The discontinuous Galerkin method for fractional degenerate convection-diffusion equations

We propose and study discontinuous Galerkin methods for strongly degenerate convection-diffusion equations perturbed by a fractional diffusion (L\'evy) operator. We prove various stability estimates along with convergence results toward properly defined (entropy) solutions of linear and nonlinear equations. Finally, the qualitative behavior of solutions of such equations are illustrated through numerical experiments

Fully adaptive multiresolution schemes for strongly degenerate parabolic equations with discontinuous flux

A fully adaptive finite volume multiresolution scheme for one-dimensional strongly degenerate parabolic equations with discontinuous flux is presented. The numerical scheme is based on a finite volume discretization using the Engquist--Osher approximation for the flux and explicit time--stepping. An adaptivemultiresolution scheme with cell averages is then used to speed up CPU time and meet memory requirements. A particular feature of our scheme is the storage of the multiresolution representation of the solution in a dynamic graded tree, for the sake of data compression and to facilitate navigation. Applications to traffic flow with driver reaction and a clarifier--thickener model illustrate the efficiency of this method

COASTWATCH'95: ERS 1/2 SAR detection of natural film on the ocean surface

Ocean mesoscale phenomena such as eddies and current convergence zones can often be seen in synthetic aperture radar (SAR) images due to characteristic patterns caused by natural film induced damping of the waves. Such films have also been found to exert a significant effect on air-sea gas exchange, which may be important for the global scale climate system. Satellite SAR may prove very useful to quantify the extent of natural film. To investigate the composition of these films and their effect on radar return, we compared samples of the sea surface with ERS 1/2 SAR images of coastal ocean areas during the COASTWATCH’95 experiment. Simultaneous observations were made with a shipmounted C band dual-polarized Doppler radar, and surface drifters were deployed to investigate the surface current variations in the vicinity of different slicks (areas where the short surface waves sensed by a radar are damped). One confirmed case of natural film was thus verified to be caused by a convergence zone. The study also showed that the films investigated during COASTWATCH’95 were generally less concentrated and originated from marine organisms, compared to the films with terrestrial influences found in a previous experiment in a fjord [Espedal et al., 1996]. The dependence of the existence of the films on wind speed is also investigated, and an estimate of natural film distribution during the experiment period is given, using a total of 71 ERS 1/2 SAR images collected over the same coastal area under a variety of wind conditions. Up to 40% natural film coverage was found for 2.5 m/s wind speeds, while already at 5–10 m/s all SAR imagery had under 5% film coverage

Application of Local Grid Refinements for simulation of fluid flow through faulted and fractured reservoirs

General local grid refinements have been used to handle flow through faulted and fractured reservoirs. Non matching refinements, which create several different boundary conditions, are accepted. A two-point flux molecule is used to approximate continuity in both the flux and the potential across interfaces. Flow through a fault is specified in a local refinement, containing lithology for that particular fault. Domain Decomposition and Multigrid methods, both based on a Galerkin approximation, have been studied. 1. Introduction Modelling and simulation of transport processes in earth's crust and faults are important fields in many applications, e.g. reservoir engineering and subsurface hydrology. In the field of ground water transport and contamination very accurate modelling of the transport processes is especially important, since the amount of the contaminant substance is often much smaller than the amount of bulk fluid in the reservoir. In this paper a simulator for secondary oil ..

Accuracy of a domain decomposition method for the recovering of discontinuous heat sources in metal sheet cutting

This paper describes a method for the retrieval of discontinuous heat sources involved in a metal cutting process. Two smoothing techniques were used in the present study in order to smooth noisy sensor data recorded by temperature sensors. The two smoothing techniques are a least squares polynomial fit and a Lagrangian smoothing. These data are then used to recover the heat source. It is found that the least squares polynomial provides over-smoothed results and the Lagrangian smoothing produces phyically acceptable results of the retrieved heat source