Article
Engineering, Multidisciplinary
G. Galindez-Ramirez, F. R. L. Contreras, D. K. E. Carvalho, P. R. M. Lyra
Summary: In this paper, a new high-order numerical methodology based on unstructured quadrilateral meshes is proposed for modeling oil-water displacements in highly heterogeneous and anisotropic petroleum reservoirs. The method achieves comparable accuracy to lower-order counterparts while reducing computational cost, and its accuracy, efficiency, and robustness are demonstrated through representative examples.
APPLIED MATHEMATICAL MODELLING
(2022)
Article
Mathematics, Applied
Fernando R. L. Contreras, Darlan K. E. Carvalho, Gustavo Galindez-Ramirez, Paulo R. M. Lyra
Summary: In this work, a finite volume scheme is proposed to simulate two-phase flows in non-homogeneous and non isotropic 2-D petroleum reservoirs. The scheme uses IMPES procedure and NL-TPFA approximation to ensure monotone solutions. By constructing one-sided fluxes on adjacent cells and using Picard iteration method with Anderson acceleration, computational efficiency is improved for solving the non-linear system of equations and guaranteeing monotone solutions for anisotropic permeability tensors.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2021)
Article
Mathematics, Applied
Daniel Boe, Khosro Shahbazi
Summary: This article presents a positivity-preserving algorithm for maintaining the hyperbolicity property and real-valued sound speed in compressible flows. The algorithm utilizes finite differences and flux limiting technique to retain high-order convergence while preserving the physical bounds of the solution. It successfully simulates several challenging problems in two-fluid compressible flows in one and two dimensions.
NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS
(2023)
Article
Physics, Fluids & Plasmas
L. M. Yang, C. Shu, Z. Chen, Y. Y. Liu, J. Wu, X. Shen
Summary: A high-order gas kinetic flux solver (GKFS) is developed for 2D compressible flows, which evaluates numerical fluxes based on the local asymptotic solution to the Boltzmann equation. It achieves high-order accuracy through a simplified local asymptotic solution and outperforms the second-order counterpart in numerical examples, demonstrating its accuracy and capability.
Article
Computer Science, Interdisciplinary Applications
Feng Zheng, Chi-Wang Shu, Jianxian Qiu
Summary: The proposed high order finite difference conservative scheme demonstrates advantages in conservation, high accuracy, and non-oscillatory solution for solving two medium flows. By utilizing nodal values and the WENO interpolation method, the algorithm shows efficient performance in maintaining equilibrium and capturing main features.
JOURNAL OF COMPUTATIONAL PHYSICS
(2021)
Article
Mechanics
Chao Zhang, Qibing Li, Peng Song, Jiequan Li
Summary: This study extends the simulation method for two-dimensional compressible flows to three-dimensional simulations and improves the efficiency and compactness by utilizing subcell divisions and two-stage fourth-order time stepping. The method increases the efficiency of high-order reconstruction by subdividing each cell into a set of subcells and sharing the reconstruction among the subcells. Additionally, the method combines a time-dependent gas-kinetic flux solver and a two-stage fourth-order temporal discretization, avoiding the use of multi-stage Runge-Kutta methods.
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
Mathematics, Applied
L. Freret, C. N. Ngigi, T. B. Nguyen, H. De Sterck, C. P. T. Groth
Summary: This paper proposes a high-order finite-volume scheme with anisotropic adaptive mesh refinement (AMR) for solving steady compressible fluid flows on multi-block body-fitted hexahedral meshes. The method combines robust and accurate high-order central essentially non-oscillatory (CENO) spatial discretization schemes with a scalable Newton-Krylov-Schwarz (NKS) algorithm and a block-based anisotropic AMR method. The numerical results demonstrate the computational performance of the combined scheme.
JOURNAL OF SCIENTIFIC COMPUTING
(2023)
Article
Computer Science, Interdisciplinary Applications
Pablo Castrillo, Alfredo Canelas, Eugenio Schillaci, Joaquim Rigola, Asensio Oliva
Summary: This paper presents a high-order finite volume method using Moving Least Squares (MLS) and Local Regression Estimators (LRE) for solving linear elasticity problems on two-dimensional unstructured meshes. The method effectively solves structural problems affected by shear locking and demonstrates accuracy and flexibility through canonical tests and analytical examples.
