Article
Water Resources
Luyu Wang, Fabrice Golfier, Anne-Julie Tinet, Weizhong Chen, Cornelis Vuik
Summary: This study investigates the numerical method and equivalent continuum approach for fluid flow in fractured porous media. By developing an efficient implicit scheme and utilizing an improved equivalent continuum approach, the proposed numerical scheme improves convergence condition and computational efficiency, and successfully simulates fluid flow in fracture networks with complex geometry.
ADVANCES IN WATER RESOURCES
(2022)
Article
Mathematics, Applied
Huangxin Chen, Shuyu Sun
Summary: A new efficient IMPES scheme for incompressible and immiscible two-phase flow in heterogeneous porous media with capillary pressure is proposed in this work. The scheme is physics-preserving, maintains continuity of total velocity, and is unbiased with regard to both phases. Key ideas include rewriting Darcy flows, discretized conservation equations, applying upwind strategy, and using mixed finite element methods for pressure-velocity systems. The new algorithm's efficiency and robustness are demonstrated through interesting examples.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2021)
Article
Geochemistry & Geophysics
Jin YiMin, Zhang Huai, Shi YaoLin
Summary: This paper presents a fully implicit method for modeling viscoelastic plastic flows in non-Newtonian mechanics, and compares it with conventional methods through numerical experiments. Results show that the proposed method is competitive with traditional ones and achieves higher numerical accuracy when the Deborah number is large. The algorithm, with a third-order WENO limiter, can simultaneously eliminate numerical oscillations and preserve high-order resolution results during long-time simulations.
CHINESE JOURNAL OF GEOPHYSICS-CHINESE EDITION
(2023)
Article
Mathematics, Applied
Wei Feng, Haibo Huang
Summary: A convolutional neural network is developed to predict multiphase flow in heterogeneous porous media efficiently compared to direct numerical methods. By utilizing a deep neural network model, the computational time for simulating new geometries of porous media can be significantly reduced, demonstrating good prediction performance across a wide range of porosity and heterogeneity. Additionally, visible explanations are provided to understand what the neural networks have learned to better understand the inherent process.
ADVANCES IN APPLIED MATHEMATICS AND MECHANICS
(2021)
Article
Water Resources
Anis Younes, Hussein Hoteit, Rainer Helmig, Marwan Fahs
Summary: The study developed a fully mixed finite element model for nonlinear flow and transport in unsaturated fractured porous media by spatial discretization of 2D matrix elements and 1D fracture elements and using efficient time discretization methods, addressing challenges such as infiltration of contaminated water into dry soil.
ADVANCES IN WATER RESOURCES
(2022)
Article
Mathematics, Applied
Rogerio M. Saldanha da Gama, Jose Julio Pedrosa Filho, Rogerio Pazetto S. da Gama, Daniel Cunha da Silva, Carlos Henrique Alexandrino, Maria Laura Martins-Costa
Summary: This work describes kinematically constrained flows through porous media using a mixture theory approach. It employs an adequate constitutive relation for pressure that preserves the problem hyperbolicity even in saturated flows. The simulations confirm the significant characteristic of the fluid establishing controlled supersaturation.
Article
Engineering, Multidisciplinary
Saeed Saeedmonir, Amir R. Khoei
Summary: This paper presents a numerical multiscale formulation for analyzing transient heat and fluid flow in deformable heterogeneous porous media. The proposed method uses first-order computational homogenization to simulate THM problems at two scales, providing an efficient computational procedure. Proper virtual power relations bridge the scales, and microscopic boundary conditions are enhanced to consider transient effects. Macroscopic properties are determined from the microscopic solution using appropriate mathematical procedures. An upwind finite element squared method is employed for accurate spatial results in highly advective heat transfer.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2022)
Article
Engineering, Civil
Payam Sarkhosh, Amgad Salama, Yee-Chung Jin
Summary: This study introduces a finite-volume method to address discontinuities in flow through porous structures, utilizing an upwind scheme to maintain solution monotonicity. Linearization of the equations is achieved using the Picard method, while the dynamic wave equation is employed to handle the continuity equation's flux term and improve convergence during iteration.
WATER RESOURCES MANAGEMENT
(2021)
Article
Mechanics
Didier Lasseux, Francisco J. Valdes-Parada
Summary: A closed expression is proposed to calculate the average pressure difference in two-phase flow in porous media. This equation takes into account the pressure gradient, body forces, and interfacial effects in each phase, and is applicable to situations where the fluid-fluid interface is not steady. The accuracy of this expression is validated by comparing it with direct numerical simulations in a model porous structure.
