Article
Mathematics, Applied
Wei-Wei Han, Yao-Lin Jiang, Zhen Miao
Summary: In this work, a first-order implicit-explicit type scheme for the EMAC formulation of the timedependent Navier-Stokes equations is constructed using the scalar auxiliary variable method. The scheme is linear and solves a series of Stokes type equations with constant coefficients at each time step. The scheme is stable without any condition on the time step and conserves momentum and angular momentum, while providing error estimates for the velocity.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2024)
Article
Mathematics, Applied
Xiaofeng Wang, Weizhong Dai, Yun Yan
Summary: This paper proposes a conservative finite difference scheme to solve the 2D generalized Rosenau-RLW equation, which is linear-implicit, mass-preserving, energy-preserving, uniquely solvable, unconditionally stable, and has numerical convergence of second order in the -norm. Numerical experiments demonstrate that the scheme is accurate, efficient, and reliable.
APPLICABLE ANALYSIS
(2021)
Article
Mathematics, Applied
Yuan Li, Rong An
Summary: This paper discusses the magnetohydrodynamics (MHD) equations with variable density and proposes a first-order Euler semi-implicit time discrete scheme to approximate the system. The scheme is unconditionally stable, and a rigorous error analysis is presented to derive the temporal convergence rate.
APPLIED NUMERICAL MATHEMATICS
(2021)
Article
Mathematics, Applied
Shuaichao Pei, Yanren Hou, Qi Li
Summary: In this study, error estimates were conducted for a linear, second-order, unconditionally energy stable, semi-discrete time stepping scheme based on the Lagrange Multiplier approach for the modified phase field crystal equation. Rigorous proofs were presented to demonstrate the unique solvability, mass conservation, and unconditional energy stability of the scheme. Various numerical experiments were performed in 2D and 3D to validate the accuracy, unconditional energy stability, and mass conservation of the proposed numerical strategy.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2021)
Article
Computer Science, Interdisciplinary Applications
Xin Zhang, Danxia Wang, Jianwen Zhang, Hongen Jia
Summary: This work focuses on the numerical approximation of the penalized Ericksen-Leslie equations. A second-order numerical scheme with the advantages of full decoupling, linearization, and unconditional stability in energy is constructed. The scheme is implemented through introducing two scalar auxiliary variables, and the accuracy and effectiveness are illustrated through numerical simulations.
MATHEMATICS AND COMPUTERS IN SIMULATION
(2023)
Article
Mathematics, Interdisciplinary Applications
Zichen Yao, Zhanwen Yang, Jianfang Gao
Summary: This paper investigates the stability of the Grunwald Letnikov method for fractional-order delay differential equations (FDDEs). The results show the unconditional stability and generally unconditional stability of the method. Numerical examples are provided to demonstrate the validity of the theoretical results.
CHAOS SOLITONS & FRACTALS
(2023)
Article
Mathematics, Applied
Tong Zhang
Summary: This paper proposes an unconditionally stable Euler implicit/explicit scheme for solving the natural convection equations, based on an introduced exponential scalar auxiliary variable. The scheme treats the linear terms implicitly and the nonlinear terms explicitly, and decouples the problem into a series of linearized subproblems, which can be solved efficiently. The analysis removes the time step limitation and achieves unconditional stability and convergence, as opposed to existing theoretical findings.
