Article
Engineering, Multidisciplinary
Shahid Manzoor, Michael G. Edwards, Ali H. Dogru
Summary: Novel three-dimensional unstructured grid generation methods are proposed in this study, which automate control-volume boundary alignment to geological features and enable control point alignment to complex wells, resulting in essentially perpendicular grids. The comparative performance study of cell-vertex versus cell centered control-volume distributed multi-point flux approximation (CVD-MPFA) finite-volume formulations demonstrates that the vertex-centered CVD-MPFA methods outperform the cell-centered methods in terms of accuracy and efficiency.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2021)
Article
Computer Science, Interdisciplinary Applications
Jaeyoung Jung, Jin Hwan Hwang
Summary: The present study developed a path-conservative high-order positivity-preserving well-balanced finite volume Riemann solver for the one-dimensional porous shallow water equations with discontinuous porosity and bottom topography. The study formulated finite difference equations using the path-conservative approach and implemented the weighted essentially non-oscillatory (WENO) and the Runge-Kutta methods for spatiotemporal discretization. The model exhibited positivity-preserving and well-balanced properties with high-order accuracy and the ability to capture shocks.
JOURNAL OF COMPUTATIONAL PHYSICS
(2023)
Article
Computer Science, Interdisciplinary Applications
Miguel Uh Zapata, Reymundo Itza Balam
Summary: This paper introduces a second-order unstructured finite-volume method developed to solve a conservative level-set equation in two-and three-dimensional geometries. The method shows good performance and accuracy in capturing interface problems, particularly in smooth framework resulting from the signed distance function.
JOURNAL OF COMPUTATIONAL PHYSICS
(2021)
Article
Mathematics, Applied
Qian-Min Huang, Yu-Xin Ren, Qian Wang
Summary: In this paper, a high order finite volume scheme for solving the non-conservative convection equations on unstructured grids is proposed. To address numerical instability and singularity issues, the integral form of the equations is solved using a convective reconstruction technique and artificial viscosity term. Numerical results demonstrate that the proposed method achieves high order accuracy and robustness.
JOURNAL OF SCIENTIFIC COMPUTING
(2021)
Article
Computer Science, Interdisciplinary Applications
Savinien Pertant, Manuel Bernard, Giovanni Ghigliotti, Guillaume Balarac
Summary: This paper presents a robust and accurate method for numerically simulating moving contact lines on complex boundaries with surface wettability effects. The method is validated on 2D and 3D test cases, demonstrating good mass conservation properties and the ability to handle realistic scenarios such as drop detachment from horizontal fibers using dynamic mesh adaptation.
JOURNAL OF COMPUTATIONAL PHYSICS
(2021)
Article
Meteorology & Atmospheric Sciences
Jie Tang, Chungang Chen, Xueshun Shen, Feng Xiao, Xingliang Li
Summary: A three-dimensional positivity-preserving and conservative transport model on a cubed-sphere grid is presented using a multimoment finite-volume (MMFV) method. The model is inherently conservative, high-accuracy, and positive-definite, and shows promising results in benchmark test cases. It has the potential for real atmospheric simulations.
QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY
(2022)
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
Computer Science, Interdisciplinary Applications
Mengqing Liu, Man Zhang, Caixia Li, Fang Shen
Summary: This paper introduces a modified reconstruction method that preserves the conservation of cell average values and combines the divergence-free constraint with conservative features to make the magnetic field locally divergence-free. The proposed scheme maintains both the divergence-free constraint and ENO property for the magnetic field without using any limiter, and is applicable to simulations of ideal MHD equations.
JOURNAL OF COMPUTATIONAL PHYSICS
(2021)
Article
Thermodynamics
S. Parameswaran, J. C. Mandal
Summary: A robust finite volume framework is developed for solving incompressible two-phase flow problems on structured meshes, and it is extended to unstructured meshes in this paper. The surface tension effect is also modeled to enhance the applicability to real-life engineering problems. Least square and Green-Gauss integral based methods are used to deal with arbitrary unstructured mesh topology. The proposed method shows improved accuracy compared to the structured mesh formulation, as demonstrated through numerical tests involving various forces.
