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Numerical schemes for tracer studies in shallow shelf seas Mercier, Christophe Doctoral thesis (2012) Nowadays, tracers have revealed to be an invaluable integrated tool to investigate the different thematics related to coastal areas, shallow shelf seas or estuaries. In this work, they are used in ... [more ▼] Nowadays, tracers have revealed to be an invaluable integrated tool to investigate the different thematics related to coastal areas, shallow shelf seas or estuaries. In this work, they are used in combination with a parallel scalable Fortran90 implementation of a 3D hydrodynamic model to study the transport of mud within the Belgian Coastal Zone. The results obtained illustrate the need for tools to understand the interactions between such highly energetic coastal areas and the sediment dynamics. The Constituent Age and Residence time Theory (CART), originally applied to passive tracers, is therefore extended to describe the sediments and used to quantify their rates of resuspension and horizontal transport. This application reveals some numerical issues that may degrade the reliability of the results. The different numerical parameterizations are thus revisited starting with the use of advection schemes, and especially, the Total Variation Diminishing (TVD) schemes built along the line defined by Harten. It is shown that the blind application of the usual TVD schemes and associated flux limiters can lead to non-TVD solutions when applied to complex geometries. Spatial and/or temporal variations of the bathymetry can indeed break the TVD property. Hopefully, really TVD schemes can be recovered by taking these variations into account in the formulation of the flux limiters. Even if its Eulerian formulation eases the implementation of CART into existing models, it is shown that CART's computation procedure lacks a numerical framework for a robust application. To address this, we enforce the consistency, defined as the requirement that the integration scheme does not introduce errors in the age field when aging is the only active process. Unfortunately, this does not guarantee the absence of overshootings. While it does not seem feasible to ensure a TVD behavior of the age field, appropriate modifications of the flux/slope limiters are derived here to prevent the occurrence of age values outside the physically acceptable range. On the bases of the solutions obtained after the advection of any numbers of tracers using high-order non-linear schemes, several control or global variables can be built. Even if the independent advection schemes used are specifically built to produce profiles free from the numerical artifacts that can spoil the physical meaning of the results, such global/control variables can exhibit these unwanted behaviors. This problematic is firstly treated with regard to the TVD schemes built from Harten's theorem. But guaranteeing the TVD property is not always feasible. Alternatively, appropriate modifications of the flux/slope limiters are implemented here to enforce a maximum principle for any global/control variable built as first-order homographic function of its components. [less ▲] Detailed reference viewed: 84 (20 ULg)Consistent computation of the age of water parcels using CART Mercier, Christophe ; Delhez, Eric in Ocean Modelling (2010), 35 The Constituent-oriented Age and Residence time Theory (CART) provides a flexible and efficient framework to diagnose the dynamics of marine systems. Beside the equation for the concentration of ... [more ▼] The Constituent-oriented Age and Residence time Theory (CART) provides a flexible and efficient framework to diagnose the dynamics of marine systems. Beside the equation for the concentration of appropriate (real or artificial) tracers, the method requires the resolution of differential problems for the so-called age concentration of each of these tracers. Thanks to its Eulerian formulation as an advection/diffusion problem with source terms, the method is easily implemented in existing models. However, some numerical artifacts should be avoided in order to produce physically meaningful results leading to a better understanding of the system under study. In this paper, we address two such issues that are related to the degree of implicitness of the different terms and to the advection scheme. To enforce the consistency between the discrete equations for the concentration of a tracer and for its age concentration, the degree of implicitness must be identical in the source/sink terms of the two equations. However, the ageing term should be computed in a completely explicit (respectively implicit) way if the discretization of the source/sink terms is implicit in time (respectively explicit). A specific attention should also be paid to the advection schemes for the concentration and the age concentration. The raw application of Total Variation Diminishing (TVD) scheme for both equations can lead to the occurrence of artificial local extreme values and spatial oscillations of the age field. While the TVD behavior of the discrete age field cannot be guaranteed, appropriate modifications of the flux/slope limiters used in the TVD schemes can be implemented to enforce a maximum principle that prevents the occurrence of age values outside the physically acceptable range. [less ▲] Detailed reference viewed: 47 (23 ULg)A modified TVD scheme for the advection of two or more variables with consideration for their sum Mercier, Christophe ; Delhez, Eric in Ocean Dynamics (2010), 60 Total variation diminishing (TVD) advection schemes are known to produce results that are free from some of the numerical artifacts (no overshooting, no spurious oscillation, small diffusion) that can ... [more ▼] Total variation diminishing (TVD) advection schemes are known to produce results that are free from some of the numerical artifacts (no overshooting, no spurious oscillation, small diffusion) that can spoil the physical significance of the results. When two or more tracers are advected separately using a TVD scheme, the sum of these variables can however exhibit some inappropriate behaviors. The total variation of the sum will not necessarily be non- increasing and local artificial oscillations and extrema can appear. We show that these can be avoided with only minor perturbations of the original solution by adjusting the slope limiters used for the different variables. If the sum of these variables has some physical significance, for instance as refinement of a larger model compartment, the correction procedure introduced in