A review of recent advances in discretization methods, a posteriori error analysis, and adaptive algorithms for numerical modeling in geosciences

International audienceTwo research subjects in geosciences which lately underwent significant progress are treated in this review. In the first part we focus on one key ingredient for the numerical approximation of the Darcy flow problem, namely the discretization of diffusion terms on general polygonal/polyhedral meshes. We present different schemes and discuss in detail their fundamental numerical properties such as stability, consistency, and robustness. The second part of the paper is devoted to error control and adaptivity for model geosciences problems. We present the available a posteriori estimates guaranteeing the maximal overall error and show how the different error components can be identified. These estimates are used to formulate adaptive stopping criteria for linear and nonlinear solvers, time step choice adjustment, and adaptive mesh refinement. Numerical experiments illustrate such entirely adaptive algorithms

Analyse mathématique et numérique d'équations aux dérivées partielles issues de la mécanique des fluides : applications aux écoulements en milieux poreux

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Reactive Flows in Deformable, Complex Media

Many processes of highest actuality in the real life are described through systems of equations posed in complex domains. Of particular interest is the situation when the domain is changing in time, undergoing deformations that depend on the unknown quantities of the model. Such kind of problems are encountered as mathematical models in the subsurface, material science, or biological systems.The emerging mathematical models account for various processes at different scales, and the key issue is to integrate the domain deformation in the multi-scale context. The focus in this workshop was on novel techniques and ideas in the mathematical modelling, analysis, the numerical discretization and the upscaling of problems as described above

A point source high power converter target to produce Bremsstrahlung for photonuclear reactions

A continually growing number of applications of radionuclides are known in medicine and various industries. In industries, radionuclides can have different applications depending on the industry in which they are used. For example, they can be employed in the automotive industry for the quality control of the produced metal sheets or accurate thickness measurements; in the oil and gas industry to detect pipe cracks; in the aerospace industry for the use as compact sources of electrical power in spacecraft with long life and almost uniform performance. On the medical side, radionuclides are employed as radiopharmaceuticals to diagnose and treat diseases depending on the radiation that they emit. Three families of radionuclides that emit α, β-, and Auger electrons are considered for therapy; the family of radionuclides that emit β+ is employed for diagnosis. A relatively new branch called theranostic has been introduced in recent years and is a combination of therapy and diagnostics. The term true theranostic pair refers to pairs of radioisotopes (one β+ emitter and another β- emitter), of the same element conjugated with the same bio-molecule. To fulfill the high demand for radionuclides, a reliable large-scale production facility that utilizes a low cost and highly efficient method is needed. Up to now, different ways for the production of different radionuclide families have been introduced and built. One of the most conventional methods is using nuclear reactors, which still are being used widely. However, the fleet of radionuclide producing reactors is relatively old and thus no longer reliable (they are scheduled to be taken offline in the next few years). The cyclotron is another method that accelerates protons, deuterons, and alpha particles in a circular path and is mainly used to produce a family of radionuclides that emit β+ with a relatively short half-life. Among the associated problems which they have, low production rates and specific activity are the main. Another radionuclide production method, which is relatively new, is based on photonuclear interaction and uses energetic photons for irradiation of the targets. In order to produce these photons, electron accelerators need to be employed, and then by using a converter, electrons produce photons in an interaction called Bremsstrahlung. This method has a relatively long history in radionuclide production; however, the problem that makes this method unsuitable is the considerable heat generation in the converter target. This problem made the use of this method restricted so that only research areas with a very low input power of incident electrons were of interest. Due to the many advantages of the photonuclear reactions over existing methods, including high production rate and specific activity, low material quantity, low impurities activation, and low post-processing, an in-depth investigation into possible new designs and optimization of the irradiation parts is essential and constitutes the motivation for this Ph.D. work. This study was performed in the framework of the project entitled “Sinergia Project (SNSF): PHOtonuclear Reactions (PHOR): breakthrough research in radionuclides for theranostics” funded by the Swiss National Science Foundation and submitted to the European Patent Organisation (No 21212627.0)