COMPUTERS & STRUCTURES
(2022)
Article
Mathematics, Applied
Zhuohang Wu, Yu-xin Ren
Summary: In this paper, a new limiter called CWBAP is proposed for shock capturing of high-order finite volume methods on unstructured grids. The distinguishing feature of this limiter is that it operates only within a compact stencil. Compared to the original WBAP limiter, the CWBAP limiter improves accuracy, resolution, and convergence properties, while preserving the order of accuracy in smooth flow simulations. Additionally, the compactness of the CWBAP limiter reduces data transfer in parallel computing, increasing its efficiency.
JOURNAL OF SCIENTIFIC COMPUTING
(2023)
Article
Computer Science, Interdisciplinary Applications
Will Thacher, Hans Johansen, Daniel Martin
Summary: We propose a higher-order finite volume method for solving elliptic PDEs with jump conditions on interfaces embedded in a 2D Cartesian grid. The method demonstrates second, fourth, and sixth order accuracy on various tests, including problems with high contrast and spatially varying coefficients, large discontinuities in the source term, and complex interface geometries. We develop a generalized truncation error analysis and a simple method based on Green's theorem for computing exact geometric moments, which enable easy inclusion of spatially-varying coefficients and jump conditions.
JOURNAL OF COMPUTATIONAL PHYSICS
(2023)
Article
Computer Science, Interdisciplinary Applications
Florian Desmons, Mathieu Coquerelle
Summary: In this study, a High-Order Momentum Preserving (HOMP) method is proposed to address the issue of significant momentum transfer between two phases, such as common air and water, when the density ratio is important. The method effectively suppresses dreadful momentum transfers at the interface, enhancing the quality of two-phase flow computation.
JOURNAL OF COMPUTATIONAL PHYSICS
(2021)
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
Jun Liu, Tobias Tolle, Dieter Bothe, Tomislav Maric
Summary: This study extends a method for handling two-phase flows with different densities and provides a theoretical basis for the numerical consistency between mass and momentum conservation. The proposed method demonstrates exact numerical stability for two-phase momentum advection and performs well in challenging fluid pairings.
JOURNAL OF COMPUTATIONAL PHYSICS
(2023)
Letter
Computer Science, Interdisciplinary Applications
Jose Cicero Araujo dos Santos, Paulo Roberto Maciel Lyra, Joao Paulo Rodrigues de Andrade, Artur Castiel Reis de Souza, Ricardo Jorge Morais de Lira Filho, Darlan Karlo Elisiario de Carvalho
Summary: This paper proposes an adaptive flow-based dual volume agglomeration strategy for correcting non-physical terms in the coarse transmissibility matrix of classical multiscale finite volume (MsFV) methods. It also presents a framework to handle non-uniform levels at each coarse control volume, in order to reduce the size of coarse scale matrices. The proposed methodologies are applied to approximate pressure solutions in an Implicit Pressure Explicit Saturation (IMPES) strategy, and their accuracy and efficiency are demonstrated through testing with challenging benchmark problems.
JOURNAL OF COMPUTATIONAL PHYSICS
(2022)
Article
Engineering, Multidisciplinary
G. Galindez-Ramirez, F. R. L. Contreras, D. K. E. Carvalho, P. R. M. Lyra
Summary: In this paper, a new high-order numerical methodology based on unstructured quadrilateral meshes is proposed for modeling oil-water displacements in highly heterogeneous and anisotropic petroleum reservoirs. The method achieves comparable accuracy to lower-order counterparts while reducing computational cost, and its accuracy, efficiency, and robustness are demonstrated through representative examples.
