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Parallel multilevel methods for solving the Darcy--Forchheimer model based on a nearly semicoercive formulation
Announce Type: replace Abstract: High-velocity fluid flow through porous media is modeled by prescribing a nonlinear relationship between the flow rate and the pressure gradient, called the Darcy--Forchheimer equation. This paper is concerned with the analysis of parallel multilevel methods for solving the Darcy--Forchheimer model. We begin by reformulating the Darcy--Forchheimer model as a nearly semicoercive convex optimization problem via the augmented Lagrangian method.
Divergence-free unfitted finite element discretisations for the Darcy problem
arXiv:2603.26212v2 Announce Type: replace Abstract: We develop an unfitted compatible finite element discretisation for the Darcy problem based on $H(\mathrm{div})$-conforming flux spaces and discontinuous pressure spaces. The method is designed to preserve pointwise discrete mass conservation while remaining robust in the presence of arbitrarily small cut cells arising from unfitted meshes. Robustness is achieved by combining an $L^2$-stabilisation of the flux with an additional mixed-term...
An experimental study on the heat transport in porous media convection
arXiv:2606.06331v1 Announce Type: new Abstract: We investigate the heat transport in porous media convection over a wide Rayleigh-- Darcy number range of $26.8\leq Ra\leq 2.62\times 10^5$, and a Darcy number range of $6.18\times10^{-7}\leq Da\leq 1.21\times 10^{-5}$. In the experiments, we employ 3D-printed lattice structures as the solid porous matrix and water as the working fluid.
Applying Two-Grid Preconditioner for Subsurface Flow Simulation using Attention-enhanced Hybrid Network to Accelerate Multiscale Discretization in High-contrast Media
arXiv:2606.02582v1 Announce Type: new Abstract: In this paper, we study the efficient numerical solution of Darcy equations in strongly heterogeneous media with high-contrast permeability and propose a hybrid framework that combines learning with multiscale numerical methods. The learning component is used for the prediction of multiscale basis functions in the mixed generalized multiscale finite element method (mixed GMsFEM), with the goal of reducing the repeated local computations...
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A Machine Learning-Enhanced Hopf-Cole Formulation for Nonlinear Gas Flow in Porous Media
Announce Type: replace-cross Abstract: Accurate modeling of gas flow through porous media is critical for many technological applications, including reservoir performance prediction, carbon capture and sequestration, and fuel cells and batteries. However, such modeling remains challenging due to strong nonlinear behavior and uncertainty in model parameters. In particular, gas slippage effects described by the Klinkenberg model introduce pressure-dependent permeability, which complicates...
A Machine Learning-Enhanced Hopf-Cole Formulation for Nonlinear Gas Flow in Porous Media
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An algebraic multiscale preconditioner for large sparse SPD matrices
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Book Dedications
To my sister, Dr. Soma Mohammed Mohammed Baroud. I write your name in full, because that is how it appeared on the white body bag that held your remains soon after the bomb was dropped. Dedications A random assortment of book dedications.