this paper should be used to ensure a physically meaningful solution. [less ▲] Detailed reference viewed: 45 (25 ULg)Really TVD advection schemes for the depth-integrated transport equation Mercier, Christophe ; Delhez, Eric in Ocean Modelling (2010), 33 Detailed reference viewed: 94 (54 ULg)Really TVD advection schemes for shelf seas Mercier, Christophe ; Delhez, Eric Conference (2010) During the last decade large efforts have been devoted to the development of high-resolution schemes to solve advection problems. High-resolution conservative numerical schemes satisfying conservative ... [more ▼] During the last decade large efforts have been devoted to the development of high-resolution schemes to solve advection problems. High-resolution conservative numerical schemes satisfying conservative, monotonicity preserving and shock-capturing properties are nowadays widely used in ocean modeling. Among these, TVD schemes, based on the concept of Total Variation Diminishing (TVD), were progressively adopted because of their good behavior that guarantees a solution free from numerical artifacts (no overshooting, no spurious oscillation, small diffusion) that can spoil the physical significance of the results. Most of the TVD schemes and associated limiters have been originally developed in idealized one-dimensional flows described by a linear advection. In finite volume marine models, one has however often to deal with the depth integrated advection equation. This formulation is usually preferred because of its conservative form that is particularly suited to numerical treatment using a finite volume approach. Conservative numerical schemes can be easily formulated to ensure that the total mass of the advected quantity is conserved. This property is very valuable in the context of environmental studies for which a strict equilibrium of the mass budget of pollutants is often more relevant that the raw accuracy of the integration scheme. In the same context, the numerical scheme should also produce neither new local extremum nor negative concentrations, i.e. it should be monotonicity preserving which is implied by the TVD property. The development of TVD schemes for the resolution of advection equations written in the conservative form is however not trivial. Numerical experiments show that the blind application to the depth-integrated equation of the usual TVD schemes and associated flux limiters introduced in the context of linear advection can lead to non-TVD solutions in presence of complex geometries. Spatial and/or temporal variations of the local bathymetry can indeed break the TVD property of the usual schemes. Really TVD schemes can be recovered by taking into account the local depth and its variations in the formulation of the flux limiters. Using this approach, a generalized superbee limiter is introduced and validated. [less ▲] Detailed reference viewed: 80 (9 ULg)Diagnosis of the sediment transport in the Belgian Coastal Zone Mercier, Christophe ; Delhez, Eric in Estuarine Coastal & Shelf Science (2007), 74(4), 670-683 Estimating the age of particles in marine environment constitutes an invaluable tool to understand the interactions between complex flows and sediment dynamics, particularly in highly energetic coastal ... [more ▼] Estimating the age of particles in marine environment constitutes an invaluable tool to understand the interactions between complex flows and sediment dynamics, particularly in highly energetic coastal areas such as the Belgian Coastal Zone (Southern Bight in the North Sea). To this end, the Constituent Age and Residence time Theory-CART-introduced by Delhez, E.J.M., Campin, J.-M., Hirst, A.C., Deleersnijder, E. [1999a. Toward a general theory of the age in ocean modelling. Ocean Modelling 1, 17-27] for passive water constituents is extended to describe the sediment dynamics. It is then used in combination with a three-dimensional coupled hydrodynamic-sediment transport model to investigate sediment processes in the Belgian Coastal Zone focusing on two complementary aspects of the sediment dynamics: the internal sediment motion and redistribution within the Belgian coast; and the horizontal transport. (C) 2007 Elsevier Ltd. All rights reserved. [less ▲] Detailed reference viewed: 130 (42 ULg)Three dimensional sediment transport model of the Belgian coastal zone: application of the CART theory Mercier, Christophe ; Delhez, Eric Conference (2006) Suspended sediment processes in the Belgian coastal zone are discussed by presenting the first results given by a 3D coupled hydrodynamic-sediment transport model covering the Southern Bight in North Sea ... [more ▼] Suspended sediment processes in the Belgian coastal zone are discussed by presenting the first results given by a 3D coupled hydrodynamic-sediment transport model covering the Southern Bight in North Sea. The hydrodynamic sub-model is three-dimensional, baroclinic and includes a refined turbulence closure. In the sediment transport sub-model, the dynamic of sediments is described by an evolution equation of the sediment concentration in the water column and an equation for the sediment load on the seabed. Sedimentation is modeled through the addition of a sedimentation velocity in the vertical advection term. For the evaluation of deposition and erosion terms, formu- lae based on the calculation of the bottom stress under the combined effect of prevailing currents and waves are used. For more realism, sediment loads has also been split into different sediment classes with different sedimentation, deposition and erosion characteristics. The equations are solved by a finite volume method based on an Arakawa C grid, using sigma-transform and mode-splitting numerical methods. The horizontal resolution is 500x500 m and 10 vertical sigma-layers are used. Advection is handled using a TVD scheme with superbee flux limiter. Boundary conditions are provided by coupling this model to a 3D coupled hydrodynamic-sediment transport model of the North-Western European Continental Shelf. The results are validated with measurements carried out by Haecon NV and are compared with those obtained with the MU-STM model. A sensitivity analysis of the model to critical parameters of erosion, deposition and sedimentation based on the concept of residence time was carried out. [less ▲] Detailed reference viewed: 81 (6 ULg)Modélisation tridimensionnelle du transport sédimentaire au large de la côte belge Mercier, Christophe Master of advanced studies dissertation (2005) Detailed reference viewed: 39 (16 ULg) |
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