Article
Computer Science, Interdisciplinary Applications
Hiroaki Nishikawa
Summary: This paper proposes a flux correction technique for achieving second-order accuracy on arbitrary polyhedral grids involving non-planar faces. The technique is derived from the k-exact finite-volume discretization approach and addresses the missing term in other practical finite-volume discretizations. It demonstrates the importance of a consistent definition of a control volume for achieving second-order accuracy.
JOURNAL OF COMPUTATIONAL PHYSICS
(2022)
Article
Environmental Sciences
Anargiros Delis, Maria Kazolea, Maria Gaitani
Summary: This work aims to supplement a higher-order well-balanced unstructured finite volume scheme for simulating weakly non-linear weakly dispersive water waves, by investigating and developing solution strategies for the sparse linear system that appears during the discretization process. An optimal strategy is proposed, combining the use of the BiCGSTAB method with the ILUT preconditioner and the Reverse Cuthill-McKee reordering.
Article
Physics, Fluids & Plasmas
Lei Xu, Rongliang Chen, Xiao-Chuan Cai
Summary: This paper presents a novel finite-volume discrete Boltzmann method for inviscid compressible flows, which is validated through seven benchmark problems. The method demonstrates close to linear strong scalability in parallel implementation.
Article
Computer Science, Interdisciplinary Applications
Dokyun Kim, Christopher B. Ivey, Frank E. Ham, Luis G. Bravo
Summary: A simple algebraic Volume-of-Fluid (VoF) method is developed based on the finite-volume formulation, utilizing a blended high-resolution scheme to preserve sharpness of material interfaces. The numerical algorithm is implemented and tested on Voronoi meshes, showing enhanced capabilities in preserving interface sharpness and shape compared to other algebraic VoF methods in the literature.
JOURNAL OF COMPUTATIONAL PHYSICS
(2021)
Article
Computer Science, Interdisciplinary Applications
Yichen Huang, Bin Xie
Summary: A generic balanced-force algorithm is proposed to solve incompressible multiphase flows with complex interfaces and large density ratios on the polyhedral unstructured grids. The algorithm combines the finite volume method based on the volume of fluid (VOF) approach with the fractional step method in a collocated framework, ensuring a complete balance between gravity, surface tension, and pressure gradients. It presents a novel approach to treat the non-orthogonal term, effectively suppressing spurious velocities in two-phase flows.
JOURNAL OF COMPUTATIONAL PHYSICS
(2023)
Article
Computer Science, Interdisciplinary Applications
Bin Xie, Xi Deng, ShiJun Liao, Feng Xiao
Summary: In this article, a novel high-order multi-moment finite volume method (MMFVM) for solving linear and nonlinear hyperbolic systems on unstructured grids is proposed. The method, combining VPM-CLS scheme with AOD limiting projection technique, achieves high accuracy and non-oscillatory numerical results for discontinuous solutions.
JOURNAL OF COMPUTATIONAL PHYSICS
(2021)
Article
Computer Science, Interdisciplinary Applications
Walter Boscheri, Raphael Loubere, Pierre-Henri Maire
Summary: This paper presents a conservative cell-centered Lagrangian Finite Volume scheme for solving hyperelasticity equations on unstructured multidimensional grids. By combining Multidimensional Optimal Order Detection (MOOD) limiting strategy and Arbitrary high order schemes using DERivatives (ADER) approach, the method ensures robustness and stability at shock waves while achieving second-order accuracy in time. The approach has been successfully tested in a hydrodynamics context and aims to extend to hyperelasticity with nodal solver and Geometrical Conservation Law compliance.
JOURNAL OF COMPUTATIONAL PHYSICS
(2022)
Article
Computer Science, Interdisciplinary Applications
Florian Setzwein, Peter Ess, Peter Gerlinger
Summary: This article presents a k-exact reconstruction method integrated into vertex-centered unstructured finite-volume flow solvers, maintaining high-order accuracy. The method employs a fractional step strategy and fully implicit discretization, demonstrating third order accuracy for convective fluxes and second order accuracy for diffusive fluxes. Implementation in ThetaCOM shows improved performance and accuracy in both two and three spatial dimensions.
