References of "Delhez, Eric"
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See detailOptimizing Perfectly Matched Layers in Discrete Contexts
Modave, Axel ULg; Delhez, Eric ULg; Geuzaine, Christophe ULg

in International Journal for Numerical Methods in Engineering (2014), 99(6), 410437

Perfectly Matched Layers (PMLs) are widely used for the numerical simulation of wave-like problems defined on large or infinite spatial domains. However, for both the time-dependent and the time-harmonic ... [more ▼]

Perfectly Matched Layers (PMLs) are widely used for the numerical simulation of wave-like problems defined on large or infinite spatial domains. However, for both the time-dependent and the time-harmonic cases, their performance critically depends on the so-called absorption function. This paper deals with the choice of this function when classical numerical methods are used (based on finite differences, finite volumes, continuous finite elements and discontinuous finite elements). After reviewing the properties of the PMLs at the continuous level, we analyse how they are altered by the different spatial discretizations. In the light of these results, different shapes of absorption function are optimized and compared by means of both one- and two-dimensional representative time-dependent cases. This study highlights the advantages of the so-called shifted hyperbolic function, which is efficient in all cases and does not require the tuning of a free parameter, by contrast with the widely used polynomial functions. [less ▲]

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See detailResidence time vs influence time
Delhez, Eric ULg; de Brye, Bejamin; de Brauwere, Anouk et al

in Journal of Marine Systems (2014), 132

The concepts of age, residence time, exposure time and influence time provide space and time dependent quantitative measures of the rate at which watermasses and pollutants enter and/or leave a control ... [more ▼]

The concepts of age, residence time, exposure time and influence time provide space and time dependent quantitative measures of the rate at which watermasses and pollutants enter and/or leave a control domain. To help avoid confusion between these concepts, this paper provides clear definitions of the residence time and the influence time. The similarities and differences between them are illustrated using both a simplified 1D advection–diffusion model and a realistic two-dimensional model of the Scheldt Estuary (Belgium and the Netherlands). The residence time of a water parcel in a control domain is the time taken by this parcel to leave the control domain for the first time. The influence time is the time required to replace the water in the domain of interest by renewing water. For steady flows, the influence time is numerically identical to the age of the renewing water, but the two timescales differ for unsteady flows. The residence timemeasures the influence of a hypothetical point discharge on a control domain. In environmental studies, it provides a measure of the effectiveness of hydrodynamic processes at helping a semi-enclosed basin to recover froma local pollution event. The influence time quantifies the local influence of a tracer that would be uniformly distributed in the control domain at the initial time. It is therefore a relevant diagnostic tool in impact studies focusing on the local persistence of a pollution problem. [less ▲]

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See detailModelling phytoplankton succession and nutrient transfer along the Scheldt estuary (Belgium, The Netherlands)
Gypens, N.; Delhez, Eric ULg; Vanhoutte-Brunier, A. et al

in Journal of Marine Systems (2013), 128

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See detailDiagnosis of the transport of adsorbed material in the Scheldt estuary: A proof of concept
Delhez, Eric ULg; Wolk, Frank ULg

in Journal of Marine Systems (2013), 128

Many contaminants can attach to suspended particles. Their transport differs therefore from the transport of dissolved substances, especially in highly turbid environment like estuaries. In this paper, we ... [more ▼]

Many contaminants can attach to suspended particles. Their transport differs therefore from the transport of dissolved substances, especially in highly turbid environment like estuaries. In this paper, we show how the Constituent Age and Residence time Theory (CART — www.climate.be/CART) can be adapted to quantify in a rigorous manner the transport rate of contaminants that are present in both the dissolved and adsorbed phases. On the basis of numerical experiment using a 1D model of the Scheldt estuary, it is shown that the interaction with suspended particles significantly affects the transport of contaminants with partition coefficients larger than 1000 ml/g. The mean transit time from Ghent to Vlissingen of such contaminants can reach 160 days while it is only 60 days for water and dissolved constituents. This increase of the transit time is mainly due to the fact that adsorbed constituents spend long periods of time on the bottom. Surprisingly, the downstream transport of adsorbed constituents in the water column appears more effective than that of dissolved constituents. This transport affects however a small fraction of the adsorbed constituent and is therefore not sufficient to compensate for the long resting phase on the bottom of the bulk of the constituent. The concept and methodology introduced in this paper are easily applicable to most model studies and provide powerful and flexible tools for the detailed understanding of the transport of contaminants in estuaries. In particular, the concept of age and modified ages taking into account specifically the time spent in the water column or in the bottom provide new diagnostic tools to understand and quantify the dynamics of contaminants. [less ▲]

