The Experts below are selected from a list of 3426 Experts worldwide ranked by ideXlab platform
Tao Yin - One of the best experts on this subject based on the ideXlab platform.
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an accurate hyper singular boundary integral equation method for dynamic Poroelasticity in two dimensions
arXiv: Computational Physics, 2020Co-Authors: Lu Zhang, Tao YinAbstract:This paper is concerned with the boundary integral equation method for solving the exterior Neumann boundary value problem of dynamic Poroelasticity in two dimensions. The main contribution of this work consists of two aspescts: the proposal of a novel regularized boundary integral equation, and the presentation of new regularized formulations of the strongly-singular and hyper-singular boundary integral operators. Firstly, turning to the spectral properties of the double-layer operator and the corresponding Calderon relation of the Poroelasticity, we propose the novel low-GMRES-iteration integral equation whose eigenvalues are bounded away from zero and infinity. Secondly, with the help of the Gunter derivatives, we reformulate the strongly-singular and hyper-singular integral operators into combinations of the weakly-singular operators and the tangential derivatives. The accuracy and efficiency of the proposed methodology are demonstrated through several numerical examples.
Eric T. Chung - One of the best experts on this subject based on the ideXlab platform.
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Online Coupled Generalized Multiscale Finite Element Method for the Poroelasticity Problem in Fractured and Heterogeneous Media
'MDPI AG', 2021Co-Authors: Aleksei Tyrylgin, Maria Vasilyeva, Dmitry Ammosov, Eric T. Chung, Yalchin EfendievAbstract:In this paper, we consider the Poroelasticity problem in fractured and heterogeneous media. The mathematical model contains a coupled system of equations for fluid pressures and displacements in heterogeneous media. Due to scale disparity, many approaches have been developed for solving detailed fine-grid problems on a coarse grid. However, some approaches can lack good accuracy on a coarse grid and some corrections for coarse-grid solutions are needed. In this paper, we present a coarse-grid approximation based on the generalized multiscale finite element method (GMsFEM). We present the construction of the offline and online multiscale basis functions. The offline multiscale basis functions are precomputed for the given heterogeneity and fracture network geometry, where for the construction, we solve a local spectral problem and use the dominant eigenvectors (appropriately defined) to construct multiscale basis functions. To construct the online basis functions, we use current information about the local residual and solve coupled Poroelasticity problems in local domains. The online basis functions are used to enrich the offline multiscale space and rapidly reduce the error using residual information. Only with appropriate offline coarse-grid spaces can one guarantee a fast convergence of online methods. We present numerical results for Poroelasticity problems in fractured and heterogeneous media. We investigate the influence of the number of offline and online basis functions on the relative errors between the multiscale solution and the reference (fine-scale) solution
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constraint energy minimizing generalized multiscale finite element method for nonlinear Poroelasticity and elasticity
Journal of Computational Physics, 2020Co-Authors: Shubin Fu, Eric T. ChungAbstract:Abstract In this paper, we apply the constraint energy minimizing generalized multiscale finite element method (CEM-GMsFEM) to first solving a nonlinear Poroelasticity problem. The arising system consists of a nonlinear pressure equation and a nonlinear stress equation in strain-limiting setting, where strains keep bounded while stresses can grow arbitrarily large. After time-discretization of the system, to tackle the nonlinearity, we linearize the resulting equations by Picard iteration. To handle the linearized equations, we employ the CEM-GMsFEM and obtain appropriate offline multiscale basis functions for the pressure and the displacement. More specifically, first, auxiliary multiscale basis functions are generated by solving local spectral problems, via the GMsFEM. Then, multiscale spaces are constructed in oversampled regions, by solving a constraint energy minimizing (CEM) problem. After that, this strategy (with the CEM-GMsFEM) is also applied to a static case of the above nonlinear Poroelasticity problem, that is, elasticity problem, where the residual based online multiscale basis functions are generated by an adaptive enrichment procedure, to further reduce the error. Convergence of the two cases is demonstrated by several numerical simulations, which give accurate solutions, with converging coarse-mesh sizes as well as few basis functions (degrees of freedom) and oversampling layers.
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constrained energy minimization based upscaling for coupled flow and mechanics
Journal of Computational Physics, 2019Co-Authors: Eric T. Chung, Yalchin Efendiev, Maria V Vasilyeva, Jihoon KimAbstract:Abstract In this paper, our aim is to present (1) an embedded fracture model (EFM) for coupled flow and mechanics problem based on the dual continuum approach on the fine grid and (2) an upscaled model for the resulting fine grid equations. The mathematical model is described by the coupled system of equation for displacement, fracture and matrix pressures. For a fine grid approximation, we use the finite volume method for flow problem and finite element method for mechanics. Due to the complexity of fractures, solutions have a variety of scales, and fine grid approximation results in a large discrete system. Our second focus in the construction of the upscaled coarse grid Poroelasticity model for fractured media. Our upscaled approach is based on the nonlocal multicontinuum (NLMC) upscaling for coupled flow and mechanics problem, which involves computations of local basis functions via an energy minimization principle. This concept allows a systematic upscaling for processes in the fractured porous media, and provides an effective coarse scale model whose degrees of freedoms have physical meaning. We obtain a fast and accurate solver for the Poroelasticity problem on a coarse grid and, at the same time, derive a novel upscaled model. We present numerical results for the two dimensional model problem.
