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The study deals with collocated Godunov type finite volume schemes applied to the two-dimensional linear wave equation with Coriolis source term. The purpose is to explain the wrong behaviour of the classic scheme and to modify it in order to avoid accuracy issues around the geostrophic equilibrium and in geostrophic adjustment processes. To do so, a Hodge-like decomposition is introduced. Then three different well-balanced strategies are introduced. Some properties of the associated modified equations are proven and then extended to the semi-discrete case. Stability of fully discrete schemes under a suitable CFL condition is established thanks to a Von Neumann analysis. Some numerical results reinforce the purpose and exhibit the concrete improvements achieved by the application of these new techniques in both linear and nonlinear cases.

International audience; The shallow water equations can be used to model many phenomena in geophysical fluid mechanics. For large scales, the Coriolis force plays an important role and the geostrophic equilibrium which corresponds to the balance between the pressure gradient and the Coriolis force is an important feature. In this communication , we investigate the stability condition and the behavior of the so-called Apparent Topography scheme which is capable of capturing a discrete version of the geostrophic equilibrium.

In this study a series of the CuO-doped materials containing zeolite with varying CuO contents were synthesized from red mud (RM) and rice husk ash (RHA). The rice husk ash/red mud with the molar ratio of , and being 1.8, 2.5 and 60, respectively, were maintained during the synthetic process of materials. The characteristic structure samples were analyzed by x-ray diffraction (XRD), Fourier transformed infrared spectroscopy (FTIR), scanning electron microscopy (SEM), transmission electron microscope (TEM), Brunauer–Emmett–Teller (BET) surface area and H2 temperature program reduction (H2-TPR). The catalytic activity of samples was evaluated in CO oxidation reaction in a microflow reactor at temperature range 200 °C–350 °C. The obtained results showed that all synthetic samples there exist the A-type zeolites with the average crystal size of 15–20 nm, the specific surface area of , and pore volume of . The material synthesized from RM and RHA with the zeolite structure (ZRM, undoped CuO) could also oxidize CO completely at 350 °C, and its activity was increase significantly when doped with CuO. CuO-doped materials with the zeolite structure exhibited excellent catalytic activity in CO oxidation. The ZRM sample loading 5 wt% CuO with particle nanosize about 10–30 nm was the best one for CO oxidation with complete conversion temperature at 275 °C.

The neutron transport equation can be used to model the physics of the nuclear reactor core. Its solution depends on several variables and requires a lot of high precision computations. One can simplify this model to obtain the SPN equation for a generalized eigenvalue problem. In order to solve this eigenvalue problem, we usually use the inverse power iteration by solving a source problem at each iteration. Classically, this problem can be recast in a mixed variational form, and then discretized by using the Raviart-Thomas-Nédélec Finite Element. In this article, we focus on the steady-state diffusion equation with heterogeneous coefficients discretized on Cartesian meshes. In this situation, it is expected that the solution has low regularity. Therefore, it is necessary to refine at the singular regions to get better accuracy. The Adaptive Mesh Refinement (AMR) is one of the most effective ways to do that and to improve the computational time. The main ingredient for the refinement techniques is the use of a posteriori error estimates, which gives a rigorous upper bound of the error between the exact and numerical solution. This indicator allows to refine the mesh in the regions where the error is large. In this work, some mesh refinement strategies are proposed on the Cartesian mesh for the source problem. Moreover, we numerically investigate an algorithm which combines the AMR process with the inverse power iteration to handle the generalized eigenvalue problem.