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See detailAn optimum PML for scattering problems in the time domain
Modave, Axel ULg; Kameni, Abelin; Lambrechts, Jonathan et al

in European Physical Journal : Applied physics (2013), 64(2), 24502

In electromagnetic compatibility, scattering problems are defined in an infinite spatial domain, while numerical techniques such as finite element methods require a computational domain that is bounded ... [more ▼]

In electromagnetic compatibility, scattering problems are defined in an infinite spatial domain, while numerical techniques such as finite element methods require a computational domain that is bounded. The perfectly matched layer (PML) is widely used to simulate the truncation of the computational domain. However, its performance depends critically on an absorption function. This function is generally tuned by using case-dependent optimization procedures. In this paper, we will present some efficient functions that overcome any tuning. They will be compared using a realistic scattering benchmark solved with the Discontinuous Galerkin method. [less ▲]

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See detailA PML for convex truncated domains in time-dependent acoustics with a DG-FE discretization
Modave, Axel ULg; Lambrechts, Jonathan; Delhez, Eric ULg et al

in Proceedings of the 11th International Conference on Mathematical and Numerical Aspects of Waves (WAVES 2013) (2013, June 03)

A new perfectly matched layer (PML) is proposed for convex truncated domains in the context of time-dependent acoustics. With this formulation, the size of the computational domain can be reduced when ... [more ▼]

A new perfectly matched layer (PML) is proposed for convex truncated domains in the context of time-dependent acoustics. With this formulation, the size of the computational domain can be reduced when classical shapes of truncated domains are less appropriate. A numerical discretization based on the discontinuous Galerkin method is then described and validated. An example of realistic three-dimensional application is finally proposed. [less ▲]

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See detailOn the concept of exposure time
Delhez, Eric ULg

in Continental Shelf Research (2013), 71

The concept of exposure time offers an interesting alternative to the residence time for the quantitative assessment of the water renewal of estuaries and semi-enclosed basins. It can cope with the ... [more ▼]

The concept of exposure time offers an interesting alternative to the residence time for the quantitative assessment of the water renewal of estuaries and semi-enclosed basins. It can cope with the oscillations or meandering of the flow around the boundary of the control domain and is therefore particularly suited for tidal seas and sub-basins with strong mesoscale activity. We show however that the exposure time in a control domain \omega cannot be properly defined if \omega is part of a larger bounded system unless some removal process is taken into account. It is therefore suggested to revise and extend the definition of the exposure time by including a first order decay : ``the exposure time for the rate constant \lambda is the total time spent in a control domain \omega by particles subject to a first order decay with a rate constant $\lambda$, irrespective of their possible excursions in and out the control domain''. The exposure time revised in this way is well-defined in all circumstances provided that the decay rate differs from zero but depends on the rate constant \lambda. Alternatively, in order to diagnose the movement of water masses, the first order decay can be considered only outside the control domain. [less ▲]

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See detailAn optimum PML for scattering problems in the time domain
Modave, Axel ULg; Delhez, Eric ULg; Kameni, Abelin et al

in Proceedings of the 7th European Conference on Numerical Methods in Electromagnetism (NUMELEC 2012) (2012, July 05)

The Perfectly Matched Layer (PML) is widely used for unbounded problems. However its performances depend critically on an absorption coefficient. This coefficient is generally tuned by using case ... [more ▼]

The Perfectly Matched Layer (PML) is widely used for unbounded problems. However its performances depend critically on an absorption coefficient. This coefficient is generally tuned by using case-dependent optimization procedures. In this paper we will present some efficient profiles of the coefficient that overcome every tuning. These profiles and others will be compared by using a scattering benchmark solved with the Discontinuous Galerkin method. [less ▲]

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See detailEstuarine Hydrology
Wolanski, Eric; Andutta, Fernando; Delhez, Eric ULg

in Bengtsson, Lars; Herschy, Reginald; Fairbridge, R. W. (Eds.) Encyclopedia of Lakes and Reservoirs (2012)

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See detailOptimisation des PML dans des contextes discrets
Modave, Axel ULg; Delhez, Eric ULg; Geuzaine, Christophe ULg

