these contributions. Turbulence friction is not represented, or is not clearly represented, in existing derivations of formulae for porous flow. This friction is normally included in one term together with resistance as a result of the convective term (shape resistance). Those two contributions together, are usually called "drag". The problem of finding suitable values for the coefficients that describe the several processes, has to be solved by doing measurements. Most of the measurements were done under stationary flow conditions. Measurements for determining values of coefficients for nonstationary flow conditions are not sufficient yet to find suitable values for CM' The other coefficients are probably different under nonstationary flow conditions. This may cause that measurements of coefficients for Cl and C2 under stationary flow conditions can not be used for Cl and C2 under nonstationary flow conditions. The coefficients are probably depending on the Renumber and the KCnumber.

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3 

Measurements of the flow field in a rotating annular flume
Annular flumes are used for studying erosion and/or deposition of cohesive sediments in the laboratory. These flumes have advantages over straight recirculating flumes in that effects of inflow and outflow conditions are avoided and that there are no pumps which break down the suspended flocculated sediment. A disadvantage of annular flumes is that, because of the curvature secondary flow, velocities are generated in the flowing water, yielding a complex 3D flow field that is not well known up to now. The present report describes experiments in a rotating annular flume, Le. an annular flume in which not only the top lid rotates but the flume itself as well. The investigation is aimed at the accurate optimization of the ratio of rotational speeds of top lid and flume. Two different optimizing criteria were considered. The first criterion (criterion I) is the minimal intensity of secondary flow (especially in the lower part of the flume) and the second criterion (criterion IT) a uniform distribution of tangential velocity and of near bottom shear stress over the flume width. The measurements were done in a rotating annular flume with a mean diameter of 3.7 m. Flow velocity measurements were done with a laserDoppler velocimeter. The water depth, the rotational speeds of top lid and flume and the top lid width were varied. Minimal secondary flow circulations near the bottom of the flume are found to occur in conjunction with nearly uniform distributions, in the radial direction, of near bottom shear stresses. The investigation also shows that in situations where the nearbottom secondary flow circulations are minimal, the remaining secondary flow velocities are generally not small compared with cohesivesediment fall velocities. This has implications for future studies of erosion, flocculation and deposition of cohesive sediments in rotating annular flumes. Another topic discussed is the generalization of the results obtained from the experiments. Conditions for (strict or only geometrical) similarity of flows in carousels are investigated. In case of similar flows, relations between optimum conditions can be deduced. An experimental verification of these relations is presented. A simplified analysis of the flow in carousels is given. This analysis provides a method to obtain several relations for carousel flow. With these relations it is possible to estimate the bottom shear stress and to compare nonsimilar carousel flows, for example. The relations obtained in this way are confronted with the experimental evidence.

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4 

The method of characteristics applied to analyse 2DH models
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 twolayer model for turbidity currents in a reservoir. Introducing a point disturbance, circular shaped wave fronts develop related to water movement, and a starshaped 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 twolayer 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.

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5 

DESCRIPTION OF THE PROJECT ON NEUTRON FILTER DESIGN FOR BNCT

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6 

Further investigation on the solution of the incompressible NavierStokes equations by Krylov subspace and multigrid methods

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7 

An ILU smoother for the incompressible NavierStokes equations in general coordinates

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8 

Hydraulic rams, a consumer guide
This report is the result of a project, called "comparative tests on commercial and newly designed waterrams", carried out by the Delft University of Technology and the Foundation of Dutch Volunteers in Rwanda. The aim of this project was twofold:
 to test new, and cheap (i.e. locally constructable and maintainable) types of hydraulic rams,
 to compare several commercial types, in order to make a "consumers guide" for developing countries.
At the Laboratory of Fluid Mechanics of the Delft University of Technology the most essential aspects of the behaviour of commercially available rams were compared. Valve behaviour, delivery head, delivered quantity and efficiency were accentuated. Samples of the rams, tested in the laboratory were checked in Rwanda on reliability, durability and possibilities for local maintenance.