JOURNAL OF FLUID MECHANICS
(2023)
Article
Mathematics, Applied
Paola F. Antonietti, Jacopo De Ponti, Luca Formaggia, Anna Scotti
Summary: This work focuses on efficiently solving the system of equations derived from mimetic finite difference discretization of a hybrid-dimensional mixed Darcy problem in fractured porous media. By investigating the spectral properties and proposing an approximation of block factorization preconditioners, the convergence of iterative solvers applied to the resulting discrete system is accelerated. Numerical tests on significant three-dimensional cases confirm the effectiveness of the proposed preconditioners.
JOURNAL OF SCIENTIFIC COMPUTING
(2021)
Article
Geosciences, Multidisciplinary
Yihuai Zhang, Branko Bijeljic, Ying Gao, Qingyang Lin, Martin J. Blunt
Summary: The study focuses on the pressure difference during two-phase flow across a sandstone sample with varying injection rates and fractional flows of water. It was observed that there is a transition from linear to non-linear flow with the power-law exponent depending on the fractional flow. By using energy balance, the onset of intermittency for a range of fractional flows, fluid viscosities, and rock types was accurately predicted.
GEOPHYSICAL RESEARCH LETTERS
(2021)
Article
Mathematics, Applied
Albert Costa-Sole, Eloi Ruiz-Girones, Josep Sarrate
Summary: The study introduces a stable high-order HDG formulation coupled with DIRK schemes for simulating single-phase flow in porous media. The formulation exhibits high-order accuracy for pressure, flux, and velocity, allowing for reduced computational costs and more accurate solutions.
JOURNAL OF SCIENTIFIC COMPUTING
(2021)
Article
Engineering, Mechanical
Ji Lang, Liyun Wang, Qianhong Wu
Summary: This theoretical study discusses the transient squeezing flow through a thin porous gap driven by an oscillating boundary, considering viscous, inertial, and Darcy effects. It reveals that increasing the squeezing depth enhances the oscillation of the velocity profiles due to the alternating dominance of viscous and inertial effects. The presence of porous media stabilizes the fluid field, showcasing potential applications in fields such as biomedical and industrial processes.
TRIBOLOGY INTERNATIONAL
(2021)
Article
Mechanics
Graham P. Benham, Mike J. Bickle, Jerome A. Neufeld
Summary: This study focuses on upscaling the effect of heterogeneities in porous media, specifically in relation to multiphase flow and the transition between viscous and capillary flow regimes. By modifying the classic Buckley-Leverett problem, the study demonstrates how and where the flow transitions between these regimes and its impact on flooding speeds. The implications of these results in the context of carbon dioxide sequestration are also discussed and compared with field data.
JOURNAL OF FLUID MECHANICS
(2021)
Article
Computer Science, Interdisciplinary Applications
Abay Molla Kassa, Kundan Kumar, Sarah E. Gasda, Florin A. Radu
Summary: In this article, a linearization scheme for a nonlocal two-phase flow model is proposed, which handles dynamic capillary pressure functions and introduces stabilization terms. The convergence and performance of the scheme are theoretically analyzed and verified through numerical simulations. The proposed scheme outperforms the iterative implicit pressure explicit saturation scheme in terms of computational efficiency and accuracy.
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS
(2021)
Article
Green & Sustainable Science & Technology
Rebecca Allen, Halvor M. Nilsen, Odd Andersen, Knut-Andreas Lie
INTERNATIONAL JOURNAL OF GREENHOUSE GAS CONTROL
(2017)
Article
Green & Sustainable Science & Technology
Rebecca Allen, Halvor M. Nilsen, Knut-Andreas Lie, Olav Moyner, Odd Andersen
INTERNATIONAL JOURNAL OF GREENHOUSE GAS CONTROL
(2018)
Article
Computer Science, Interdisciplinary Applications
Masoud Ghaderi Zefreh, Halvor M. Nilsen, Knut Andreas Lie, Xavier Raynaud, Florian Doster
COMPUTATIONAL GEOSCIENCES
(2019)
Review
Computer Science, Interdisciplinary Applications
Runar Lie Berge, Oystein Strengehagen Klemetsdal, Knut-Andreas Lie
COMPUTATIONAL GEOSCIENCES
(2019)
Article
Energy & Fuels
Shuai Ma, Binshan Ju, Lin Zhao, Knut-Andreas Lie, Yintao Dong, Qilong Zhang, Yapeng Tian
Summary: This paper discusses incorporating non-Darcy flow correction into embedded discrete fracture modeling (EDFM) and validating the resulting method. It also explores formulating grid-based flow diagnostics on top of the new EDFM method for computationally inexpensive predictions of flow patterns and dynamic heterogeneity measurements. Finally, it demonstrates how flow diagnostics can be utilized to optimize well placement and enhance oil recovery.