JOURNAL OF COMPUTATIONAL PHYSICS
(2021)
Article
Computer Science, Interdisciplinary Applications
Pedro M. P. Costa, Duarte M. S. Albuquerque
Summary: In this paper, a new operator is proposed to convert point values into mean ones, enabling simpler high-order spatial schemes for unsteady problems. The method is verified for different orders and grid types, and the numerical spatial error evolution, solver runtime, and memory requirement are compared as efficiency metrics. The results show that high-order schemes provide faster and more accurate results compared to second-order schemes.
JOURNAL OF COMPUTATIONAL PHYSICS
(2022)
Article
Physics, Mathematical
Yana Di, Guanghui Hu, Ruo Li, Feng Yang
Summary: In this paper, we improved the numerical study framework of the Zeldovich-Neumann-Doring model by introducing the Strang splitting method and a new h-adaptive method to ensure the quality resolution of the dynamics of the detonation front. By proposing a cheap numerical approach, unphysical influences on the detonation front can be effectively avoided, and a sufficiently dense mesh resolution can be guaranteed around the detonation front using the proposed h-adaptive method. The numerical results demonstrate the robustness of the proposed method for long time calculations and the ability to obtain high-quality dynamics of detonation.
COMMUNICATIONS IN COMPUTATIONAL PHYSICS
(2021)
Article
Computer Science, Interdisciplinary Applications
Y. Y. Liu, C. Shu, L. M. Yang, Y. G. Liu, W. Liu, Z. L. Zhang
Summary: This paper presents a high-order implicit radial basis function-based differential quadrature-finite volume (IRBFDQ-FV) method for simulating inviscid and viscous compressible flows using unstructured grids. The method guarantees conservation of mass, momentum, and energy through finite volume discretization. It uses a fourth-order approximation based on Taylor series expansion for computing flow field variables and employs the meshless RBF-based differential quadrature technique for calculating spatial derivatives. The method shows excellent accuracy, efficiency, and robustness in simulating compressible flow problems compared to other high-order finite volume methods.
JOURNAL OF COMPUTATIONAL PHYSICS
(2023)
Article
Mechanics
An Liu, Dongliang Sun, Bo Yu, Jinjia Wei, Zhizhu Cao
Summary: The study introduces an adaptive coupled volume-of-fluid and level set (VOSET) method based on unstructured grids for simulating incompressible interfacial flows. Through validation with four classical test cases, it is found that the adaptive VOSET algorithm enhances accuracy near the interface, particularly in capturing curvature and surface tension, while also improving computational efficiency by significantly reducing the number of grid cells.Comparatively, the adaptive VOSET requires only 4.85%-24.5% of the number of adaptive grid cells and 5.31%-15.93% of the computational time compared to fixed unstructured grid cells, demonstrating outstanding properties in terms of time and computational cost savings.
Article
Computer Science, Interdisciplinary Applications
Johannes Kromer, Fabio Leotta, Dieter Bothe
Summary: This paper introduces a new method for computing accurate normal fields from volume fractions on unstructured polyhedral meshes. The method achieves second-order accuracy for surfaces with significant curvature variation and first-order accuracy for normal field angular deviation. By fitting a plane to the volume fraction data of neighboring cells, an averaged normal is computed locally in each mesh cell, while considering volume conservation. The resulting minimization problem is approximately solved using a Newton-type method, and the regularity and error measures are discussed. Numerical results and convergence studies demonstrate the effectiveness of the method.
JOURNAL OF COMPUTATIONAL PHYSICS
(2023)
Article
Computer Science, Interdisciplinary Applications
Zedong Chen, Fan Zhang, Jun Liu, Biaosong Chen
Summary: Recently, a vertex-based spatial reconstruction method has been proposed for unstructured cell-centered finite volume method, showing advantages in accuracy, convergence, and efficiency. This method has been extended for the solution of viscous flows and includes a WENO-type nonlinear weighting strategy to replace conventional slope limiters. The method also incorporates an iterative near-boundary treatment to ensure linear exactness near boundaries without sacrificing computational efficiency. Numerical tests demonstrate the superior performance of the method in solving viscous flows and shock waves, particularly on high aspect-ratio irregular triangular grids.
JOURNAL OF COMPUTATIONAL PHYSICS
(2022)
Article
Computer Science, Interdisciplinary Applications
N. Yavich, N. Koshev, M. Malovichko, A. Razorenova, M. Fedorov
Summary: In this paper, the performance of the mixed-hybrid finite element method (MHFEM) for EEG and MEG modeling is assessed. The study concludes that although MHFEM is computationally demanding, it improves the accuracy of modeling on low-resolution head models compared to the conventional nodal finite element method (P-1 FEM).