APPLICABLE ANALYSIS
(2023)
Article
Engineering, Multidisciplinary
Qian Yu, Yibao Li
Summary: A numerical scheme with fast convergence, second-order accuracy, and unconditional energy stability is introduced to solve a multimaterial topology optimization problem. The modeling is based on the energy of a multi-phase-field elasticity system, including classical Ginzburg-Landau, elastic potential, and some constraints. The material layout is updated using the volume constrained gradient flow of the system. The proposed second-order scheme combines a linearly stabilized splitting method and Crank-Nicolson scheme, and its unconditional energy stability is theoretically proven. Numerical results demonstrate its fast convergence compared to traditional Cahn-Hilliard type equations, and classical benchmarks verify the feasibility and efficiency of the method.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2023)
Article
Mathematics, Applied
Yanxia Qian, Yongchao Zhang, Yunqing Huang
Summary: In this article, a linear, second-order, semi-discrete time stepping scheme for the phase field crystal equation based on the generalized positive auxiliary variable (GPAV) approach is proposed. This scheme reduces the operation counts by half compared to previous works and demonstrates robustness and accuracy through numerical experiments.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2023)
Article
Engineering, Multidisciplinary
Chongmin Song, Sascha Eisentrager, Xiaoran Zhang
Summary: This paper introduces a high-order implicit time integration scheme for solving transient and wave propagation problems, which is computationally efficient and does not require direct inversion of the mass matrix. The derived second-order scheme is analytically equivalent to the Newmark constant average acceleration method, showcasing exceptional accuracy and efficiency in numerical examples compared to established second-order methods.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2022)
Article
Mathematics, Applied
Hyun Geun Lee, Jaemin Shin, June-Yub Lee
Summary: The use of convex splitting idea combined with a specially designed numerical method ensures exact mass conservation and unconditionally energy stability for solving the conservative Allen-Cahn equation with nonlocal Lagrange multiplier. Analytically, the scheme is shown to be uniquely solvable and energy stable due to the exact mass conservation guarantee. Numerical experiments demonstrate the accuracy and energy stability of the proposed scheme.
JOURNAL OF SCIENTIFIC COMPUTING
(2022)
Article
Mathematics, Applied
Yuan Li, Rong An
Summary: This paper proposes a linear and decoupled Euler finite element scheme for numerically solving the 3D incompressible Navier-Stokes equations with mass diffusion. The proposed algorithm is unconditionally stable at the full discrete level when the time step size and mesh size are sufficiently small, and optimal temporal-spatial error estimates for velocity and density are provided without any constraint on the time step size and mesh size using error splitting technique.
JOURNAL OF SCIENTIFIC COMPUTING
(2022)
Article
Thermodynamics
Xiaoyu Liu, Suchuan Dong, Zhi Xie
Summary: This paper presents an unconditionally energy-stable scheme for approximating the convective heat transfer equation. The scheme is based on the generalized positive auxiliary variable (gPAV) idea and provides a special treatment for the convection term. By replacing the original convection term with its linear approximation plus a correction term, controlled by an auxiliary variable, the scheme achieves expanded accuracy range and more accurate simulations at large time step sizes. Extensive numerical experiments demonstrate the accuracy and stability performance of the scheme.
INTERNATIONAL JOURNAL OF NUMERICAL METHODS FOR HEAT & FLUID FLOW
(2023)
Article
Mathematics, Applied
Guo-Dong Zhang, Xiaoming He, Xiaofeng Yang
Summary: This paper investigates numerical approximations of a phase field model for two-phase ferrofluids, and proposes an efficient decoupled finite element scheme, which has been validated through numerous numerical examples to demonstrate its stability and accuracy.
SIAM JOURNAL ON SCIENTIFIC COMPUTING
(2021)
Article
Mathematics, Interdisciplinary Applications
Ren Liu, Xiaozhong Yang, Peng Lyu
Summary: A parallelized computation method for inhomogeneous time-fractional Fisher equation is proposed in this paper. The method shows high precision and distinct parallel computing characteristics, and its unique existence, unconditional stability, and convergence are theoretically proved.