JOURNAL OF PETROLEUM SCIENCE AND ENGINEERING
(2022)
Article
Computer Science, Interdisciplinary Applications
Francesca Watson, Stein Krogstad, Knut-Andreas Lie
Summary: Ensembles of geomodels can be ranked and selected based on flow diagnostics techniques, which provide a quick way to analyze flow behaviors and estimate oil recovery. These tools serve as proxies for full-featured dynamic modeling and help in evaluating a range of possible outcomes for reservoirs.
COMPUTATIONAL GEOSCIENCES
(2022)
Article
Energy & Fuels
Knut-Andreas Lie, Stein Krogstad
Summary: This paper compares two graph-based approaches for building simplified field management optimization models. The first approach represents the reservoir as a graph of 1D numerical flow models, while the second approach aims at building richer models that mimic the intercell connections in a conventional 3D grid model. The comparisons show that graph models with connectivity that mimics the intercell connectivity in coarse 3D models can represent a wider range of fluid connections and are generally more robust and easier to train.
GEOENERGY SCIENCE AND ENGINEERING
(2023)
Proceedings Paper
Mathematics, Applied
Knut-Andreas Lie
NON-LINEAR PARTIAL DIFFERENTIAL EQUATIONS, MATHEMATICAL PHYSICS, AND STOCHASTIC ANALYSIS: THE HELGE HOLDEN ANNIVERSARY VOLME
(2018)
Proceedings Paper
Green & Sustainable Science & Technology
Halvor Moll Nilsen, Stein Krogstad, Odd Andersen, Rebecca Allen, Knut-Andreas Lie
13TH INTERNATIONAL CONFERENCE ON GREENHOUSE GAS CONTROL TECHNOLOGIES, GHGT-13
(2017)
Proceedings Paper
Green & Sustainable Science & Technology
Rebecca Allen, Halvor M. Nilsen, Odd Andersen, Knut-Andreas Lie
13TH INTERNATIONAL CONFERENCE ON GREENHOUSE GAS CONTROL TECHNOLOGIES, GHGT-13
(2017)
Article
Computer Science, Interdisciplinary Applications
Trine S. Mykkeltvedt, Xavier Raynaud, Knut-Andreas Lie
COMPUTATIONAL GEOSCIENCES
(2017)
Article
Computer Science, Interdisciplinary Applications
K. -A. Lie, O. Moyner, J. R. Natvig, A. Kozlova, K. Bratvedt, S. Watanabe, Z. Li
COMPUTATIONAL GEOSCIENCES
(2017)
Article
Computer Science, Interdisciplinary Applications
Stein Krogstad, Knut-Andreas Lie, Halvor Moll Nilsen, Carl Fredrik Berg, Vegard Kippe
COMPUTATIONAL GEOSCIENCES
(2017)
Article
Computer Science, Interdisciplinary Applications
Kai Bao, Knut-Andreas Lie, Olav Moyner, Ming Liu
COMPUTATIONAL GEOSCIENCES
(2017)
Article
Computer Science, Interdisciplinary Applications
Rebecca Allen, Halvor Moll Nilsen, Odd Andersen, Knut-Andreas Lie
COMPUTATIONAL GEOSCIENCES
(2017)
Article
Computer Science, Interdisciplinary Applications
Tian Liang, Lin Fu
Summary: In this work, a new shock-capturing framework is proposed based on a new candidate stencil arrangement and the combination of infinitely differentiable non-polynomial RBF-based reconstruction in smooth regions with jump-like non-polynomial interpolation for genuine discontinuities. The resulting scheme achieves high order accuracy and resolves genuine discontinuities with sub-cell resolution.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Lukas Lundgren, Murtazo Nazarov
Summary: In this paper, a high-order accurate finite element method for incompressible variable density flow is introduced. The method addresses the issues of saddle point system and stability problem through Schur complement preconditioning and artificial compressibility approaches, and it is validated to have high-order accuracy for smooth problems and accurately resolve discontinuities.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Gabriele Ciaramella, Laurence Halpern, Luca Mechelli
Summary: This paper presents a novel convergence analysis of the optimized Schwarz waveform relaxation method for solving optimal control problems governed by periodic parabolic PDEs. The analysis is based on a Fourier-type technique applied to a semidiscrete-in-time form of the optimality condition, which enables a precise characterization of the convergence factor at the semidiscrete level. The behavior of the optimal transmission condition parameter is also analyzed in detail as the time discretization approaches zero.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Jonas A. Actor, Xiaozhe Hu, Andy Huang, Scott A. Roberts, Nathaniel Trask
Summary: This article introduces a scientific machine learning framework that uses a partition of unity architecture to model physics through control volume analysis. The framework can extract reduced models from full field data while preserving the physics. It is applicable to manifolds in arbitrary dimension and has been demonstrated effective in specific problems.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Nozomi Magome, Naoki Morita, Shigeki Kaneko, Naoto Mitsume
Summary: This paper proposes a novel strategy called B-spline based SFEM to fundamentally solve the problems of the conventional SFEM. It uses different basis functions and cubic B-spline basis functions with C-2-continuity to improve the accuracy of numerical integration and avoid matrix singularity. Numerical results show that the proposed method is superior to conventional methods in terms of accuracy and convergence.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Timothy R. Law, Philip T. Barton
