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The study of fractured porous media is an important and challenging problem in hydrogeology. One of the difficulties is that mathematical models have to account for heterogeneity introduced by fractures in hydrogeological media. Heterogeneity may strongly influence the physical processes taking place in these media. Moreover, the thickness of the fractures, which is usually negligible in...
Simulation of salinization of coastal aquifers plays an important role in prediction of availability of pure water resources. In these geological formations, fractures introduce strong heterogeneities and their influence on the groundwater flow and the transport of the salt is significantly (cf. [1]). However uncertain variations in hydrogeological parameters such as porosity, permeability,...
Coupled free-flow and porous-medium systems have received rising attention in recent years due to their broad applications in the environment, biology, and industry. A suitable coupling concept should be applied to characterize fluid behavior between the free flow and porous medium. However, the majority of coupling conditions are restricted to flows parallel to the fluid-porous...
In this talk, we present a two-level overlapping domain decomposition preconditioner for solving linear algebraic systems obtained from simulating Darcy flow in high-contrast media. Our preconditioner starts at a mixed finite element method for discretizing the partial differential equation by Darcy?s law with the no-flux boundary condition and is then followed by a velocity elimination...
Nonlinear advection diffusion equations model diverse physical phenomena.
Some examples include flow through porous media (as found in subsurface and reactive flows),biological processes, Stefan problem and permafrost models; and many others. In this work, we investigate numerical methods for nonlinear parabolic equations that show doubly degeneracy, i.e. for example the diffusion coefficient...
The traditional finite element method requires that the mesh must match with various discontinuous, which can significantly increase the difficulty of preprocessing for hydrodynamic coupling problems with complex boundaries and material interfaces. In such case, the finite element method using unfitted mesh is obviously more advantageous, however, this method also has certain problems, for...
In the prevailing context of the 21st century, characterized by a predominant reliance on oil and gas, or in the promising future where green energy shapes a human society committed to net-zero emissions, the role of underground fractured formations in energy production (geothermal) and storage remains pivotal and irreplaceable. In the past decade, hazardous consequences of failing to predict...
In this talk we will introduce a thermodynamically consistent mathematical model for incompressible and immiscible two-phase flow in porous media with rock compressibility. An energy stable numerical method will be introduced, which can preserve multiple physical properties, including the energy dissipation law, full conservation law for both fluids and pore volumes, and bounds of porosity and...
Understanding the coupling between multiphase fluid flow in pores with distinct sizes and solid deformation induced by flow or external stresses is crucial for the development of many important geotechnics. Most well-established models for describing coupled fluid-solid mechanics are not capable of characterizing hybrid-scale systems containing both solid-free regions and porous media. The...
Particle tracking schemes, including random walk (RW)-based methods, are attractive for modeling advective transport, since they do not suffer from numerical diffusion [Salamon et al. (2006)]$^1$. In scenarios involving multi-species transport, these schemes meticulously capture the degree of spatial mixing across all scales. With such schemes, one can leverage thermodynamic rate laws which...
In this study, we explore the complex behavior of multiphase flows, exemplified by CO2 movement in underground reservoirs, within the context of heterogeneous porous media such as carbonate rocks. These materials display a wide range of pore sizes, posing significant challenges for imaging-based models due to the inherent trade-off between image size and resolution. Often, finer details are...
Tight subsurface formations and shales often act as seals for subsurface systems that are envisioned to store fluids such as CO2 and H2 as part of a transition to low-carbon economies of the future. These seals often comprise complex nano-confined systems with heterogeneous physical and chemical features. The extreme confinement and heterogeneity in such systems present difficulties in terms...
The transport of immiscible two-phase in porous media involves many scientific and engineering fields, such as hydrogeology, reservoir development and electrochemical energy storage. This kind of flow phenomenon usually occurs in multiscale pores from micro to macro, making direct numerical simulations suffered from huge computational costs. Considering the demand for simultaneously mimicking...
To comprehensively understand and predict the behavior of CO2 storage, the development of precise mathematical models and advanced numerical schemes for large-scale simulations is demanding. The advection and diffusion or even interaction between injected supercritical CO2 and other fluids in the storage reservoirs should be able to be described by multiphase flow models. Notably, the...