FRACTAL AND FRACTIONAL
(2022)
Article
Engineering, Multidisciplinary
Jihoon Kim
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2018)
Article
Engineering, Multidisciplinary
Hyun C. Yoon, Jihoon Kim
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING
(2018)
Article
Energy & Fuels
Jihoon Kim, Evan Schankee Um, George J. Moridis
JOURNAL OF PETROLEUM SCIENCE AND ENGINEERING
(2018)
Article
Geochemistry & Geophysics
Evan Schankee Um, Jihoon Kim, Michael J. Wilt, Michael Commer, Seung-Sep Kim
Article
Computer Science, Interdisciplinary Applications
Maria Vasilyeva, Eric T. Chung, Yalchin Efendiev, Jihoon Kim
JOURNAL OF COMPUTATIONAL PHYSICS
(2019)
Article
Engineering, Geological
Hyun C. Yoon, Xuyang Guo, Jihoon Kim, John Killough
INTERNATIONAL JOURNAL OF ROCK MECHANICS AND MINING SCIENCES
(2019)
Article
Computer Science, Interdisciplinary Applications
Hyun C. Yoon, Peng Zhou, Jihoon Kim
JOURNAL OF COMPUTATIONAL PHYSICS
(2020)
Article
Geochemistry & Geophysics
Evan Schankee Um, Jihoon Kim, Michael Wilt
Article
Engineering, Geological
Sangcheol Yoon, Jihoon Kim, Evan Schankee Um
Summary: This study investigates the effects of coupled multiphase flow and geomechanics in hydraulically fractured reservoirs using numerical simulations. A new numerically stable sequential method for all-way coupled geomechanics and flow in discrete fractured systems is proposed. The study identifies vacuum areas and dry zones at the fracture tip, with the vacuum area being attributed to different time scales between flow and geomechanics.
INTERNATIONAL JOURNAL OF ROCK MECHANICS AND MINING SCIENCES
(2021)
Article
Engineering, Geological
Hyun C. Yoon, Jihoon Kim
Summary: In this study, two operator splitting methods, two-pass and spectral deferred correction (SDC), are investigated for high-order accuracy in time integration for poroelastic problems. The research shows that SDC in conjunction with the monolithic method can achieve the desired second-order accuracy, while when combined with the two sequential methods, it only maintains first order.
INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS
(2021)
Article
Engineering, Geological
Jihoon Kim, Joo Yong Lee, Tae Woong Ahn, Hyun Chul Yoon, Jaehyung Lee, Sangcheol Yoon, George J. Moridis
Summary: In this study, we validate a coupled flow-geomechanics simulator called T+M-AM for gas hydrate deposits. Two laboratory experiments are conducted to replicate the production of gas hydrates by depressurization in the Ulleung Basin. The results show that T+M-AM is a reliable simulator for strongly coupled flow and geomechanics systems in both permafrost and deep oceanic hydrate deposits.
INTERNATIONAL JOURNAL OF ROCK MECHANICS AND MINING SCIENCES
(2022)
Article
Energy & Fuels
Hyun Chul Yoon, Sangcheol Yoon, Joo Yong Lee, Jihoon Kim
Summary: The study investigates depressurization strategies for gas hydrate reservoirs using a multiple porosity model, finding that a periodic depressurization scenario exhibits less subsidence compared to continuous depressurization, while maintaining similar productivity.
JOURNAL OF NATURAL GAS SCIENCE AND ENGINEERING
(2021)
Article
Energy & Fuels
Hyun Chul Yoon, Jihoon Kim, Evan Schankee Um, Joo Yong Lee
Summary: This study investigates the feasibility of using electromagnetic geophysics methods to detect gas hydrate dissociation in the Ulleung Basin, East Sea, Korea. Flow and geomechanics simulations were performed and the electrical conductivity model for electromagnetic simulation was established based on the obtained saturation and porosity fields. Two different approaches in the electromagnetic configuration were compared, and it was found that the surface-to-borehole method showed improved sensitivity in monitoring gas flow. This integrated simulation can be a potential tool for monitoring gas hydrate deposits.
Article
Engineering, Chemical
George J. Moridis, Jihoon Kim, Matthew T. Reagan, Se-Joon Kim
Summary: This study investigates the feasibility of long-term production from a marine hydrate accumulation in the Ulleung Basin in the Korean East Sea. The analysis shows that production from this hydrate accumulation is technically possible, although gas production rates are generally low and there is a high water-to-gas ratio. Additionally, there are uncertainties in the predictions of the geomechanical system's behavior. The long-term production potential of the reservoir appears challenging due to limited dissociation effectiveness, significant water production, and substantial subsidence.