Summary: This paper presents a practical cell-centred volume-of-fluid method for simulating compressible solid-fluid problems within a pure Eulerian setting. The method incorporates a mixed-cell update to maintain sharp interfaces, and can be easily extended to include other coupled physics. Various challenging test problems are used to validate the method, and its robustness and application in a multi-physics context are demonstrated.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Xing Ji, Fengxiang Zhao, Wei Shyy, Kun Xu
Summary: This paper presents the development of a third-order compact gas-kinetic scheme for compressible Euler and Navier-Stokes solutions, constructed particularly for an unstructured tetrahedral mesh. The scheme demonstrates robustness in high-speed flow computation and exhibits excellent adaptability to meshes with complex geometrical configurations.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Alsadig Ali, Abdullah Al-Mamun, Felipe Pereira, Arunasalam Rahunanthan
Summary: This paper presents a novel Bayesian statistical framework for the characterization of natural subsurface formations, and introduces the concept of multiscale sampling to localize the search in the stochastic space. The results show that the proposed framework performs well in solving inverse problems related to porous media flows.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Jacob Rains, Yi Wang, Alec House, Andrew L. Kaminsky, Nathan A. Tison, Vamshi M. Korivi
Summary: This paper presents a novel method called constrained optimized DMD with Control (cOptDMDc), which extends the optimized DMD method to systems with exogenous inputs and can enforce the stability of the resulting reduced order model (ROM). The proposed method optimally places eigenvalues within the stable region, thus mitigating spurious eigenvalue issues. Comparative studies show that cOptDMDc achieves high accuracy and robustness.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Andrea La Spina, Jacob Fish
Summary: This work introduces a hybridizable discontinuous Galerkin formulation for simulating ideal plasmas. The proposed method couples the fluid and electromagnetic subproblems monolithically based on source and employs a fully implicit time integration scheme. The approach also utilizes a projection-based divergence correction method to enforce the Gauss laws in challenging scenarios. Numerical examples demonstrate the high-order accuracy, efficiency, and robustness of the proposed formulation.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Junhong Yue, Peijun Li
Summary: This paper proposes two numerical methods (IP-FEM and BP-FEM) to study the flexural wave scattering problem of an arbitrary-shaped cavity on an infinite thin plate. These methods successfully decompose the fourth-order plate wave equation into the Helmholtz and modified Helmholtz equations with coupled conditions on the cavity boundary, providing an effective solution to this challenging problem.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
William Anderson, Mohammad Farazmand
Summary: We develop fast and scalable methods, called RONS, for computing reduced-order nonlinear solutions. These methods have been proven to be highly effective in tackling challenging problems, but become computationally prohibitive as the number of parameters grows. To address this issue, three separate methods are proposed and their efficacy is demonstrated through examples. The application of RONS to neural networks is also discussed.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Marco Caliari, Fabio Cassini
Summary: In this paper, a second order exponential scheme for stiff evolutionary advection-diffusion-reaction equations is proposed. The scheme is based on a directional splitting approach and uses computation of small sized exponential-like functions and tensor-matrix products for efficient implementation. Numerical examples demonstrate the advantage of the proposed approach over state-of-the-art techniques.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Sebastiano Boscarino, Seung Yeon Cho, Giovanni Russo
Summary: This work proposes a high order conservative semi-Lagrangian method for the inhomogeneous Boltzmann equation of rarefied gas dynamics. The method combines a semi-Lagrangian scheme for the convection term, a fast spectral method for computation of the collision operator, and a high order conservative reconstruction and a weighted optimization technique to preserve conservative quantities. Numerical tests demonstrate the accuracy and efficiency of the proposed method.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Jialei Li, Xiaodong Liu, Qingxiang Shi
Summary: This study shows that the number, centers, scattering strengths, inner and outer diameters of spherical shell-structured sources can be uniquely determined from the far field patterns. A numerical scheme is proposed for reconstructing the spherical shell-structured sources, which includes a migration series method for locating the centers and an iterative method for computing the inner and outer diameters without computing derivatives.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)