Lu Zhang - One of the best experts on this subject based on the ideXlab platform.
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an accurate hyper singular boundary integral equation method for dynamic Poroelasticity in two dimensions
arXiv: Computational Physics, 2020Co-Authors: Lu Zhang, Tao YinAbstract:This paper is concerned with the boundary integral equation method for solving the exterior Neumann boundary value problem of dynamic Poroelasticity in two dimensions. The main contribution of this work consists of two aspescts: the proposal of a novel regularized boundary integral equation, and the presentation of new regularized formulations of the strongly-singular and hyper-singular boundary integral operators. Firstly, turning to the spectral properties of the double-layer operator and the corresponding Calderon relation of the Poroelasticity, we propose the novel low-GMRES-iteration integral equation whose eigenvalues are bounded away from zero and infinity. Secondly, with the help of the Gunter derivatives, we reformulate the strongly-singular and hyper-singular integral operators into combinations of the weakly-singular operators and the tangential derivatives. The accuracy and efficiency of the proposed methodology are demonstrated through several numerical examples.
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An accurate hyper-singular boundary integral equation method for dynamic Poroelasticity in two dimensions
2020Co-Authors: Lu Zhang, Xu Liwei, Yin TaoAbstract:This paper is concerned with the boundary integral equation method for solving the exterior Neumann boundary value problem of dynamic Poroelasticity in two dimensions. The main contribution of this work consists of two aspescts: the proposal of a novel regularized boundary integral equation, and the presentation of new regularized formulations of the strongly-singular and hyper-singular boundary integral operators. Firstly, turning to the spectral properties of the double-layer operator and the corresponding Calder\'{o}n relation of the Poroelasticity, we propose the novel low-GMRES-iteration integral equation whose eigenvalues are bounded away from zero and infinity. Secondly, with the help of the G\"{u}nter derivatives, we reformulate the strongly-singular and hyper-singular integral operators into combinations of the weakly-singular operators and the tangential derivatives. The accuracy and efficiency of the proposed methodology are demonstrated through several numerical examples.Comment: 22 pages, 6 figures, 4 table
Af Frangi - One of the best experts on this subject based on the ideXlab platform.
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fluid structure interaction for highly complex statistically defined biological media homogenisation and a 3d multi compartmental poroelastic model for brain biomechanics
Journal of Fluids and Structures, 2019Co-Authors: Jc Vardakis, Za Taylor, Liwei Guo, Thomas W Peach, Toni Lassila, Micaela Mitolo, Dean Chou, Susheel Varma, Annalena Venneri, Af FrangiAbstract:Abstract Numerous problems of relevance in physiology and biomechanics, have at their core, the presence of a deformable solid matrix which experiences flow-induced strain. Often, this fluid–structure interaction (FSI) is directed the opposite way, i.e. it is solid deformation that creates flow, with the heart being the most prominent example. In many cases, this interaction of fluid and solid is genuinely bidirectional and strongly coupled, with solid deformation inducing flow and fluid pressure deforming the solid. Although an FSI problem, numerous cases in biomechanics are not tractable via the traditional FSI methodologies: in the internal flows that are of interest to use, the number and range of fluid passages is so vast that the direct approach of a deterministically defined boundary between fluid and solid is impossible to apply. In these cases, homogenisation and statistical treatment of the material-fluid system is possibly the only way forward. Such homogenisation,quite common to flow-only systems through porous media considerations, is also possible for FSI systems, where the loading is effectively internal to the material. A prominent technique of this type is that of Poroelasticity. In this paper, we discuss a class of poroelastic theory techniques that allow for the co-existence of a multitude of – always statistically treated – channels and passages of widely different properties: termed multiple-network Poroelasticity (or multicompartmental Poroelasticity). This paradigm is particularly suitable for the study of living tissue, that is invariably permeated – perfused – by fluids, often different in nature and across a wide range of scales. Multicompartmental Poroelasticity is capable of accounting for bidirectional coupling between the fluids and the solid matrix and allows us to track transport of a multitude of substances together with the deformation of the solid material that this transport gives rise to or is caused by, or both. For the purposes of demonstration, we utilise a complex and physiologically very important system, the human brain (specifically, we target the hippocampus), to exemplify the qualities and efficacy of this methodology during the course of Alzheimer’s Disease. The methodology we present has been implemented through the Finite Element Method, in a general manner, allowing for the co-existence of an arbitrary number of compartments. For the applications used in this paper to exemplify the method, a four-compartment implementation is used. A unified pipeline is used on a cohort of 35 subjects to provide statistically meaningful insight into the underlying mechanisms of the neurovascular unit (NVU) in the hippocampus, and to ascertain whether physical activity would have an influence in both swelling and drainage by taking into account both the scaled strain field and the proportion of perfused blood injected into the brain tissue. A key result garnered from his study is the statistically significant differences in right hemisphere hippocampal NVU swelling between males in the control group and females with mild cognitive impairment during high and low activity states.