IEEE TRANSACTIONS ON MEDICAL IMAGING
(2022)
Article
Computer Science, Interdisciplinary Applications
Ammar H. Alali, Francois P. Hamon, Bradley T. Mallison, Hamdi A. Tchelepi
Summary: Investigating the use of discrete interface conditions at the matrix-fracture interface to improve flux computation accuracy without extreme grid refinement. Analyzing the interaction of the upwinding scheme with discrete interface conditions and illustrating the importance of interface conditions in accurately capturing matrix-fracture flux and flow dynamics representation.
COMPUTATIONAL GEOSCIENCES
(2021)
Article
Computer Science, Interdisciplinary Applications
Yashar Mehmani, Nicola Castelletto, Hamdi A. Tchelepi
Summary: This study introduces a pore-level multiscale method that efficiently approximates direct numerical simulation with controllable accuracy for predicting the elastic response of solid media containing cracks or defects.
JOURNAL OF COMPUTATIONAL PHYSICS
(2021)
Article
Engineering, Chemical
Michael Connolly, Huanquan Pan, Motonao Imai, Hamdi A. Tchelepi
Summary: Thermal enhanced oil recovery involves complex interplays of mass and energy transport processes with phase behavior, requiring thermal compositional simulation and isenthalpic flash calculations. Isothermal flash algorithms have been refined over the years, while isenthalpic flash remains a challenge due to unknown temperatures and nonlinear enthalpy behavior. The injection of steam in thermal EOR further complicates phase equilibrium calculations, making water a thermodynamically dominant component that cannot be excluded from simulations.
CHEMICAL ENGINEERING SCIENCE
(2021)
Article
Engineering, Geological
Jie Yang, Hamdi A. Tchelepi, Anthony R. Kovscek
Summary: This study presents a thermodynamically consistent rate-dependent fracture model, coupled with single-phase fluid flow, to investigate solid-fluid coupling, fluid-driven fracture propagation, and rate-dependent viscoelastic deformation. The model is based on rigorous thermodynamic principles and ensures energy conservation during fracture propagation, making it a strong basis for studying rate-dependent fracturing experiments and predicting material behaviors under new conditions.
INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS
(2021)
Review
Multidisciplinary Sciences
K. Kashinath, M. Mustafa, A. Albert, J-L. Wu, C. Jiang, S. Esmaeilzadeh, K. Azizzadenesheli, R. Wang, A. Chattopadhyay, A. Singh, A. Manepalli, D. Chirila, R. Yu, R. Walters, B. White, H. Xiao, H. A. Tchelepi, P. Marcus, A. Anandkumar, P. Hassanzadeh, Prabhat
Summary: This study explores systematic approaches to incorporating physics and domain knowledge into machine learning models, showing successful applications in emulating, downscaling, and forecasting weather and climate processes. Through 10 case studies, it demonstrates improvements in physical consistency, reduced training time, enhanced data efficiency, and better generalization.
PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES
(2021)
Article
Energy & Fuels
Huanquan Pan, Motonao Imai, Michael Connolly, Hamdi Tchelepi
Summary: This paper introduces a new method for solving the Rachford-Rice equations, which achieves convergence through the minimization of a convex function and trust-region method. Test results demonstrate the robustness, efficiency, and insensitivity to initial values of this method.
JOURNAL OF PETROLEUM SCIENCE AND ENGINEERING
(2021)
Article
Engineering, Multidisciplinary
Sebastian B. M. Bosma, Francois P. Hamon, Brad T. Mallison, Hamdi A. Tchelepi
Summary: In subsurface multiphase flow simulations, poor performance of nonlinear solvers is a significant issue, but a new optimized scheme can greatly reduce the number of nonlinear iterations and improve efficiency.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2022)
Article
Engineering, Petroleum
I Shovkun, H. A. Tchelepi
Summary: The study aims to develop a spatial discretization scheme that cuts the matrix grid with fracture planes to model fluid flow and mechanical deformation in fractured reservoirs. It utilizes traditional formulations and numerical harmonic shape functions to accurately describe the behavior of fractured formations. The proposed approach is validated and compared with existing methods, demonstrating its feasibility and effectiveness.
