Article
Engineering, Multidisciplinary
Stein K. F. Stoter, Marco F. P. ten Eikelder, Frits de Prenter, Ido Akkerman, E. Harald van Brummelen, Clemens V. Verhoosel, Dominik Schillinger
Summary: In this study, we investigate the weak enforcement of essential boundary conditions through Nitsche's method in the variational multiscale framework, showing that it corresponds to a specific choice of projection operator. The consistency, symmetry, and penalty terms of Nitsche’s method are derived from the fine-scale closure dictated by the corresponding scale decomposition. By incorporating non-vanishing fine scales at Dirichlet boundaries in a residual-based model for the advection-diffusion equation, we introduce an additional boundary term with a new model parameter that leads to a more accurate representation of fine-scale behavior.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2021)
Article
Mechanics
T. Medjnoun, E. Rodriguez-Lopez, M. A. Ferreira, T. Griffiths, J. Meyers, B. Ganapathisubramani
Summary: This experimental study investigates the effects of roughness-scale hierarchy on turbulent boundary layers using multiscale rough surfaces with regular elements. The aerodynamic roughness length scale between iterations varies linearly and the contribution of different roughness iterations to the overall drag varies. The presence of large-scale secondary motions in the cross-plane is shown to cause substantial changes in the flow field, with implications on classical similarity laws.
JOURNAL OF FLUID MECHANICS
(2021)
Article
Mechanics
Anthony Peirce, Emmanuel Detournay
Summary: This paper discusses the construction of tip asymptotes for a hydraulic fracture in a permeable elastic medium. It describes the changing nature of the asymptotic fields during the arrest and recession phases of the fracture after fluid injection has ended. The paper shows that as the fracture deflates, the dominance of the linear elastic fracture mechanics tip asymptote shrinks, giving way to an intermediate asymptote. The front velocity affects the development of a linear asymptote at the fracture tip, with the intermediate asymptote reappearing. These universal multiscale asymptotes are crucial for determining the decaying stress intensity factor, transition from arrest to recession, and front velocity during recession using computational algorithms.
JOURNAL OF FLUID MECHANICS
(2022)
Article
Mechanics
Michael Heisel, Charitha M. de Silva, Nicholas Hutchins, Ivan Marusic, Michele Guala
Summary: The statistical properties of prograde spanwise vortex cores and internal shear layers in high-Reynolds-number turbulent boundary layers are evaluated. Results show the importance of the local large-eddy turnover time in determining the strain rate confining the size of the vortex cores and shear layers. The study highlights the relevance of the turnover time and the Taylor microscale in explaining the interaction of coherent velocity structures in the boundary layer flows.
JOURNAL OF FLUID MECHANICS
(2021)
Article
Engineering, Multidisciplinary
Zeyu Xiong, Mian Xiao, Nikolaos Vlassis, Waiching Sun
Summary: This paper introduces a neural kernel method for generating machine learning models for complex materials that lack material symmetry and have internal structures. By introducing representation learning and constructing a feature vector space, this method enables more accurate characterization of these materials. Numerical examples validate the effectiveness of this method and compare it with other machine learning approaches.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2023)
Article
Geosciences, Multidisciplinary
Hongxiong Xu, Yuqing Wang
Summary: The study investigated the effects of horizontal grid spacing on the simulation of an idealized tropical cyclone using the ARW-WRF model. Results showed that reducing grid spacing from 2 km to 500 m strengthened the cyclone, while further reducing to 166 m and 55 m led to changes in intensity and core size. A grid spacing of sub-100 meters was found to be desirable for capturing detailed features, although coarser grids like 500 m were more cost-effective for practical forecasting purposes.
FRONTIERS IN EARTH SCIENCE
(2021)
Article
Computer Science, Interdisciplinary Applications
Felipe Rocha, Simone Deparis, Pablo Antolin, Annalisa Buffa
Summary: The effective properties of materials with random heterogeneous structures are determined by homogenizing the mechanical behavior in a window of observation. The choice of the local domain and boundary conditions govern the modeling errors, and there are standard methods to determine the formulation except for these two choices. This study proposes a machine learning procedure to select suitable boundary conditions for multiscale problems, which reduces computational cost significantly.