APPLIED MATHEMATICAL MODELLING
(2022)
Article
Engineering, Multidisciplinary
Artur Castiel Reis de Souza, Darlan Karlo Elisiario de Carvalho, Jose Cicero Araujo dos Santos, Ramiro Brito Willmersdorf, Paulo Roberto Maciel Lyra, Michael G. Edwards
Summary: This paper introduces a new multiscale finite volume framework for simulating multi-phase flow in heterogeneous and anisotropic porous media. The framework allows the use of geophysical grid defined properties on high-definition grids, addressing the issues of basis function leakage and mass conservation. The accuracy of the framework is validated through comparisons with direct simulations on fine-scale, and the results demonstrate its ability to produce well-resolved solutions for complex geological formations found in petroleum reservoir problems.
APPLIED MATHEMATICAL MODELLING
(2022)
Letter
Computer Science, Interdisciplinary Applications
Jose Cicero Araujo dos Santos, Paulo Roberto Maciel Lyra, Joao Paulo Rodrigues de Andrade, Artur Castiel Reis de Souza, Ricardo Jorge Morais de Lira Filho, Darlan Karlo Elisiario de Carvalho
Summary: This paper proposes an adaptive flow-based dual volume agglomeration strategy for correcting non-physical terms in the coarse transmissibility matrix of classical multiscale finite volume (MsFV) methods. It also presents a framework to handle non-uniform levels at each coarse control volume, in order to reduce the size of coarse scale matrices. The proposed methodologies are applied to approximate pressure solutions in an Implicit Pressure Explicit Saturation (IMPES) strategy, and their accuracy and efficiency are demonstrated through testing with challenging benchmark problems.
JOURNAL OF COMPUTATIONAL PHYSICS
(2022)
Article
Computer Science, Interdisciplinary Applications
J. C. Teixeira, D. K. E. Carvalho, T. M. Cavalcante, K. C. L. Angelim, P. R. M. Lyra
Summary: This paper presents a numerical formulation for simulating two-phase flow in naturally fractured oil reservoirs using unstructured quadrilateral meshes and Hybrid-Grid MPFA-Streamline method. It can handle irregular polygonal grids and decouples transport equations using streamline-based method to solve advective saturation problems.
COMPUTERS AND GEOTECHNICS
(2022)
Article
Mathematics, Applied
T. M. Cavalcante, R. J. M. Lira Filho, A. C. R. Souza, D. K. E. Carvalho, P. R. M. Lyra
Summary: In this paper, we solve the steady state diffusion equation in 3D domains using the MPFA-DNL method, which guarantees the Discrete Maximum Principle by introducing a non-linear defect correction strategy. The method is locally conservative and capable of handling arbitrary anisotropic diffusion tensors and unstructured meshes while maintaining second order convergence rates.
JOURNAL OF SCIENTIFIC COMPUTING
(2022)
Review
Water Resources
Fernando R. L. Contreras, Uewerton A. O. Vaz, Gustavo L. S. S. Pacheco, Alessandro R. E. Antunes, Paulo R. M. Lyra, Darlan K. E. Carvalho
Summary: This paper proposes a novel full finite volume method to solve the advection-dispersion transport equation, combining various numerical methods to ensure accuracy and robustness of the numerical solution. Numerical experiments show that the method can provide accurate solutions when simulating groundwater processes with complex physical and geological properties.
ADVANCES IN WATER RESOURCES
(2023)
Article
Energy & Fuels
M. E. S. Galindo, I. V. Lacerda, G. Galindez-Ramirez, P. R. M. Lyra, D. K. E. Carvalho
Summary: Compositional reservoir simulation is a crucial tool for modeling fluid flow in complex petroleum reservoirs, especially for volatile reservoir fluids or those involving enhanced oil recovery. Simple black-oil models are inadequate in these cases. The compositional model involves solving a large system of partial differential equations that describe mass conservation, Darcy's law, and fugacity constraints. However, the complexity and computational demands of the compositional problems are high due to the large number of equations and constraints. To improve accuracy and reduce computational costs, higher-order methods can be used to approximate the advective flux terms in the reservoir's multicomponent transport.
GEOENERGY SCIENCE AND ENGINEERING
(2023)
