An optimum PML for scattering problems in time-domain

in Proceedings of the 7th European Conference on Numerical Methods in Electromagnetism (NUMELEC2012) (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 ▲]

Optimisation des PML dans des contextes discrets

Conference (2012, May 21)

Water renewal timescales in the Scheldt Estuary

in Journal of Marine Systems (2012), 94

On the Parameters of the Perfectly Matched Layer in Discrete Contexts

Conference (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 ▲]

Mécanique Rationnelle - Modèle Mathématique de Newton

Book published by Editions du Perron (2011)

On the parameters of absorbing layers for shallow water models

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 ▲]

Consistent computation of the age of water parcels using CART

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 ▲]

Residence time and exposure time of sinking phytoplankton in the euphotic layer

in Journal of Theoretical Biology (2010), 262

Really TVD advection schemes for shelf seas

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 ▲]

Timescale- and tracer-based methods for understanding the results of complex marine models

in Estuarine Coastal & Shelf Science (2007), 74(4), -