JOURNAL OF COMPUTATIONAL PHYSICS
(2023)
Article
Meteorology & Atmospheric Sciences
Qingfang Jiang, Qing Wang
Summary: The study focused on the characteristics of a stable internal boundary layer (SIBL) offshore of Duck, North Carolina under the influence of offshore winds. The analysis showed that the offshore area can be divided into three zones, with local similarity theory applicable only in the nearshore zone. The advection of turbulence from land plays a significant role in the momentum and scalar budgets over the NSZ, while becoming less important but still non-negligible in the IOZ.
JOURNAL OF GEOPHYSICAL RESEARCH-ATMOSPHERES
(2021)
Article
Meteorology & Atmospheric Sciences
Yubin Li, Ping Zhu, Zhiqiu Gao, K. W. Cheung
Summary: This study investigates the surface wind structure and vertical turbulent transport processes in the eyewall of hurricane Isabel (2003) using large-eddy simulations (LESs) and a convection permitting simulation. The LESs are able to produce sub-kilometer and kilometer scale eddy circulations in the eyewall, while the convection permitting simulation lacks small-scale disturbances. The results suggest that sub-kilometer eddies are mainly responsible for the vertical turbulent transport within the boundary layer, while eddies greater than 1 km become the dominant contributors to the vertical momentum transport above the boundary layer in the eyewall.
ATMOSPHERIC RESEARCH
(2022)
Article
Energy & Fuels
Tian-Wen Jiang, Zhong-Wei Huang, Jing-Bin Li, Yi-Su Zhou
Summary: The study utilizes LES and RNG k-epsilon model to analyze the flow characteristics inside the cone-straight nozzle, revealing the transition of flow from laminar to turbulent with increasing inlet velocity, with the main flow resistance mainly produced in the throat section.
Article
Mechanics
Mouad Fergoug, Augustin Parret-Freaud, Nicolas Feld, Basile Marchand, Samuel Forest
Summary: In this article, the effectiveness of higher-order homogenization in estimating heterogeneous solutions for elastic composite materials is demonstrated, particularly for cases with low scale separation. A higher-order general boundary layer method is also proposed to correct estimations near the boundaries. The efficiency and accuracy of these methods are studied through various numerical examples.
EUROPEAN JOURNAL OF MECHANICS A-SOLIDS
(2022)
Article
Engineering, Aerospace
Kalyani Bhide, Kiran Siddappaji, Shaaban Abdallah
Summary: This study numerically investigates the internal flow and exit flow of rectangular nozzles with low to high aspect ratios, and explores factors related to supersonic jet mixing. Results show that as the aspect ratio increases, shock waves weaken, boundary layer thickness increases, and significantly affect the characteristics of the exit flow.
Article
Mathematics, Applied
Fatemeh Mazlumi, Mehdi Mosharaf-Dehkordi, Morteza Dejam
Summary: This study investigates the effects of localization assumption on the accuracy of the Multiscale Finite Volume (MsFV) method in simulating two-phase incompressible fluid flow through highly heterogeneous porous media. Results show that the modified variable boundary condition generally produces the most accurate results, compared to other localization schemes.
APPLIED MATHEMATICS AND COMPUTATION
(2021)
Article
Mathematics, Applied
Aleksei Tyrylgin, Yaoyao Chen, Maria Vasilyeva, Eric T. Chung
Summary: This paper discusses a class of multiscale methods for solving nonlinear problems in perforated domains. By discretizing, model reduction, and residual adjustment, the efficiency of solving is improved.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2021)
Article
Mechanics
Xiaoying Shao, Yongbin Zhang
Summary: This study numerically calculated and compared the pressure distributions of a multiscale hydrodynamic wedge-platform thrust bearing with different fluid-bearing surface interactions, in order to verify the previously derived approximate analytical solutions.
