Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 2609.37833

An advanced hybrid-dimensional Stokes-Darcy model for fractured porous media

Paula Strohbeck·Linheng Ruan·Iryna Rybak
View original source ↗Read source document ↗Export metadata ↓

Abstract

Thin fluid-filled channels in porous media are prevalent in a wide range of environmental settings including fractures in geological formations. Transport of fluid in such multi-domain systems is commonly described by Darcy's law and formulated either in a fully dimensional framework or through a hybrid-dimensional approach, where fractures are represented as inclusions of co-dimension one enclosed in the porous matrix. These mixed-dimensional models enable accurate representation of the corresponding full-dimensional systems while significantly reducing computational complexity. Models available in literature usually do not properly account for channel-wall roughness while applying coupling conditions on the fracture-matrix interface and are usually developed for flow directions parallel to the fracture. The goal of this work is to advance and study the hybrid-dimensional Stokes-Darcy model developed by the authors in their previous work. We consider a thin open channel embedded within a porous matrix, where the channel walls are in contact with porous regions of distinct permeabilities. We incorporate channel-wall roughness effects into the model and improve it to accommodate arbitrary flow directions. We prove existence and uniqueness of the weak solution for the new model and demonstrate its advantages over existing hybrid-dimensional Stokes-Darcy models using pore-scale resolved simulations.

Explore related subjects

math.AP

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Paula Strohbeck, Linheng Ruan, Iryna Rybak. 2026-09-29. An advanced hybrid-dimensional Stokes-Darcy model for fractured porous media. https://arxiv.org/abs/2609.37833

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Optimizers in Sobolev-curl inequalities

We study a Sobolev-type inequality involving the $p$-curl operator in $\mathbb{R}^3$. We prove the existence of a minimizer $u:\mathbb{R}^3\to \mathbb{R}^3$ which yields a solution to the $p$-curl-curl equation in the critical case $$ \nabla\times (|\nabla\times u|^{p-2}\nabla\times u)= |u|^{p^*-2}u\quad \hbox{in }\mathbb{R}^3.$$ The cases $p=2$ and $p=3/2$ are motivated, respectively, by nonlinear Maxwell equations and zero modes of three-dimensional Dirac operators. The infinite-dimensional kernel of curl and the critical exponent prevent a direct application of standard compactness arguments. Our proof combines local compactness under the nonlinear constraint $\operatorname{div}(|u|^{p^*-2}u)=0$ and a new variational approach that allows to treat quasilinear strongly indefinite problems by direct minimization on a Nehari-type constraint. We also establish existence and compactness results in axially symmetric classes, including two types of solutions for $p=3/2$ distinct from the explicit Loss--Yau fields. Finally, the same minimization strategy gives a new proof of compactness modulo translations and dilations for minimizing sequences in the classical critical Sobolev inequality.

math.AP↗
arXiv2026

A remark on the log-Sobolev inequality for the Gibbs measure of the focusing Schrödinger equation

We consider the question of showing a log-Sobolev inequality for the Gibbs measure of the focusing Schrödinger equation built by Lebowitz-Rose-Speer (1988), formally given by $$ dρ\propto \exp\big(\frac 1 p\int_{\mathbb T} |u|^p d x - \frac 12\int_{\mathbb T} |\nabla u|^2 d x - \frac 12\int_{\mathbb T} |u|^2 d x\big) \mathbf 1_{\| u \|_{L^2(\mathbb T)}^2 \le K}dud\overline{u}. $$ When $2 \le p \le 4$, we show that these measures indeed satisfy a log-Sobolev inequality. When $p> 4$, we show a lower bound for the Hessian of the potential, which implies that the known techniques to show these inequalities cannot apply to the measure $ρ$.

math.AP↗
arXiv2026

On the inhomogeneous discounted Hamilton-Jacobi equations

In this paper, we study the family of inhomogeneous discounted Hamilton-Jacobi equations \begin{equation}\label{hjs1} λ(x)u+h(x,d_x u)=c \quad \tag{$\ast$} \end{equation} on a closed manifold $M$ with a non-identically vanishing discount factor $λ(x)$. There is a critical value $c_0\in[-\infty,\infty)$ such that \eqref{hjs1} admits a viscosity solution if $c>c_0$ and no solution if $c c_0$. In this case, we determine the basin of the stable solution and investigate the long-time behavior of the solution semigroup associated with \eqref{hjs1}. In particular, we obtain a formula relating the lowest convergence rate of the solution semigroup near a stable solution to a minimizing problem concerning the integral of $λ$ over Mather measures supporting on the $1$-graph of the stable solution. This formula has two direct consequences: 1) it yields a description of their asymptotic behavior as $c$ tends to infinity; 2) it helps to classify the ergodic Mather measures and locate their distribution in the phase space. The second consequence leads to a dynamical necessary condition for $c=c_0$.

math.AP↗