Related papers: Modeling an Aquifer: Numerical Solution to the Gro…
We showcase the plain diffusion models with Transformers are effective predictors of fluid dynamics under various working conditions, e.g., Darcy flow and high Reynolds number. Unlike traditional fluid dynamical solvers that depend on…
In this paper we develop an a priori error analysis of a new unified mixed finite element method for the coupling of fluid flow with porous media flow in $\mathbb{R}^N$, $N\in\{2,3\}$ on isotropic meshes. Flows are governed by the Stokes…
Despite its numerical challenges, finite element method is used to compute viscous fluid flow. A consensus on the cause of numerical problems has been reached; however, general algorithms---allowing a robust and accurate simulation for any…
Fractured porous media or double porosity media are common in nature. At the same time, accurate modeling remains a significant challenge due to bi-modal pore size distribution, anisotropy, multi-field coupling, and various flow patterns.…
In this article, we model Earth's lower small-scale eddies motion in the atmosphere as a compressible neutral fluid flow on a rotating sphere. To justify the model, we carried out a numerical computation of the thermodynamic and…
We study the numerical approximation of advection-diffusion equations with highly oscillatory coefficients and possibly dominant advection terms by means of the Multiscale Finite Element Method. The latter method is a now classical, finite…
An evolving surface finite element discretisation is analysed for the evolution of a closed two-dimensional surface governed by a system coupling a generalised forced mean curvature flow and a reaction--diffusion process on the surface,…
This article presents numerical investigations on accuracy and convergence properties of several numerical approaches for simulating steady state flows in heterogeneous aquifers. Finite difference, finite element, discontinuous Galerkin,…
As a simplified model for subsurface flows elliptic equations may be utilized. Insufficient measurements or uncertainty in those are commonly modeled by a random coefficient, which then accounts for the uncertain permeability of a given…
In this article we consider the numerical modeling and simulation via the phase field approach of two-phase flows of different densities and viscosities in superposed fluid and porous layers. The model consists of the…
The contribution deals with the mathematical modelling of fluid flow in porous media, in particular water flow in soils, with the aim of describing the competition between transport and diffusion. The analysis is based on a mathematical…
A microscopic model able to describe simultaneously the dynamic viscosity and the self-diffusion coefficient of fluids is presented. This model is shown to emerge from the introduction of fractional calculus in a usual model of condensed…
Porous materials are ubiquitous in various engineering and geological applications, where their permeability plays a critical role in viscous fluid flow and transport phenomena. Understanding and characterizing the microscale properties,…
Understanding groundwater dynamics is critical for sustainable water management, particularly as climate extremes intensify. However, the resolutions of existing subsurface observational tools are still inadequate for detailed aquifer…
In this study, we investigate the Shallow Water Equations incorporating source terms accounting for Manning friction and a non-flat bottom topology. Our primary focus is on developing and validating numerical schemes that serve a dual…
Mathematical models for flow through porous media typically enjoy the so-called maximum principles, which place bounds on the pressure field. It is highly desirable to preserve these bounds on the pressure field in predictive numerical…
The work is devoted to the development and computational implementation of the homogenization method for modeling unsteady flows of a viscous incompressible fluid in periodic porous media taking into account memory effects. At the…
In this article, a finite element model is implemented to analyze hydro-thermal convective flow in a porous medium. The mathematical model encompasses Darcy's law for incompressible fluid behavior, which is coupled with a…
A high-order combined interpolation/finite element technique is developed for solving the coupled groundwater-surface water system that governs flows in karst aquifers. In the proposed high-order scheme we approximate the time derivative…
Several recent tropical cyclones, e.g., Hurricane Harvey (2017), have lead to significant rainfall and resulting runoff. When the runoff interacts with storm surge, the resulting floods can be greatly amplified and lead to effects that…