Article
Mathematics, Applied
Y. I. N. I. N. G. Cao, X. I. A. O. M. I. N. G. Wang
Summary: This study proves that the difference between the solutions to the Stokes-Darcy system derived using the Beavers-Joseph or Beavers-Joseph-Saffman-Jones interfacial conditions is proportional to the Darcy number when the Reynolds number is below a certain threshold. Therefore, the Beavers-Joseph-Saffman-Jones interface boundary condition is an excellent approximation of the classical Beavers-Joseph interface boundary condition in the regime of small Darcy numbers.
SIAM JOURNAL ON APPLIED MATHEMATICS
(2022)
Article
Mathematics, Applied
Yingzhi Liu, Yinnian He, Xuejian Li, Xiaoming He
Summary: This paper demonstrates the convergence analysis of the Robin-Robin domain decomposition method for the Stokes-Darcy system with Beavers-Joseph interface condition, focusing on the case of convergence for small viscosity and hydraulic conductivity. Utilizing discrete techniques, the almost optimal geometric convergence rate for gamma(f) > gamma(p) is obtained. The results provide a general guideline for choosing parameters to achieve convergence and geometric convergence rate, which is confirmed by numerical simulations.
APPLIED MATHEMATICS LETTERS
(2021)
Article
Mathematics, Applied
Zhipeng Yang, Ju Ming, Changxin Qiu, Maojun Li, Xiaoming He
Summary: A multigrid multilevel Monte Carlo (MGMLMC) method is developed for the stochastic Stokes-Darcy interface model with random hydraulic conductivity. The method aims to efficiently solve the stochastic model, especially focusing on the interface and the random Beavers-Joseph interface condition.
JOURNAL OF SCIENTIFIC COMPUTING
(2022)
Article
Mathematics, Applied
Luling Cao, Yinnian He, Jian Li, Di Yang
Summary: This paper develops the numerical theory of decoupled modified characteristic FEMs for the fully evolutionary Navier-Stokes-Darcy model with the Beavers-Joseph interface condition. The optimal L-2-norm error convergence order of the solutions is proved by mathematical induction, implying the uniform L-2-boundedness of the fully discrete velocity solution. High efficiency of this method is demonstrated through numerical tests.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2021)
Article
Mathematics, Applied
Di Yang, Yinnian He, Luling Cao
Summary: In this study, a new analysis strategy is proposed to establish an a priori estimate of weak solutions to the steady-state dual-porosity Navier-Stokes fluid flow model with the Beavers-Joseph-Saffman interface condition. The a priori estimate and existence result are shown to be independent of small data and large viscosity restriction, with global uniqueness of the weak solution also proven.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2022)
Article
Mathematics, Applied
Feng Shi, Yizhong Sun, Haibiao Zheng
Summary: In this paper, an efficient ensemble domain decomposition algorithm is proposed for fast solving the fully mixed random Stokes--Darcy model with the physically realistic Beavers-Joseph interface conditions. The algorithm utilizes the Monte Carlo method to derive deterministic numerical models for the coupled model with random inputs, and uses the idea of ensemble to realize fast computation of multiple problems. The algorithm achieves comparable accuracy with traditional methods by sharing a common coefficient matrix in each deterministic numerical model, significantly reducing computational cost.
SIAM JOURNAL ON NUMERICAL ANALYSIS
(2023)
Article
Mathematics, Applied
Xinhui Wang, Guangzhi Du, Yi Li
Summary: In this paper, a modified local and parallel finite element method (MLPFEM) is proposed for the coupled Stokes-Darcy problem. The method combines a partition of unity with backtracking technique to improve computational efficiency while maintaining global continuity, and achieves optimal error bounds.
NUMERICAL ALGORITHMS
(2023)
Article
Engineering, Chemical
Paula Strohbeck, Elissa Eggenweiler, Iryna Rybak
Summary: Physically consistent coupling conditions and effective parameters are crucial for accurate modeling and simulation of various applications at the fluid-porous interface. The commonly used Beavers-Joseph condition for tangential velocity is only suitable for parallel flows and its slip coefficient value is uncertain.