NUMERICAL HEAT TRANSFER PART B-FUNDAMENTALS
(2023)
Article
Mathematics, Applied
S. Mousavi Yeganeh, J. Farzi
Summary: This paper utilizes MPP and PP parametrized flux limiters to achieve strict maximum principle and positivity-preserving property for solving hyperbolic conservation laws, demonstrating efficiency and effectiveness through high-order MPP RK-SV and PP RK-SV schemes. The proposed schemes maintain the maximum principle without additional time step restrictions and preserve the high-order accuracy for linear advection problems.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(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
Mechanics
Y. Y. Liu, C. Shu, H. W. Zhang, L. M. Yang
Summary: This study presents a high-order implicit least squares-based finite difference-finite volume method for simulating two-dimensional incompressible flows, showing improved convergence and computational efficiency compared to its explicit counterpart.
Article
Computer Science, Interdisciplinary Applications
Y. Y. Liu, L. M. Yang, C. Shu, Z. L. Zhang, Z. Y. Yuan
Summary: This work presents a high-order implicit radial basis function-based differential quadrature-finite volume (IRBFDQ-FV) method for efficiently simulating incompressible flows with heat transfer on unstructured mesh. The method solves the velocity and temperature fields by locally using the lattice Boltzmann flux solver and the high-order finite volume method. It utilizes a high-order Taylor polynomial to approximate the solution within each control cell and approximates the spatial derivatives using the meshless radial basis function-based differential quadrature (RBFDQ) method. The proposed method is validated through numerical experiments and shows a high degree of accuracy and reliability for complex flows on unstructured mesh.
JOURNAL OF COMPUTATIONAL PHYSICS
(2022)
Article
Computer Science, Interdisciplinary Applications
Y. Y. Liu, C. Shu, H. W. Zhang, L. M. Yang, Cunbiao Lee
Summary: This paper presents an efficient high-order finite volume method for solving the compressible Navier-Stokes equations on unstructured grids, utilizing a high-order polynomial based on Taylor series expansion to approximate the solution function. The method employs a least square-based finite difference scheme to approximate derivatives, and a discrete gas-kinetic flux solver to compute numerical fluxes at cell interfaces. Efficient time marching strategy and local reconstruction of solutions are used to solve ordinary differential equations with matching accuracy.
COMPUTERS & FLUIDS
(2021)
Article
Engineering, Multidisciplinary
Sadok Lamine, Michael G. Edwards
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2015)
Article
Computer Science, Interdisciplinary Applications
R. Ahmed, M. G. Edwards, S. Lamine, B. A. H. Huisman, M. Pal
JOURNAL OF COMPUTATIONAL PHYSICS
(2015)
Article
Computer Science, Interdisciplinary Applications
Raheel Ahmed, Michael G. Edwards, Sadok Lamine, Bastiaan A. H. Huisman, Mayur Pal
JOURNAL OF COMPUTATIONAL PHYSICS
(2015)
Article
Mathematics, Interdisciplinary Applications
Elliot Parramore, Michael G. Edwards, Mayur Pal, Sadok Lamine
MULTISCALE MODELING & SIMULATION
(2016)
Article
Engineering, Multidisciplinary
Sadok Lamine, Michael G. Edwards
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2013)
Article
Computer Science, Interdisciplinary Applications
Michael G. Edwards, Hongwen Zheng, Sadok Lamine, Mayur Pal
COMPUTERS & FLUIDS
(2011)
Article
Computer Science, Interdisciplinary Applications
Mayur Pal, Michael G. Edwards
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS
(2012)
Article
Computer Science, Interdisciplinary Applications
Michael G. Edwards
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS
(2011)
Article
Computer Science, Interdisciplinary Applications
Mayur Pal, Michael G. Edwards
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS
(2011)
Article
Computer Science, Interdisciplinary Applications
Mayur Pal, Michael G. Edwards
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS
(2011)
Article
Computer Science, Interdisciplinary Applications
Mayur Pal, Michael G. Edwards
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS
(2012)
Article
Mathematics, Applied
Sadok Lamine, Michael G. Edwards
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2010)
Article
Computer Science, Interdisciplinary Applications
Michael G. Edwards, Hongwen Zheng
JOURNAL OF COMPUTATIONAL PHYSICS
(2010)
Article
Computer Science, Interdisciplinary Applications
Helmer A. Friis, Michael G. Edwards
JOURNAL OF COMPUTATIONAL PHYSICS
(2011)