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Fluid–structure interaction for highly complex, statistically defined, biological media: Homogenisation and a 3D multi-compartmental poroelastic model for brain biomechanics
'Elsevier BV', 2019Co-Authors: Jc Vardakis, Guo L, Tw Peach, Lassila T, Mitolo M, Chou D, Za Taylor, Varma S, Venneri A, Af FrangiAbstract:Numerous problems of relevance in physiology and biomechanics, have at their core, the presence of a deformable solid matrix which experiences flow-induced strain. Often, this fluid-structure interaction (FSI) is directed the opposite way, i.e. it is solid deformation that creates flow, with the heart being the most prominent example. In many cases, this interaction of fluid and solid is genuinely bidirectional and strongly coupled, with solid deformation inducing flow and fluid pressure deforming the solid. Although an FSI problem, numerous cases in biomechanics are not tractable via the traditional FSI methodologies: in the internal flows that are of interest to use, the number and range of fluid passages is so vast that the direct approach of a deterministically defined boundary between fluid and solid is impossible to apply. In these cases, homogenisation and statistical treatment of the material-fluid system is possibly the only way forward. Such homogenisation, quite common to flow-only systems through porous media considerations, is also possible for FSI systems, where the loading is effectively internal to the material. A prominent technique of this type is that of Poroelasticity. In this paper, we discuss a class of poroelastic theory techniques that allow for the co-existence of a multitude of – always statistically treated –channels and passages of widely different properties: termed multiple-network Poroelasticity (or multicompartmental Poroelasticity). This paradigm is particularly suitable for the study of living tissue, that is invariably permeated – perfused – by fluids, often different in nature and across a wide range of scales. Multicompartmental Poroelasticity is capable of accounting for a full bidirectional coupling between the fluids and the solid matrix and allows us to track transport of a multitude of substances together with the deformation of the solid material that this transport gives rise to or is caused by, or both. For the purposes of demonstration, we utilise a complex and physiologically very important system, the human brain (specifically, we target the hippocampus), to exemplify the qualities and efficacy of this methodology during the course of Alzheimer’s Disease. The methodology we present has been implemented through the Finite Element Method, in a general manner, allowing for the co-existence of an arbitrary number of compartments. For the applications used in this paper to exemplify the method, a four-compartment implementation is used. A unified pipeline is used on a cohort of 35 subjects to provide statistically meaningful insight into the underlying mechanisms of the neurovascular unit (NVU) in the hippocampus, and to ascertain whether physical activity would have an influence in both swelling and drainage by taking into account both the scaled strain field and the proportion of perfused blood injected into the brain tissue. A key result garnered from his study is the statistically significant differences in right hemisphere hippocampal NVU swelling between males in the control group and females with mild cognitive impairment during high and low activity states
Yaoru Liu - One of the best experts on this subject based on the ideXlab platform.
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on the mechanisms of impoundment induced foundation deformations of super high arch dams
International Conference of the International Association for Computer Methods and Advances in Geomechanics, 2021Co-Authors: Qiang Yang, Man Zhang, Shouguang Wang, Yaoru LiuAbstract:During the impoundment process of two super-high arch dams, Jingping and Xiluodu arch dams in China, significant width reduction up to 10–90 mm of the valleys and dams have been observed. It is indicated in this report that the width reductions essentially belong to plastic deformation and the mechanism behind the width reduction is related to the change of effective stress in the dam foundation induced by the impoundment. By comparing the numerical results with the measurements, the width reduction of the Jinping arch dam can be well described by poroplasticity theory as a continuum approach. It is shown that the difference between Biot’s effective stress and the plastic effective stress for yield condition plays a key role in the width reduction. The large width reduction of the Xiluodu arch dam, about 90 mm, cannot be described by the poroplasticity theory and may be related to Hubbert’s effective stress principle as a discontinuous approach.
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Analysis of the Abutment Movements of High Arch Dams due to Reservoir Impoundment
Rock Mechanics and Rock Engineering, 2020Co-Authors: Wang Shouguang, Yaoru Liu, Qiang Yang, Xingwang WangAbstract:The deformation of mountains induced by reservoirs around high arch dams may influence the safety of those arch dams, but the underlying mechanisms of this phenomenon have not yet been elucidated. The abutment movements of the Jinping-I and Xiluodu arch dams during reservoir impoundment are analyzed systematically in this paper, and the analysis reveals that impoundment led to basin irreversible uplifts. The underlying mechanisms are analyzed from the viewpoint of the constitutive relation of rock mechanics. Based on the theories of Poroelasticity and poroplasticity, the effective stress principle of rock is deduced considering the effect of high pore pressure. The modified nonlinear finite element program TFINE is used to simulate the abutment movements of the Jinping-I arch dam, and the calculated values are in accordance with the measured values, verifying the validity of the revised effective stress principle.