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9 

Velocityinversion in spacetime domain

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10 

Book review: David Banister. Transport planning

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11 

A boundary element model for nonlinear free surface phenomena
A boundary element method has been developed that can be used to calculate twodimensional potential flow phenomena with a free surface. The unsteady Bernoulli equation is applied at the actual position of the free surface. A solution for corners arising in the geometry of the boundary has been found. Comparison of results of the present model with results obtained with other numerical methods shows that reliable results can be obtained with the present model as long as the gap between two adjacent normals at a nodal point is less than about 40 degrees. At this limit the calculations break down. Within this limit, a forward directed jet is well developed in the case of breaking waves. The calculations can proceed if two points at the tip of the jet are considered as corner points. With these special points, the calculations can be continued up to the moment the jet falls down the forward face of the wave.

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12 

Flow and salt transport in mangrove swamps
An analytical mathematical model is presented for flow and salinity in tidal mangrove swamps that is based onedimensional approaches. The model is designed with the purpose to develop a method for rapid assessment of effects in mangrove swamps due to changes in river discharges that can also be used in situations with few data. A literature study demonstrated that the changes in salinity control the effects in mangrove swamps on the shortest timescale. The flow section of the model is based on linearisation of the momentum equation as introduced by Lorentz (1926). The salinity section of the model for open water in the swamps (creeks) is based on the equation for trapping in tidal swamps originally proposed by Ridd (1990). The salinity section of the model for groundwater is based on the description of hydrodynamic dispersion. A model with predictive value for groundwater salinity could be developed by incorporating the analytical solution of the flow section in the description of hydrodynamic dispersion and by using the solutions for salinity in creeks as boundary condition. The theoretical model can be used in practice with a relatively small set of field measurements and in combination with an existing model for flow and salt transport in rivers and estuaries.

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13 

Bedforms and undertow in the surf zone; an analysis of the LIP 11Ddata
The present report gives the results of a study on bedforms and undertow in the surf zone. It is the objective of this study to get a better insight into the physical processes in the surf zone. In this study, we make use of the data obtained during the LIP llDexperiments (Arcilla et al. [1994] and Roelvink and Reniers [1994]). We derive the characteristics of bedforms from measured profiles. We relate these bedform characteristics to the hydraulic conditions and analyse if they can be predicted with present prediction methods. Further, we develop an inverse modelling technique, which is based on the mass and momentum balance equations. With this technique we derive values of important physical parameters, like eddy viscosity, shear stresses, friction factors, bed roughness and mass flux. The derived physical parameters are compared with present methods to describe these parameters.

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14 

Land disposal options of contaminated dredged material
The problems associated with contaminated dredged material disposal (basically lack of disposal sites and potential adverse environmental impacts) have become major issues in many industrialized and developing countries. The sediment removed for environmental reasons is obviously contaminated, but in many cases the sediment removed during normal maintenance dredging of waterways and harbours also contains a wide range of potentially toxic substances. In the Netherlands for instance, out of the 50 million m3 of dredged material produced annually during normal maintenance dredging work 20 million m is contaminated to such a degree that its dispersion into the environment without measures to impede contaminant release is unacceptable (Vellinga, 1989). This paper gives a review of the disposal and treatment options currently in use or considered to have the potential for practical use in the near future with an emphasis on land disposal. It briefly discusses the main contaminant release pathways, the governing processes and the stateoftheart methodology, used to assess potential environmental impacts.

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15 

Financially independent public transport; its impacts on the public transport system in the Netherlands