Article
Mathematics, Applied
Eric Chung, Kazufumi Ito, Masahiro Yamamoto
Summary: This paper proposes a least squares formulation for ill-posed inverse problems in partial differential equations, establishing the existence, uniqueness, and continuity of the inverse solution for noisy data in L-2. The method can be applied to a general class of non-linear inverse problems, and a stability analysis is developed. Numerical tests show the applicability and performance of the proposed method.
APPLICABLE ANALYSIS
(2022)
Article
Mathematics, Applied
Siu Wun Cheung, Eric Chung, Yalchin Efendiev, Wing Tat Leung, Sai-Mang Pun
Summary: This paper develops an iterative scheme within the framework of CEM-GMsFEM to construct multiscale basis functions for the mixed formulation. The iterative procedure starts with constructing an energy minimizing snapshot space and performing spectral decomposition to form global multiscale space, where each global basis function can be split into non-decaying and decaying parts. The decaying part is approximated using a modified Richardson scheme with an appropriately defined preconditioner, leading to first-order convergence with respect to the coarse mesh size under suitable regularization parameters.
APPLIED MATHEMATICS AND COMPUTATION
(2022)
Article
Mathematics, Applied
Lina Zhao, Dohyun Kim, Eun-Jae Park, Eric Chung
Summary: In this paper, a staggered discontinuous Galerkin method for Darcy flows in fractured porous media is presented and analyzed. The method uses a staggered discontinuous Galerkin method and a standard conforming finite element method with appropriate inclusion of interface conditions. The optimal convergence estimates for all the variables are proved, and the error estimates are shown to be fully robust with respect to the heterogeneity and anisotropy of the permeability coefficients.
JOURNAL OF SCIENTIFIC COMPUTING
(2022)
Article
Engineering, Multidisciplinary
Yiran Wang, Eric Chung, Shubin Fu
Summary: In this paper, a local-global multiscale method is proposed for highly heterogeneous stochastic groundwater flow problems. The method combines the reduced basis method and the generalized multiscale finite element method to achieve computational efficiency. The authors provide rigorous analysis and extensive numerical examples to demonstrate the accuracy and efficiency of the method.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2022)
Article
Mathematics, Applied
Dmitry Ammosov, Maria Vasilyeva, Eric T. Chung
Summary: In this paper, the thermoporoelasticity problem in heterogeneous and fractured media is considered. The proposed multiscale method reduces the size of the discrete system and provides good accuracy by solving local spectral problems to compute the multiscale basis functions.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2022)
Article
Computer Science, Interdisciplinary Applications
Eric T. Chung, Yalchin Efendiev, Wing Tat Leung, Petr N. Vabishchevich
Summary: This work proposes contrast-independent partially explicit time discretizations for wave equations in heterogeneous high-contrast media. The spatial space is split into contrast-dependent and contrast-independent components through multiscale space decomposition. The proposed splitting is unconditionally stable under suitable conditions and identifies local features for implicit treatment. The numerical results demonstrate that the proposed methods yield results similar to implicit methods with contrast-independent timestep.
JOURNAL OF COMPUTATIONAL PHYSICS
(2022)
Article
Computer Science, Interdisciplinary Applications
Eric T. Chung, Uygulaana Kalachikova, Maria Vasilyeva, Valentin Alekseev
Summary: In this study, a Generalized Multiscale Discontinuous Galerkin Method (GMsDGM) is proposed for the convection-diffusion equation in perforated media. The method utilizes fine and coarse grid approximations and investigates various constructions of multiscale basis functions for numerical solutions.
MATHEMATICS AND COMPUTERS IN SIMULATION
(2022)
Article
Mathematics, Applied
Yanfang Yang, Shubin Fu, Eric T. Chung
Summary: In this paper, a efficient and robust two-grid preconditioner is proposed for solving the linear elasticity equation with high contrasts. The challenges imposed by multiple scales and high-contrast are addressed by constructing a coarse space within the framework of GMsFEM and controlling its dimension adaptively. The paper also introduces a parameter-independent efficient preconditioner for dealing with linear elasticity problems with stochastic coefficients.