Article
Computer Science, Interdisciplinary Applications
Andrea Franceschini, Nicola Castelletto, Joshua A. White, Hamdi A. Tchelepi
Summary: In this paper, a family of preconditioning strategies for the contact problem in fractured and faulted porous media is presented. The strategies combine low-order continuous finite elements and piecewise constant Lagrange multipliers to simulate bulk deformation and impose frictional contact constraints. A novel jump stabilization technique is introduced to improve previous work, and scalable preconditioning strategies that exploit the block structure of the Jacobian matrix are designed. The proposed preconditioners achieve success by eliminating the Lagrange multiplier degrees of freedom and efficiently solving the pseudo-Schur complement. Numerical results demonstrate the theoretical properties, scalability, and robustness of the preconditioner, along with a comparison to other approaches in the literature.
JOURNAL OF COMPUTATIONAL PHYSICS
(2022)
Article
Engineering, Multidisciplinary
Bazyli Klockiewicz, Leopold Cambier, Ryan Humble, Hamdi Tchelepi, Eric Darve
Summary: This paper presents a second-order accurate approach to sparsify the off-diagonal matrix blocks in solving sparse linear systems. By sparsifying the fill-in matrix blocks in block Gaussian elimination, an approximate factorization of the given matrix is computed. The new approach incorporates squared 2-norm of the incurred error in the sparsification of a matrix block, resulting in faster convergence and improved overall performance of the algorithm.
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING
(2022)
Article
Electrochemistry
Weiyu Li, Hamdi A. Tchelepi, Yiguang Ju, Daniel M. Tartakovsky
Summary: Dendritic growth is a major cause of degradation and failure in lithium-metal batteries. This study shows that changes in the local electric field and the use of anisotropic electrolytes can suppress dendritic growth of lithium metal.
JOURNAL OF THE ELECTROCHEMICAL SOCIETY
(2022)
Article
Computer Science, Interdisciplinary Applications
Ricardo H. Deucher, Hamdi A. Tchelepi
Summary: The Adaptive Implicit Method (AIM) is a technique that reduces computational costs in simulations of field scale displacements in porous media. By using a mixed implicit/explicit time discretization and high-order fluxes, AIM overcomes limitations of purely explicit approaches and improves accuracy. A new scheme is introduced that blends implicit and explicit time discretizations along with single-point upwind and a high-order flux-limited total variation diminishing approximation of numerical fluxes, resulting in reduced numerical diffusion and improved accuracy.
JOURNAL OF COMPUTATIONAL PHYSICS
(2022)
Article
Computer Science, Interdisciplinary Applications
Jiawei Li, Pavel Tomin, Hamdi Tchelepi
Summary: There is an increasing interest in developing robust and efficient sequential methods for reservoir simulation. The sequential fully implicit Newton (SFIN) method addresses the slow sequential coupling convergence issue when flow and transport problems are strongly coupled. However, the original SFIN algorithm requires fixed primary variables during the simulation. In this work, strategies are proposed to handle inconsistent primary variables and extend the SFIN method to the natural black-oil formulation.
COMPUTATIONAL GEOSCIENCES
(2023)
Article
Computer Science, Interdisciplinary Applications
Mamadou N'diaye, Francois P. Hamon, Hamdi A. Tchelepi
Summary: This work focuses on the development of a two-step field-split nonlinear preconditioner to accelerate the convergence of two-phase flow and transport in heterogeneous porous media. The proposed Field-Split Multiplicative Schwarz Newton (FSMSN) algorithm consists of a preconditioning step and a global step, achieving faster convergence compared to existing preconditioners and standard solution strategies. The impact of the upwinding scheme and the dynamic adaptation of subproblem tolerance in the preconditioning step are highlighted.
COMPUTATIONAL GEOSCIENCES
(2023)
Article
Geosciences, Multidisciplinary
Catherine Spurin, Gareth G. Roberts, Conor P. B. O'Malley, Takeshi Kurotori, Samuel Krevor, Martin J. Blunt, Hamdi Tchelepi
Summary: Complex pore-scale dynamics during multiphase flow through porous rocks are not accounted for in large-scale models. However, we demonstrate that pressure fluctuations measured at the core-scale can reflect fluid displacements at the pore-scale. The spectral characteristics of pressure data provide information about flow dynamics, sample size, and rock heterogeneity. Understanding fluid flow in porous rocks is crucial for the safe storage of CO2 and hydrogen.
GEOPHYSICAL RESEARCH LETTERS
(2023)
