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We provide an entropy formulation for porous medium-type equations with a stochastic, non-linear, spatially inhomogeneous forcing. Well - posedness and $L_1$-contraction is obtained in the class of entropy solutions. Our scope allows for…
We study the axisymmetric propagation of a viscous gravity current over a deep porous medium into which it also drains. A model for the propagation and drainage of the current is developed and solved numerically in the case of constant…
In this paper we propose an efficient second order well balanced finite volume method for modeling complex free surface flows at the aid of a simple diffuse interface method. The employed physical model is a two-phase model derived from the…
Modeling mass flows is classically based on hydrostatic balance equations. However, if momentum transfers scale similarly in slope parallel and flow depth directions, then the gravity and acceleration can have the same order of magnitude…
We propose a description for transient penetration simulations of miscible and immiscible fluid mixtures into anisotropic porous media, using the lattice Boltzmann (LB) method. Our model incorporates hydrodynamic flow, diffusion, surface…
Recent advances in reservoir simulation increasingly utilize hybrid approaches that couple physics-based simulators with machine-learning (ML) components. ML components offer high fidelity to training data and fast inference, enabling…
In this paper we present analytical and random walk based solutions to diffusion in semi-permeable layered media with varying diffusivity. We propose a new random walk transit model (hybrid model) based on treating the membrane permeability…
Knowledge of the underlying mechanisms of multiphase flow dynamics in porous media is crucial for optimizing subsurface engineering applications like geological carbon sequestration. However, studying the micro-mechanisms of multiphase…
We develop a framework for constructing mixed multiscale finite volume methods for elliptic equations with multiple scales arising from flows in porous media. Some of the methods developed using the framework are already known…
Fluid flow through bimodal porous media, characterized by a distinct separation in pore size distribution, is critical in various scientific and engineering applications, including groundwater management, oil and gas production, and carbon…
We construct an ensemble distribution to describe steady immiscible two-phase flow of two incompressible fluids in a porous medium. The system is found to be ergodic. The distribution is used to compute macroscopic flow parameters. In…
Predicting the permeability of porous media in saturated and partially saturated conditions is of crucial importance in many geo-engineering areas, from water resources to vadose zone hydrology or contaminant transport predictions. Many…
In this paper we present a complete framework for the energy-stable simulation of stratified incompressible flow in channels, using the one-dimensional two-fluid model. Building on earlier energy-conserving work on the basic two-fluid…
In this paper, we propose a new formulation and a suitable finite element method for the steady coupling of viscous flow in deformable porous media using divergence-conforming filtration fluxes. The proposed method is based on the use of…
Thermodynamically consistent models for two-phase flow in porous media have attracted significant attention in recent years. In this paper, we prove the existence, uniqueness and regularity of the weak solution to such a recent model…
Shale gas recovery has seen a major boom in recent years due to the increasing global energy demands; but the extraction technologies are very expensive. It is therefore important to develop realistic transport modelling and simulation…
The flow of incompressible fluids through porous media plays a crucial role in many technological applications such as enhanced oil recovery and geological carbon-dioxide sequestration. The flow within numerous natural and synthetic porous…
The accurate and stable simulation of viscoelastic flows remains a significant computational challenge, exacerbated for flows in non-trivial and practical geometries. Here we present a new high-order meshless approach with variable…
Immersed nonlinear elements are prevalent in biological systems that require a preferential flow direction, such as the venous and the lymphatic system. We investigate here a certain class of models where the fluid is driven by peristaltic…
Molecular communication (MC) is a communication paradigm in which information is conveyed through the controlled release, propagation, and reception of molecules. Many envisioned healthcare applications of MC are expected to operate inside…