CANADIAN JOURNAL OF CHEMICAL ENGINEERING
(2023)
Article
Engineering, Multidisciplinary
Akshay J. Thomas, Mateusz Jaszczuk, Eduardo Barocio, Gourab Ghosh, Ilias Bilionis, R. Byron Pipes
Summary: We propose a physics-guided transfer learning approach to predict the thermal conductivity of additively manufactured short-fiber reinforced polymers using micro-structural characteristics obtained from tensile tests. A Bayesian framework is developed to transfer the thermal conductivity properties across different extrusion deposition additive manufacturing systems. The experimental results demonstrate the effectiveness and reliability of our method in accounting for epistemic and aleatory uncertainties.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2024)
Article
Engineering, Multidisciplinary
Zhen Zhang, Zongren Zou, Ellen Kuhl, George Em Karniadakis
Summary: In this study, deep learning and artificial intelligence were used to discover a mathematical model for the progression of Alzheimer's disease. By analyzing longitudinal tau positron emission tomography data, a reaction-diffusion type partial differential equation for tau protein misfolding and spreading was discovered. The results showed different misfolding models for Alzheimer's and healthy control groups, indicating faster misfolding in Alzheimer's group. The study provides a foundation for early diagnosis and treatment of Alzheimer's disease and other misfolding-protein based neurodegenerative disorders using image-based technologies.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2024)
Article
Engineering, Multidisciplinary
Jonghyuk Baek, Jiun-Shyan Chen
Summary: This paper introduces an improved neural network-enhanced reproducing kernel particle method for modeling the localization of brittle fractures. By adding a neural network approximation to the background reproducing kernel approximation, the method allows for the automatic location and insertion of discontinuities in the function space, enhancing the modeling effectiveness. The proposed method uses an energy-based loss function for optimization and regularizes the approximation results through constraints on the spatial gradient of the parametric coordinates, ensuring convergence.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2024)
Article
Engineering, Multidisciplinary
Bodhinanda Chandra, Ryota Hashimoto, Shinnosuke Matsumi, Ken Kamrin, Kenichi Soga
Summary: This paper proposes new and robust stabilization strategies for accurately modeling incompressible fluid flow problems in the material point method (MPM). The proposed approach adopts a monolithic displacement-pressure formulation and integrates two stabilization strategies to ensure stability. The effectiveness of the proposed method is validated through benchmark cases and real-world scenarios involving violent free-surface fluid motion.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2024)
Article
Engineering, Multidisciplinary
Chao Peng, Alessandro Tasora, Dario Fusai, Dario Mangoni
Summary: This article discusses the importance of the tangent stiffness matrix of constraints in multibody systems and provides a general formulation based on quaternion parametrization. The article also presents the analytical expression of the tangent stiffness matrix derived through linearization. Examples demonstrate the positive effect of this additional stiffness term on static and eigenvalue analyses.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2024)
Article
Engineering, Multidisciplinary
Thibaut Vadcard, Fabrice Thouverez, Alain Batailly
Summary: This contribution presents a methodology for detecting isolated branches of periodic solutions to nonlinear mechanical equations. The method combines harmonic balance method-based solving procedure with the Melnikov energy principle. It is able to predict the location of isolated branches of solutions near families of autonomous periodic solutions. The relevance and accuracy of this methodology are demonstrated through academic and industrial applications.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2024)
Article
Engineering, Multidisciplinary
Weisheng Zhang, Yue Wang, Sung-Kie Youn, Xu Guo
Summary: This study proposes a sketch-guided topology optimization approach based on machine learning, which incorporates computer sketches as constraint functions to improve the efficiency of computer-aided structural design models and meet the design intention and requirements of designers.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2024)
Article
Engineering, Multidisciplinary
Leilei Chen, Zhongwang Wang, Haojie Lian, Yujing Ma, Zhuxuan Meng, Pei Li, Chensen Ding, Stephane P. A. Bordas
