A hyperbolic-elliptic PDE model and conservative numerical method for gravity-dominated variably-saturated groundwater flow

Richards equation is often used to represent two-phase fluid flow in an unsaturated porous medium when one phase is much heavier and more viscous than the other. However, it cannot describe the fully saturated flow due to degeneracy in the capillary pressure term. Mathematically, gravity-driven variably saturated flows are interesting because their governing partial differential equation switches from hyperbolic in the unsaturated region to elliptic in the saturated region. Moreover, the presence of wetting fronts introduces strong spatial gradients often leading to numerical instability. In this work, we develop a robust, multidimensional mathematical and computational model for such variably saturated flow in the limit of negligible capillary forces. The elliptic problem for saturated regions is built-in efficiently into our framework for a reduced system corresponding to the saturated cells, with the boundary condition of the fixed head at the unsaturated cells. In summary, this coupled hyperbolic-elliptic PDE framework provides an efficient, physics-based extension of the hyperbolic Richards equation to simulate fully saturated regions. Finally, we provide a suite of easy-to-implement yet challenging benchmark test problems involving saturated flows in one and two dimensions. These simple problems, accompanied by their corresponding analytical solutions, can prove to be pivotal for the code verification, model validation (V&V) and performance comparison of such simulators. Our numerical solutions show an excellent comparison with the analytical results for the proposed problems. The last test problem on two-dimensional infiltration in a stratified, heterogeneous soil shows the formation and evolution of multiple disconnected saturated regions.Comment: 21 pages, 9 figure

The Athena X-ray Integral Field Unit (X-IFU)

The X-ray Integral Field Unit (X-IFU) is the high resolution X-ray spectrometer of the ESA Athena X-ray observatory. Over a field of view of 5' equivalent diameter, it will deliver X-ray spectra from 0.2 to 12 keV with a spectral resolution of 2.5 eV up to 7 keV on similar to 5 '' pixels. The X-IFU is based on a large format array of super-conducting molybdenum-gold Transition Edge Sensors cooled at similar to 90 mK, each coupled with an absorber made of gold and bismuth with a pitch of 249 mu m. A cryogenic anti-coincidence detector located underneath the prime TES array enables the non X-ray background to be reduced. A bath temperature of similar to 50 mK is obtained by a series of mechanical coolers combining 15K Pulse Tubes, 4K and 2K Joule-Thomson coolers which pre-cool a sub Kelvin cooler made of a He-3 sorption cooler coupled with an Adiabatic Demagnetization Refrigerator. Frequency domain multiplexing enables to read out 40 pixels in one single channel. A photon interacting with an absorber leads to a current pulse, amplified by the readout electronics and whose shape is reconstructed on board to recover its energy with high accuracy. The defocusing capability offered by the Athena movable mirror assembly enables the X-IFU to observe the brightest X-ray sources of the sky (up to Crab-like intensities) by spreading the telescope point spread function over hundreds of pixels. Thus the X-IFU delivers low pile-up, high throughput (> 50%), and typically 10 eV spectral resolution at 1 Crab intensities, i.e. a factor of 10 or more better than Silicon based X-ray detectors. In this paper, the current X-IFU baseline is presented, together with an assessment of its anticipated performance in terms of spectral resolution, background, and count rate capability. The X-IFU baseline configuration will be subject to a preliminary requirement review that is scheduled at the end of 2018. The X-IFU will be provided by an international consortium led by France, the Netherlands and Italy, with further ESA member state contributions from Belgium, Czech Republic, Finland, Germany, Ireland, Poland, Spain, Switzerland and contributions from Japan and the United States.Peer reviewe

Mathematical modeling and multiscale simulation of carbon dioxide storage in saline aquifers

Carbon capture and storage (CCS) is a key technology to reduce CO 2 emissions from industrial processes, in particular from fossil-fuel based electricity generation. One important aspect of CCS is the safe long-term storage of the captured CO2 in geological formations, especially in deep regional saline aquifers. Predicting the long-term evolution of the injected CO2 requires an understanding of the basic physical mechanisms and the ability to capture them in field-scale numerical simulations. Simple mathematical models of trapping processes are developed to allow the identification of the dominant physical processes during CO2 storage and their associated length and time scales. First-order estimates of the duration of the active storage period and the migration distance are obtained as a function of the average properties of the aquifer. These estimates support the selection of storage sites, in particular at the early stages when limited data is available. They also show that the length scales associated with the physical processes in regional aquifers can span several orders of magnitude. Multiscale simulation techniques are necessary to resolve physical processes and geological heterogeneity. In particular, robust multiscale methods of elliptic flow problems, must be developed. The multiscale finite volume method is analyzed in the context of multipoint flux approximations and shown to lose monotonicity for anisotropic problems. Strong anisotropy arises in the simulation of CO2 storage, because of the large aspect ratios of regional aquifers. A new compact coarse operator and new local fine-scale problems are introduced to obtain monotone coarse pressure solutions for anisotropic domains. This development presents a major step towards multiscale simulation of CO2 storage in large regional saline aquifers

Overall survival in the OlympiA phase III trial of adjuvant olaparib in patients with germline pathogenic variants in BRCA1/2 and high-risk, early breast cancer

International audienc