arXiv subjects

Yashar Mehmani

Publications and source records attributed to Yashar Mehmani.

6 recordsLinked to original sources

arXiv2026

Modeling Ostwald Ripening Dynamics in Porous Microstructures

Partially miscible ganglia trapped in a porous medium evolve through Ostwald ripening, driven by differences in interfacial curvature. In practice, ganglia can span multiple pores and undergo discrete capillary events - invasion, snap-off, retraction, fragmentation, coalescence, and dislocation - that alter their topology and induce local flow. Existing pore-network models (PNMs) for ripening are limited to single-pore ganglia, assume idealized pore shapes, and operate under quasi-static conditions that preclude flow. We present an image-based pore-network model (iPNM) that removes these limitations. Unlike existing PNMs, iPNM requires no idealization of pore shapes, as the effect on capillarity is encoded locally in curvature-saturation curves computed via the pore-morphology method. iPNM couples two-phase flow, solute transport, and Ostwald ripening within a unified framework. We first verify iPNM against a prior quasi-static PNM, then validate it against recent high-resolution microfluidic experiments of hydrogen ripening in a sandstone-patterned micromodel over 15-24 days at 40C and 80C. Good agreement is obtained without adjustable parameters. Comparison with a continuum model shows that while macroscopic saturation is captured by both approaches, iPNM uniquely resolves population statistics, individual ganglion curvatures, and pre-equilibrium ripening dynamics within a representative elementary volume. Its computational efficiency over direct numerical simulation makes it suitable for guiding the development of improved theories of ripening in confined geometries.

physics.flu-dyn↗

arXiv2025

Kinetic Theory of Multicomponent Ostwald Ripening in Porous Media

Partially miscible bubble populations trapped in porous media are ubiquitous in subsurface applications such as underground hydrogen storage (UHS), where cyclic injections fragment gas into numerous bubbles with distributions of sizes and compositions. These bubbles exchange mass through Ostwald ripening, driven by differences in composition and interfacial curvature. While kinetic theories have been developed for single-component ripening in porous media, accounting for bubble deformation and spatial correlations in pore size, no such theory exists for multicomponent systems. We present the first kinetic theory for multicomponent Ostwald ripening of bubbles in porous media. The formulation describes the bubble population with a number-density function $g(s; t)$ in a 3D statistical space of bubble states $s = (R_p, S^b, y)$, consisting of pore size, bubble saturation, and composition. Evolution is governed by a population balance equation with closure through mean-field approximations that account for spatial correlations in pore size and ensure mass conservation. The theory generalizes previous single-component formulations, removing key limitations such as the inability to capture interactions between distant bubbles. Systematic validation against pore-network simulations across homogeneous, heterogeneous, correlated, and uncorrelated networks demonstrates good agreement without adjustable parameters. Pending challenges and limitations are discussed. Since the theory imposes no constraints on bubble count or correlation length, it enables predictions beyond the pore scale.

cond-mat.soft↗

arXiv2025

Preconditioning and Reduced-Order Modeling of Navier-Stokes Equations in Complex Porous Microstructures

We aim to solve the incompressible Navier-Stokes equations within the complex microstructure of a porous material. Discretizing the equations on a fine grid using a staggered (e.g., marker-and-cell, mixed FEM) scheme results in a nonlinear residual. Adopting the Newton method, a linear system must be solved at each iteration, which is large, ill-conditioned, and has a saddle-point structure. This demands an iterative (e.g., Krylov) solver, that requires preconditioning to ensure rapid convergence. We propose two monolithic \textit{algebraic} preconditioners, $a\mathrm{PLMM_{NS}}$ and $a\mathrm{PNM_{NS}}$, that are generalizations of previously proposed forms by the authors for the Stokes equations ($a\mathrm{PLMM_{S}}$ and $a\mathrm{PNM_{S}}$). The former is based on the pore-level multiscale method (PLMM) and the latter on the pore network model (PNM), both successful approximate solvers. We also formulate faster-converging geometric preconditioners $g\mathrm{PLMM}$ and $g\mathrm{PNM}$, which impose $\partial_n\boldsymbol{u}\!=\!0$ (zero normal-gradient of velocity) exactly at subdomain interfaces. Finally, we propose an accurate coarse-scale solver for the steady-state Navier-Stokes equations based on $g\mathrm{PLMM}$, capable of computing approximate solutions orders of magnitude faster. We benchmark our preconditioners against state-of-the-art block preconditioners and show $g\mathrm{PLMM}$ is the best-performing one, followed closely by $a\mathrm{PLMM_{S}}$ for steady-state flow and $a\mathrm{PLMM_{NS}}$ for transient flow. All preconditioners can be built and applied on parallel machines.

