arXiv subjects

Guillem Sole-Mari

Publications and source records attributed to Guillem Sole-Mari.

6 recordsLinked to original sources

arXiv2026

Topological origin of flow distributions in disordered porous media

We investigate steady Stokes flow through porous media composed of two-dimensional disordered arrays of circular obstacles. We develop a theory for the statistics of flow rates based on a pore-network model that captures local flow correlations. We show that the flow rate distribution across the ensemble of pore bodies follows a Gamma distribution, and that the flow rate distribution through pore throats is fully determined in terms of it. Furthermore, this Gamma distribution can be directly linked to simple geometrical properties such as the coefficient of variation of pore throat widths, rendering the model parameterisable from minimal medium information. The resulting predictions agree closely with computational fluid dynamics simulations and show markedly better agreement than prior mean-field models that neglect local flow-rate correlations, clarifying how local splitting and merging shape flow in disordered porous networks.

physics.flu-dyn↗

arXiv2024

Linking Mixing Interface Deformation to Concentration Gradients in Porous Media

We study the pore-scale transport of a conservative scalar forming an advancing mixing front, which can be re-interpreted to predict instantaneous mixing-limited bimolecular reactions. We investigate this using a set of two-dimensional, high-resolution numerical simulations within a poly-disperse granular porous medium, covering a wide range of Peclet numbers. The aim is to show and exploit the direct link between pore-scale concentration gradients and mixing interface (midpoint concentration isocontour). We believe that such a perspective provides a complementary new lens for better understanding mixing and spreading in porous media. We develop and validate a theoretical model that quantifies the temporal elongation of the mixing interface and the upscaled reaction kinetics in mixing-limited systems accounting for pore-scale concentration fluctuations. Contrary to the classical belief that, given sufficient time, pore-scale fluctuations would eventually be washed out, we show that for $Pe>1$ advection generates pore-scale concentration fluctuations more rapidly than they can be fully dissipated. For such P'eclet numbers, once incomplete mixing is established, it will persist indefinitely.

physics.flu-dyn↗

arXiv2024

3D Pore-Scale Mixing Interface Evolution

The effective mixing behavior of solutes in porous media is fundamentally connected to the development of a local mixing interface between the two initial solutions, which is characterized by a complex lamellar structure. The deformation of the interface is controlled by the interplay of advection and diffusion, which generate the mechanisms of lamella stretching and shrinking, respectively. Based on the results of pore-scale numerical simulations, we develop a mechanistic single parabolic lamella model (SPLM) to capture the interface evolution across various temporal and Péclet number scales. The model shows near-perfect agreement with a 2D parallel plates scenario and promising results for a 3D porous medium. The SPLM model also establishes Péclet regimes for the equilibrium area and temporal regimes for the transient behavior of the interface. These findings represent a step forward towards eventually incorporating mixing limitation into general macroscopic reactive transport models.

physics.flu-dyn↗

arXiv2019

Particle Density Estimation with Grid-Projected Adaptive Kernels

The reconstruction of smooth density fields from scattered data points is a procedure that has multiple applications in a variety of disciplines, including Lagrangian (particle-based) models of solute transport in fluids. In random walk particle tracking (RWPT) simulations, particle density is directly linked to solute concentrations, which is normally the main variable of interest, not just for visualization and post-processing of the results, but also for the computation of non-linear processes, such as chemical reactions. Previous works have shown the superiority of kernel density estimation (KDE) over other methods such as binning, in terms of its ability to accurately estimate the "true" particle density relying on a limited amount of information. Here, we develop a grid-projected KDE methodology to determine particle densities by applying kernel smoothing on a pilot binning; this may be seen as a "hybrid" approach between binning and KDE. The kernel bandwidth is optimized locally. Through simple implementation examples, we elucidate several appealing aspects of the proposed approach, including its computational efficiency and the possibility to account for typical boundary conditions, which would otherwise be cumbersome in conventional KDE.

physics.comp-ph↗

arXiv2019

Entropy: The former trouble with particles (including a new numerical model computational penalty for the Akaike information criterion)

Traditional random-walk particle-tracking (PT) models of advection and dispersion do not track entropy, because particle masses remain constant. Newer mass-transfer particle tracking (MTPT) models have the ability to do so because masses of all compounds may change along trajectories. Additionally, the probability mass functions (PMF) of these MTPT models may be compared to continuous solutions with probability density functions, when a consistent definition of entropy (or similarly, the dilution index) is constructed. This definition reveals that every numerical model incurs a computational entropy. Similar to Akaike's entropic penalty for larger numbers of adjustable parameters, the computational complexity of a model (e.g., number of nodes) adds to the entropy and, as such, must be penalized. The MTPT method can use a particle-collision based kernel or an SPH-derived adaptive kernel. The latter is more representative of a locally well-mixed system (i.e., one in which the dispersion tensor equally represents mixing and solute spreading), while the former better represents the separate processes of mixing versus spreading. We use computational means to demonstrate the viability of each of these methods.

physics.comp-ph↗

arXiv2019

Numerical Equivalence Between SPH and Probabilistic Mass Transfer Methods for Lagrangian Simulation of Dispersion

Several Lagrangian methodologies have been proposed in recent years to simulate advection-dispersion of solutes in fluids as a mass exchange between numerical particles carrying the fluid. In this paper, we unify these methodologies, showing that mass transfer particle tracking (MTPT) algorithms can be framed within the context of smoothed particle hydrodynamics (SPH), provided the choice of a Gaussian smoothing kernel whose bandwidth depends on the dispersion and the time discretization. Numerical simulations are performed for a simple dispersion problem, and they are compared to an analytical solution. Based on the results, we advocate for the use of a kernel bandwidth of the size of the characteristic dispersion length $\ell=\sqrt{2DΔt}$, at least given a "dense enough" distribution of particles, for in this case the mass transfer operation is not just an approximation, but in fact the exact solution, of the solute's displacement by dispersion in a time step.

physics.comp-ph↗