Related papers: Geometric Methods in the Analysis on Non-linear Fl…
We consider discrete porous medium equations of the form \partial_t \rho_t = \Delta \phi(\rho_t), where \Delta is the generator of a reversible continuous time Markov chain on a finite set X, and \phi is an increasing function. We show that…
In this paper we consider modifications to Darcy's equation wherein the drag coefficient is a function of pressure, which is a realistic model for technological applications like enhanced oil recovery and geological carbon sequestration. We…
Reduction of flow compressibility with the corresponding ideally invariant helicities, universally for various fluid models of neutral and ionized gases, can be argued statistically and associated with the geometrical scenario in the…
This paper presents a geometric variational discretization of compressible fluid dynamics. The numerical scheme is obtained by discretizing, in a structure preserving way, the Lie group formulation of fluid dynamics on diffeomorphism groups…
In this paper, a pore-scale network modeling method, based on the flow continuity residual in conjunction with a Newton-Raphson non-linear iterative solving technique, is proposed and used to obtain the pressure and flow fields in a network…
A challenge in physical oceanography is quantifying the energy content of waves and balanced flows and the fluxes that connect these reservoirs with their sources and sinks. Methodological limitations have prevented decompositions for…
The accurate description of fluid flow and transport in fractured porous media is of paramount importance to capture the macroscopic behaviour of an oil reservoir, a geothermal system, or a CO2 sequestration site, to name few applications.…
This study addresses the well-posedness of a hemivariational inequality derived from the convective Brinkman-Forchheimer extended Darcy (CBFeD) model in both two and three dimensions. The CBFeD model describes the behavior of incompressible…
Convective mixing in porous media is crucial in both geophysical and industrial fields, spanning applications ranging from carbon dioxide sequestration to contaminant transport in groundwater. Key processes are affected by convective heat…
This work introduces the framed curvature flow, a generalization of both the curve shortening flow and the vortex filament equation. Here, the magnitude of the velocity vector is still determined by the curvature, but its direction is given…
Motivated by Pan-Yang [PY] and Ma-Cheng [MC], we study a general linear nonlocal curvature flow for convex closed plane curves and discuss the short time existence and asymptotic convergence behavior of the flow. Due to the linear structure…
Isogeometric analysis was applied very successfully to many problem classes like linear elasticity, heat transfer and incompressible flow problems but its application to compressible flows is very rare. However, its ability to accurately…
This paper investigates the gradient flow structure, well-posedness, and asymptotic behavior of the Fokker-Planck equation defined on locally uniformly finite graphs, which is highly non-trivial compared with the finite case. We first…
Convection-driven porous media flows are common in industrial processes and in nature. The multiscale and multiphase character of these systems and the inherent non-linear flow dynamics make convection in porous media a complex phenomenon.…
We review opportunities for stochastic geometric mechanics to incorporate observed data into variational principles, in order to derive data-driven nonlinear dynamical models of effects on the variability of computationally resolvable…
Single component nonrelativistic dissipative fluids are treated independently of reference frames and flow-frames. First the basic fields and their balances, then the related thermodynamic relations and the entropy production are calculated…
Most organic liquids exhibit a pressure-dependent viscosity, making it crucial to consider this behavior in applications where pressures significantly exceed ambient conditions (e.g., geological carbon sequestration). Mathematical models…
Lie symmetry group method is applied to study Newtonian incompressible fluid's equations flow in turbulent boundary layers. The symmetry group and its optimal system are given, and group invariant solutions associated to the symmetries are…
We consider single-phase flow in a fractured porous medium governed by Darcy's law with spatially varying hydraulic conductivity matrices in both bulk and fractures. The width-to-length ratio of a fracture is of the order of a small…
The fracturing-flooding technology is a new process for the development of low-permeability oil reservoirs, achieving a series of successful applications in oilfield production. However, existing numerical simulation methods for pressure…