math.NA↗

arXiv2025

High-order Multiscale Preconditioner for Elasticity of Arbitrary Structures

We present a two-level preconditioner for solving linear systems arising from the discretization of the elliptic, linear-elastic deformation equation, in displacement unknowns, over domains that have arbitrary geometric and topological complexity and heterogeneity in material properties (including fractures). The preconditioner is an algebraic translation of the high-order pore-level multiscale method (hPLMM) proposed recently by the authors, wherein a domain is decomposed into non-overlapping subdomains, and local basis functions are numerically computed over the subdomains to construct a high-quality coarse space (or prolongation matrix). The term "high-order" stands in contrast to the recent low-order PLMM preconditioner, where BCs of local basis problems assume rigidity of all interfaces shared between subdomains. In hPLMM, interfaces are allowed to deform, through the use of suitable mortar spaces, thereby capturing local bending/twisting moments under challenging loading conditions. Benchmarked across a wide range of complex (porous) structures and material heterogeneities, we find hPLMM exhibits superior performance in Krylov solvers than PLMM, as well as state-of-the-art Schwarz and multigrid preconditioners. Applications include risk analysis of subsurface CO2/H2 storage and optimizing porous materials for batteries, prosthetics, and aircraft.

math.NA↗

arXiv2025

Ostwald Ripening in Underground Gas Storage

Underground gas storage is central to both climate mitigation and energy transition strategies, supporting both long-term carbon sequestration and seasonal hydrogen storage. A key mechanism governing the fate of injected gases is Ostwald ripening, the curvature-driven mass transfer between trapped gas ganglia in porous media. While ripening is well understood in open systems, its behavior in geometrically confined porous structures remains poorly characterized, especially over long timescales relevant to subsurface operations. Here, we present ultra-high-resolution microfluidic experiments that capture the evolution of residually trapped hydrogen over weeks in realistic, heterogeneous pore geometries under well-defined boundary conditions. We observe a distinct two-stage dynamic: a rapid local equilibration among neighboring bubbles, followed by slow global depletion driven by long-range diffusion toward low-chemical potential boundaries. Building on these insights, we develop and validate a continuum model that couples microscale capillary pressure-saturation (Pc-s) relationships, extracted via the pore-morphology method, with macroscopic diffusive transport. The model accurately predicts gas saturation evolution without fitting parameters and collapses experimental results across a range of experimental conditions. Extending the model to reservoir scales, we estimate equilibration timescales for CO2 and H2 in homogeneous sandstone aquifers. We find that ripening occurs much faster than convective dissolution in CO2 sequestration, and on timescales comparable to seasonal H2 storage operations. These findings establish a quantitative framework linking pore-scale heterogeneity to field-scale gas redistribution, with implications for the design and longevity of subsurface storage strategies.

cond-mat.soft↗

arXiv2018

Wrinkle-Free Interface Compression for Two-Fluid Flows

Pure advection of a conservative scalar is relevant to several applications including two-phase flow. Successful numerical schemes must capture the sharp interface between the phases while maintaining a smooth (wrinkle-free) interfacial contour. Among other methods, algebraic schemes that are based on the addition of an extra artificial interface compression term to the scalar transport equation have gained recent popularity (e.g., OpenFOAM; porous media). While the approach offers unique flexibilities in spatiotemporal discretizations, common numerical treatments result in the wrinkling of the interface. In this short note, an easy-to-implement solution to this problem is presented.

physics.flu-dyn↗