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16 

Application of sediment transport formulae to sanddike breach erosion
The Technical Advisory Committee on Water Defences in the Netherlands has decided to develop a mathematical model for breach erosion in dunes and dikes, with which it will be possible to predict the growth of the breach and the discharge rate through the breach in case of a dikeburst. An essential part of such a mathematical model is the description of the entrainment of the sediment (sand or clay) and its transport through the breach. The process of breach erosion, especially in the first phases, is characterized by relatively steep slopes and large flow velocities. None of the existing sediment transport formulae has been derived and tested for these circumstances. This report presents the results of an investigation into the applicability of sediment transport formulae to sanddike breach erosion. In view of the steep slopes and the large flow velocities, the following sediment transport conceptions have been included in the study:
formulae for sandwater mixture flows: Wilson (1966), Wilson (1987), Mastbergen and Winterwerp (1987);
formulae for sediment transport in flows on relatively steep slopes: Mizuyama (1977), Smart and Jaeggi (1983), Bathurst et al. (1987), Takahashi (1987), Rickenmann (1991);
formulae for river regimes which have been tested for (relatively) large flow velocities (large shear stress velocities): Engelund and Hansen (1967), Van Rijn (1984a, 1984c);
energeticsbased sediment transport conceptions: Bagnold (1963, 1966), Yang (1979), BagnoldBailard, see Bailard (1981), BagnoldVisser, see Visser (1988), these last two formulae are modifications of the original conception of Bagnold (1963, 1966);
formulae for debris flows: Takahashi (1978, 1980, 1987, 1991). These sediment transport formulae, combined with Galappatti's model (1983) for the pickup of sediment, are compared with the data of two laboratory experiments (Schelde Flume experiments, see Steetzel and Visser, 1992a, 1992b) and the data of a field experiment (Zwin'89 experiment, see Visser et al., 1990). Experimental sediment transport rates have been determined as volumes of sand eroded over a certain period of time. All tests concern supercritical flow (Froude number Fr > 1, i.e. here 2.8<5 Fr<5 4.1), large values for Shields' mobility parameter (10 < theta < 100) and high concentrations (depthaveraged values rising up to about 0.25 by volume). Most of the tested sediment transport formulae predict sand transport rates being much larger than the observed quantities. Only the BagnoldVisser formula, see Visser (1988), predicts sand transport rates within a factor two of the experimental values. With the formulation of Van Rijn (1984a, 1984c) this is possible within about a factor three. All other formulae give larger deviations from the experimental data. These conclusions hold for the three initial phases of the process of breach erosion, when the flow is supercritical, and confirm the good results obtained up to now with the BagnoldVisser formula, see Visser (1988, 1994). Once more it should be emphasized that this formula has not been derived for a situation where the rate of sand entrainment is so large as in the first three phases of the breach erosion process (this applies to both the energeticsbased method and the semiempirical determination of the efficiency factor). The relatively large entrainment of sediment causes a relatively large increase of both the flow rate and the sediment concentration of the sandwater mixture along the inner slope (so that the effect of 'hindered entrainment' is possibly not negligible). Further study is necessary to establish the effects of the large rate of sediment entrainment on the breach erosion process. For the time being it is recommended to apply the formula of BagnoldVisser in a mathematical breach growth model for the description of the first phases (i.e. as long as the flow is supercritical) of the breach erosion process. The present study does not recommend a formula for the important later phases of breach growth (when the flows becomes subcritical), in which most of the breach erosion takes place and in which also the dimensions of the ultimate breach are determined. Probably the data of the recent Zwin'94 field experiment (see Visser et al, 1995) will allow such a recommendation in the near future. For the present the conclusion of Voogt et al. (1991) is still valid, i.e. that the formulae of Engelund and Hansen (1967) and in particular Van Rijn (1984a, 1984c) can also be applied for relatively large current velocities in subcritical flow.

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17 

A multigrid method combined with defect correction for free convection problems at high Rayleigh numbers

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18 

In search of a better sediment mixing coefficient model
Results of sediment transport calculations are often necessary in solving practical coastal engineering problems. (Sediment transport due to waves and currents). Many transport formulae have been proposed in literature in the past. Selection of the proper one while solving a particular problem, is a difficult task for a coastal engineer. In considering sediment transport under wavecurrent conditions it is worthwhile to make a distinction between two situations, viz.: The fluctuations in the orbital motion have to be fully taken into account in order to find the resulting sediment transport (intrawave type of description; often: crossshore sediment transport);  It is sufficient to take timeaveraged effects of the waves into account in order to find the resulting sediment transport rate (intrawave type of description is not required; often: longshore sediment transport). For the longshore sediment transport mode, transport formulae based on timeaveraged velocity distributions and timeaveraged sediment concentration distributions over the water depth can often be used. The present paper is restricted to this type of formula.

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19 

Book review: L. Dorn. Driver behaviour and training

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20 

Flying is the safest way to travel: How aviation was a pioneer in independent accident investigation

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