Modelling of advection-dominated transport in fluid-saturated porous media

The modelling of contaminant transport in porous media is an important topic to geosciences and geo-environmental engineering. An accurate assessment of the spatial and temporal distribution of a contaminant is an important step in the environmental decision-making process. Contaminant transport in porous media usually involves complex non-linear processes that result from the interaction of the migrating chemical species with the geological medium. The study of practical problems in contaminant transport therefore usually requires the development of computational procedures that can accurately examine the non-linear coupling processes involved. However, the computational modelling of the advection-dominated transport process is particularly sensitive to situations where the concentration profiles can exhibit high gradients and/or discontinuities. This thesis focuses on the development of an accurate computational methodology that can examine the contaminant transport problem in porous media where the advective process dominates.The development of the computational method for the advection-dominated transport problem is based on a Fourier analysis on stabilized semi-discrete Eulerian finite element methods for the advection equation. The Fourier analysis shows that under the Courant number condition of Cr=1, certain stabilized finite element scheme can give an oscillation-free and non-diffusive solution for the advection equation. Based on this observation, a time-adaptive scheme is developed for the accurate solution of the one-dimensional advection-dominated transport problem with the transient flow velocity. The time-adaptive scheme is validated with an experimental modelling of the advection-dominated transport problem involving the migration of a chemical solution in a porous column. A colour visualization-based image processing method is developed in the experimental modelling to quantitatively determinate the chemical concentration on the porous column in a non-invasive way. A mesh-refining adaptive scheme is developed for the optimal solution of the multi-dimensional advective transport problem with a time- and space-dependent flow field. Such mesh-refining adaptive procedure is quantitative in the sense that the size of the refined mesh is determined by the Courant number criterion. Finally, the thesis also presents a brief study of a numerical model that is capable to capture coupling Hydro-Mechanical-Chemical processes during the advection-dominated transport of a contaminant in a porous medium

Seismic Waves

The importance of seismic wave research lies not only in our ability to understand and predict earthquakes and tsunamis, it also reveals information on the Earth's composition and features in much the same way as it led to the discovery of Mohorovicic's discontinuity. As our theoretical understanding of the physics behind seismic waves has grown, physical and numerical modeling have greatly advanced and now augment applied seismology for better prediction and engineering practices. This has led to some novel applications such as using artificially-induced shocks for exploration of the Earth's subsurface and seismic stimulation for increasing the productivity of oil wells. This book demonstrates the latest techniques and advances in seismic wave analysis from theoretical approach, data acquisition and interpretation, to analyses and numerical simulations, as well as research applications. A review process was conducted in cooperation with sincere support by Drs. Hiroshi Takenaka, Yoshio Murai, Jun Matsushima, and Genti Toyokuni

Modeling Callisto's Ionosphere, Airglow and Magnetic Field Environment

Previous observations of the Galileo spacecraft and the Hubble Space Telescope indicate that Callisto possesses a neutral atmosphere which is mostly composed of O2 and additionally contains H2O and CO2. The first aim of our study is to constrain density and structure of the atmospheric O2. Based on existent observations and findings, we construct a phenomenological model of Callisto's atmosphere. Then, we use this atmosphere model as input information for an ionosphere model, which is based on physical principles and has been developed by us specifically for Callisto. Using this coupled description of Callisto's atmosphere-ionosphere system, we calculate the spatial distribution of ionospheric electron densities and the atmospheric ultraviolet emission, i.e., airglow. By varying the prescribed O2 atmosphere and comparing calculated electron densities with Galileo radio occultation measurements and calculated UV emission intensities with Hubble Space Telescope observations, we are able to constrain density and structure of Callisto's O2 atmosphere. We find an average O2 column density of 2.1 (+/-1.1) x 10^{19} 1/m^2 and a likely day-night asymmetry of the O2 atmosphere. In the framework of our ionosphere model we calculate the electron energy distribution function at each point in the ionosphere by solving a coupled set of equations consisting of the Boltzmann equation for suprathermal electrons and the continuity and energy equation for thermal electrons. Since we can neglect electron transport for our purposes, we assume a stationary balance between local sources and sinks of electrons and electron energy. Photoionization is expected to be the major source of ionospheric electrons at Callisto. Therefore, our model includes photoionization and secondary ionization processes from collisions of photoelectrons with neutrals. Using our ionosphere model, we also investigate the formation process of Callisto's O2 atmosphere. Atmospheric O2 is most likely generated by surface sputtering and sublimation. Assuming that surface sputtering is the main source and causes an orbital phase dependent atmospheric O2 density, we predict atmospheric UV emission intensities for different orbital phases of Callisto. These predictions can be used by other scientists to interpret telescope observations of Callisto regarding the question about the origin of Callisto's atmosphere. Further, we wonder whether electromagnetic induction within Callisto’s ionosphere can explain observed magnetic field disturbances that have been interpreted as evidence for a subsurface ocean. The rotation of Jupiter’s magnetic field causes a periodically time varying magnetic field in the rest frame of Callisto, which induces currents within Callisto’s ionosphere. We derive the conductivity structure of Callisto’s ionosphere from our ionosphere model and simulate this induction process. From analytic considerations, we expect a nearly perfect Cowling channel in Callisto’s ionosphere and, hence, only a weak continuation of ionospheric currents in the surrounding magnetospheric plasma. Based on these findings, we construct a detailed numerical model to calculate the induced currents and according secondary magnetic fields quantitatively. We compare our results with the magnetic field measurements from the Galileo flybys C-3 and C-9, during which magnetic field disturbances have been observed that are diagnostic for induction in a conductive spherical shell. Our model results show that induction within Callisto’s ionosphere is an important and non-negligible process that is responsible for a major part of the observed magnetic field disturbances. Due to the present model-uncertainties regarding Callisto's ionosphere, we can not rule out the existence of an conductive subsurface layer like a subsurface ocean. However, if properties of such a subsurface layer are derived from future observations, for example, observations of the JUpiter ICy moon Explorer (JUICE) spacecraft, a consideration of induction in the ionosphere is mandatory