Conference (2012, May 21)

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See detailResidence and exposure times : when diffusion does not matter
Delhez, Eric ULg; Deleersnijder, Eric

in Ocean Dynamics (2012), 62

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See detailWater renewal timescales in the Scheldt Estuary
de Brye, Benjamin; de Brauwere, Anouk; Gourgue, Olivier et al

in Journal of Marine Systems (2012), 94

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See detailScience based management of coastal waters
Delhez, Eric ULg; Barth, Alexander ULg

in Journal of Marine Systems (2011, October), 88(1),

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See detailOn the Parameters of the Perfectly Matched Layer in Discrete Contexts
Modave, Axel ULg; Delhez, Eric ULg; Geuzaine, Christophe ULg

in Proceedings of the 10th International Conference on Mathematical and Numerical Aspects of Waves (WAVES 2011) (2011, July 26)

Perfectly Matched Layer (PML) techniques are widely used for dealing with unbounded problems. However their performance depends critically on both an absorption coefficient and the numerical method. The ... [more ▼]

Perfectly Matched Layer (PML) techniques are widely used for dealing with unbounded problems. However their performance depends critically on both an absorption coefficient and the numerical method. The coefficient is generally tuned by using costly and case-dependent optimization procedures or set empirically. In this paper we present some efficient profiles of the coefficient that allow to avoid any tuning in discrete contexts. These profiles are compared by means of two benchmarks with different numerical methods. [less ▲]

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See detailOptimization of the PML in the Discrete Context for Wave-Like Problems
Modave, Axel ULg; Delhez, Eric ULg; Geuzaine, Christophe ULg

Conference (2011, July 18)

The Perfectly Matched Layer (PML) is widely used for unbounded problems. However its performances depend critically on both an absorption coefficient and the numerical method. The coefficient is generally ... [more ▼]

The Perfectly Matched Layer (PML) is widely used for unbounded problems. However its performances depend critically on both an absorption coefficient and the numerical method. The coefficient is generally tuned by using optimization procedures. In this talk we will present some efficient profiles of the coefficient that overcome every tuning in discrete contexts. These profiles and others will be compared by using benchmarks with different numerical methods. [less ▲]

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See detailMécanique Rationnelle - Modèle Mathématique de Newton
Delhez, Eric ULg

Book published by Editions du Perron (2011)

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See detailAbsorbing layers for shallow water models
Modave, Axel ULg; Deleersnijder, Eric; Delhez, Eric ULg

Conference (2010, May 11)

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See detailOn the parameters of absorbing layers for shallow water models
Modave, Axel ULg; Deleersnijder, Eric; Delhez, Eric ULg

in Ocean Dynamics (2010), 60(1), 65-79

Absorbing/sponge layers used as boundary conditions for ocean/marine models are examined in the context of the shallow water equations with the aim to minimize the reflection of outgoing waves at the ... [more ▼]

Absorbing/sponge layers used as boundary conditions for ocean/marine models are examined in the context of the shallow water equations with the aim to minimize the reflection of outgoing waves at the boundary of the computationaldomain. The ptimization of the absorption coefficient is not an issue in continuous models, for the reflection coefficient of outgoing waves can then be made as small as we please by increasing the absorption coefficient. The optimization of the parameters of absorbing layers is therefore a purely discrete problem. A balance must be found between the efficient damping of outgoing waves and the limited spatial resolution with which the resulting spatial gradients must be described. Using a one-dimensional model as a test case, the performances of various spatial distributions of the absorption coefficient are compared. Two shifted hyperbolic distributions of the absorption coefficient are derived from theoretical considerations for a pure propagative and a pure advective problems. These distribution show good performances. Their free parameter has a well-defined interpretation and can therefore be determined on a physical basis. The properties of the two shifted hyperbolas are illustrated using the classical two-dimensional problems of the collapse of a Gaussianshaped mound of water and of its advection by a mean current. The good behavior of the resulting boundary scheme remains when a full non-linear dynamics is taken into account. [less ▲]

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See detailCapturing the residence time boundary layer - Application to the Scheldt Estuary.
Blaise, Sébastien; de Brye, Benjamin; de Brauwere, Anouk et al

in Ocean Dynamics (2010), 60(3), 535-554

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See detailConsistent computation of the age of water parcels using CART
Mercier, Christophe ULg; Delhez, Eric ULg

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 ▲]

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