TRANSPORT IN POROUS MEDIA
(2023)
Article
Mathematics, Applied
Guangzhi Du, Shilin Mi, Xinhui Wang
Summary: This paper provides and studies some local and parallel finite element methods based on two-grid discretizations for the non-stationary Stokes-Darcy model with the Beavers-Joseph interface condition. Two local algorithms, the semi-discrete and fully discrete finite element algorithms, are introduced and related error estimates are derived. Two fully discrete parallel algorithms are subsequently developed based on the fully discrete local algorithm. The validity of the algorithms is illustrated through numerical results.
NUMERICAL ALGORITHMS
(2023)
Article
Mathematics, Applied
Aycil Cesmelioglu, Sander Rhebergen
Summary: We present and analyze a strongly conservative hybridizable discontinuous Galerkin finite element method for the coupled incompressible Navier-Stokes and Darcy problem with Beavers-Joseph-Saffman interface condition. An a priori error analysis shows that the velocity error does not depend on the pressure, and that velocity and pressure converge with optimal rates. These results are confirmed by numerical examples.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2023)
Article
Mathematics, Applied
Md Abdullah Al Mahbub, Li Shan, Haibiao Zheng
Summary: This paper investigates the robust numerical methods for solving the time-dependent Stokes-Darcy multiphysics problem. These methods can be implemented using existing surface water and groundwater codes. A stabilized mixed discretization technique is developed for the porous media problem coupled with the fluid region across an interface. The proposed decoupled algorithm is stable and exhibits good convergence.
NUMERICAL ALGORITHMS
(2023)
Article
Mathematics, Applied
Eduard Marusic-Paloka
Summary: An effective boundary condition for a porous wall is derived based on basic principles of mechanics. The study focuses on the Stokes system governing the flow of viscous fluid through a reservoir with small pores on the boundary. Through rigorous asymptotic analysis, a macroscopic model is obtained. Assuming periodicity of the pores, a Darcy-type effective boundary condition is derived using homogenization and boundary layer techniques. Further asymptotic analysis with respect to the porosity reveals a sequence of recursive boundary value problems indicating a significant pressure jump on the boundary.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2023)
Article
Mechanics
Essam Nabil Ahmed, Alessandro Bottaro
Summary: This study focuses on the fully developed, steady, incompressible, laminar flow in a channel with rough and/or permeable walls. The influence of micro-structured boundary surfaces on the flow behavior is simulated using high-order effective boundary conditions derived from homogenization theory without empirical parameters. A closed-form solution of the Navier-Stokes equations is obtained for the flow in the channel, incorporating slip velocities, shear stress, and streamwise pressure gradient at each virtual boundary. The accuracy and applicability of the model are validated against full feature-resolving simulations for different textures. The Stokes-based model used to identify slip and interface permeability coefficients in the effective boundary conditions is reliable and accurate up to a certain threshold, beyond which advective effects need to be considered.
EUROPEAN JOURNAL OF MECHANICS B-FLUIDS
(2024)
Article
Engineering, Multidisciplinary
Eduard Marusic-Paloka, Igor Pazanin
Summary: The study derived a new effective boundary condition for fluid flow in a porous boundary domain, showing that the condition splits into different flow modes if the pore geometry is isotropic.
INTERNATIONAL JOURNAL OF ENGINEERING SCIENCE
(2022)
Article
Mathematics, Applied
Luling Cao, Yinnian He, Jian Li
Summary: This paper proposes and analyzes a parallel Robin-Robin domain decomposition method based on the modified characteristic finite element method for solving the time-dependent dual-porosity-Navier-Stokes model. The coupling terms are treated explicitly, taking advantage of previous time steps' information to construct a non-iterative domain decomposition method. Numerical examples demonstrate the effectiveness and efficiency of the proposed method.
JOURNAL OF SCIENTIFIC COMPUTING
(2022)
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)