Summary: This paper presents a model order reduction method for electromagnetic boundary element analysis and extends it to computer-aided design integrated shape optimization of multi-frequency electromagnetic scattering problems. The proposed method utilizes a series expansion technique and the second-order Arnoldi procedure to reduce the order of original systems. It also employs the isogeometric boundary element method to ensure geometric exactness and avoid re-meshing during shape optimization. The Grey Wolf Optimization-Artificial Neural Network is used as a surrogate model for shape optimization, with radar cross section as the objective function.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2024)
Article
Engineering, Multidisciplinary
C. Pilloton, P. N. Sun, X. Zhang, A. Colagrossi
Summary: This paper investigates the smoothed particle hydrodynamics (SPH) simulations of violent sloshing flows and discusses the impact of volume conservation errors on the simulation results. Different techniques are used to directly measure the particles' volumes and stabilization terms are introduced to control the errors. Experimental comparisons demonstrate the effectiveness of the numerical techniques.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2024)
Article
Engineering, Multidisciplinary
Ye Lu, Weidong Zhu
Summary: This work presents a novel global digital image correlation (DIC) method based on a convolution finite element (C-FE) approximation. The C-FE based DIC provides highly smooth and accurate displacement and strain results with the same element size as the usual finite element (FE) based DIC. The proposed method's formulation and implementation, as well as the controlling parameters, have been discussed in detail. The C-FE method outperformed the FE method in all tested examples, demonstrating its potential for highly smooth, accurate, and robust DIC analysis.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2024)
Article
Engineering, Multidisciplinary
Mojtaba Ghasemi, Mohsen Zare, Amir Zahedi, Pavel Trojovsky, Laith Abualigah, Eva Trojovska
Summary: This paper introduces Lung performance-based optimization (LPO), a novel algorithm that draws inspiration from the efficient oxygen exchange in the lungs. Through experiments and comparisons with contemporary algorithms, LPO demonstrates its effectiveness in solving complex optimization problems and shows potential for a wide range of applications.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2024)
Article
Engineering, Multidisciplinary
Jingyu Hu, Yang Liu, Huixin Huang, Shutian Liu
Summary: In this study, a new topology optimization method is proposed for structures with embedded components, considering the tension/compression asymmetric interface stress constraint. The method optimizes the topology of the host structure and the layout of embedded components simultaneously, and a new interpolation model is developed to determine interface layers between the host structure and embedded components.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2024)
Article
Engineering, Multidisciplinary
Qiang Liu, Wei Zhu, Xiyu Jia, Feng Ma, Jun Wen, Yixiong Wu, Kuangqi Chen, Zhenhai Zhang, Shuang Wang
Summary: In this study, a multiscale and nonlinear turbulence characteristic extraction model using a graph neural network was designed. This model can directly compute turbulence data without resorting to simplified formulas. Experimental results demonstrate that the model has high computational performance in turbulence calculation.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2024)
Article
Engineering, Multidisciplinary
Jacinto Ulloa, Geert Degrande, Jose E. Andrade, Stijn Francois
Summary: This paper presents a multi-temporal formulation for simulating elastoplastic solids under cyclic loading. The proper generalized decomposition (PGD) is leveraged to decompose the displacements into multiple time scales, separating the spatial and intra-cyclic dependence from the inter-cyclic variation, thereby reducing computational burden.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2024)
Article
Engineering, Multidisciplinary
Utkarsh Utkarsh, Valentin Churavy, Yingbo Ma, Tim Besard, Prakitr Srisuma, Tim Gymnich, Adam R. Gerlach, Alan Edelman, George Barbastathis, Richard D. Braatz, Christopher Rackauckas
Summary: This article presents a high-performance vendor-agnostic method for massively parallel solving of ordinary and stochastic differential equations on GPUs. The method integrates with a popular differential equation solver library and achieves state-of-the-art performance compared to hand-optimized kernels.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2024)