JOURNAL OF SCIENTIFIC COMPUTING
(2022)
Article
Computer Science, Interdisciplinary Applications
Lina Zhao, Eric Chung
Summary: This paper introduces a novel residual-type a posteriori error estimator for Darcy flows in fractured porous media, using staggered DG methods on general polygonal meshes. The method is capable of handling fairly general meshes and incorporating hanging nodes for adaptive mesh refinement, demonstrating reliability and efficiency in error estimation.
COMPUTATIONAL GEOSCIENCES
(2022)
Article
Mathematics, Applied
Lina Zhao, Eric Chung, Eun-Jae Park
Summary: This paper proposes and analyzes a staggered discontinuous Galerkin method for a five-field formulation of the Biot system of poroelasticity on general polygonal meshes. The method is locking-free and can handle highly distorted grids, and a fixed stress splitting scheme is introduced to reduce the size of the global system.
IMA JOURNAL OF NUMERICAL ANALYSIS
(2023)
Article
Computer Science, Interdisciplinary Applications
Tak Shing Au Yeung, Ka Chun Cheung, Eric T. Chung, Shubin Fu, Jianliang Qian
Summary: We propose a deep learning approach to extract ray directions at discrete locations by analyzing wave fields. A deep neural network is trained to predict ray directions based on local plane-wave fields. The resulting network is then applied to solve the Helmholtz equations at higher frequencies. The numerical results demonstrate the efficiency and accuracy of the proposed scheme.
JOURNAL OF COMPUTATIONAL PHYSICS
(2022)
Article
Computer Science, Software Engineering
Changqing Ye, Eric T. Chung
Summary: This paper studies the convergences of several FFT-based discretization schemes in computational micromechanics, including Moulinec-Suquet's scheme, Willot's scheme, and the FEM scheme. It proves that the effective coefficients obtained by these schemes converge to the theoretical ones under reasonable assumptions. Convergence rate estimates are provided for the FEM scheme under additional regularity assumptions.
BIT NUMERICAL MATHEMATICS
(2023)
Article
Mathematics, Applied
Denis Spiridonov, Maria Vasilyeva, Min Wang, Eric T. Chung
Summary: In this paper, a class of Mixed Generalized Multiscale Finite Element Methods is proposed for solving elliptic problems in thin two-dimensional domains. The method utilizes multiscale basis functions and local snapshot space to construct a lower dimensional model and achieve multiscale approximation.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2022)
Article
Mathematics, Applied
Uygulaana Kalachikova, Maria Vasilyeva, Isaac Harris, Eric T. Chung
Summary: This paper investigates the scattering problem in a heterogeneous domain using the Helmholtz equation and absorbing boundary conditions. A fine unstructured grid that resolves grid-level perforation is constructed for the finite element method solution. The large system of equations resulting from these approximations is reduced using the Generalized Multiscale Finite Element Method. The method constructs a multiscale space using the solution of local spectral problems on the snapshot space in each local domain, and two types of multiscale basis functions are presented and studied. Numerical results for the Helmholtz problem in a heterogeneous domain with obstacles of varying properties are provided, examining different wavenumbers and numbers of multiscale basis functions.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2023)
Article
Mathematics, Applied
Leonardo A. Poveda, Shubin Fu, Eric T. Chung, Lina Zhao
Summary: This paper presents a new Finite Element Method called CEM-GMsFEM for solving single-phase non-linear compressible flows in highly heterogeneous media. The method constructs basis functions by solving local spectral problems and local energy minimization problems. The convergence of the method is shown to only depend on the coarse grid size and the method is enhanced with an online enrichment guided by an a posteriori error estimator. Numerical experiments confirm the theoretical findings and demonstrate the efficiency and accuracy of the method.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2023)