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Adaptive Extended Isogeometric Analysis for Steady-State Heat Transfer in heterogeneous media

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Computer Modeling in Engineering & Sciences 2021年第3期126卷 1315-1332页

作者： Weihua Fang Tiantang Yu Yin Yang Nanjing Automation Institute of Water Conservancy and Hydrology Ministry of Water ResourcesNanjing210012China Department of Engineering Mechanics Hohai UniversityNanjing211100China Lake Research Institute Hydraulic Research Institute of Jiangsu ProvinceNanjing210017China

Steady-state heat transfer problems in heterogeneous solid are simulated by developing an adaptive extended isogeometric analysis(XIGA)method based on locally refined non-uniforms rational B-splines(LR NURBS).In the XIGA,the LR NURBS,which have a simple local refinement algorithm and good description ability for complex geometries,are employed to represent the geometry and discretize the field variables;and some special enrichment functions are introduced into the approximation of temperature field,thus the computational mesh is independent of the material interfaces,which are described with the level setmethod.Similar to the approximation of temperature field,a temperature gradient recovery technique for heterogeneous media is proposed,and based on the Zienkiewicz–Zhu recovery technique a posteriori error estimator is defined to automatically identify the locally refined regions.The convergence and performance properties of the developed method are verified by using three numerical examples.The numerical results show that(1)The convergence speed of the adaptive local refinement is faster than that of the uniform global refinement;(2)The convergence rate of the high-order basis functions is faster than that of the low-order basis functions;and(3)The existing inclusions change the local distributions of the temperature,and the extreme values of the temperature gradients take place around the inclusion interfaces.

关键词： heterogeneous media steady-state heat transfer adaptive XIGA LR NURBS heat dissipation

COMPUTATIONAL MULTISCALE METHODS FOR LINEAR heterogeneous POROELASTICITY

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Journal of Computational Mathematics 2020年第1期38卷 41-57页

作者： Robert Altmann Eric Chung Roland Maier Daniel Peterseim Sai-Mang Pun Department of Mathematics University of AugsburgAugsburgGermany Department of Mathematics The Chinese University of Hong KongHong KongChina Department of Mathematics Texas UniversityUSA

We consider a strongly heterogeneous medium saturated by an incompressible viscous fluid as it appears in geomechanical modeling.This poroelasticity problem suffers from rapidly oscillating material parameters,which calls for a thorough numerical treatment.In this paper,we propose a method based on the local orthogonal decomposition technique and motivated by a similar approach used for linear thermoelasticity.Therein,local corrector problems are constructed in line with the static equations,whereas we propose to consider the full system.This allows to benefit from the given saddle point structure and results in two decoupled corrector problems for the displacement and the pressure.We prove the optimal first-order convergence of this method and verify the result by numerical experiments.

关键词： Poroelasticity heterogeneous media Numerical homogenization Multiscale methods

A NUMERICAL SIMULATION OF CHANNEL RESERVOIRS CONTAINING VERTICAL AND HORIZONTAL WELLS

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Journal of Hydrodynamics 2006年第5期18卷 527-536页

作者： LIU Fu-ping WANG Xu-song WANG Jun WANG An-ling Beijing Institute of Graphic Communication Beijing 102600 China Institute of Geology and Geophysics Chinese Academy of Sciences Beij ing 100029 China

In this article, the bounding surfaces of channels were modeled by Bayesian stochastic simulation, which is a boundary-valued problem with observed valley erosion thickness at the locations of wells （hard data）. In this study, it was assumed that the cross-section of the channel shows a parabolic shape, and the case that the vertical well and the horizontal well are located in the channel was considered. Peaceman＇s equations were modified to simultaneously solve both the vertical well problem and the horizontal well problem. In porous media, a 3D fluid equation was solved with iteration in the spatial domain, which had channels, vertical wells, and horizontal wells. As an example, the spatial distributions of pressure were calculated for channel reservoirs containing vertical and horizontal wells.

关键词： fluid equations in porous media porosity channel reservoirs numerical simulation heterogeneous media hrizontal well vertical well

TAILORED FINITE CELL METHOD FOR SOLVING HELMHOLTZ EQUATION IN LAYERED heterogeneous MEDIUM

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Journal of Computational Mathematics 2012年第4期30卷 381-391页

作者： Zhong-yi Huang Xu Yang Mathematical Sciences Tsinghua University Beijing 100084 China Department of Mathematics Courant Institute of Mathematical Sciences New York UniversityNew York NY 10012 USA

In this paper, we propose a tailored finite cell method for the computation of two- dimensional Helmholtz equation in layered heterogeneous medium. The idea underlying the method is to construct a numerical scheme based on a local approximation of the solution to Helmholtz equation. This provides a computational tool of achieving high accuracy with coarse mesh even for large wave number （high frequency）. The stability analysis and error estimates of this method are also proved. We present several numerical results to show its efficiency and accuracy.

关键词： Tailored finite cell method Helmholtz equation heterogeneous media Som-merfeld condition.

A Layer-IntegratedModel of Solute Transport in heterogeneousmedia

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Advances in Applied Mathematics and Mechanics 2014年第6期6卷 699-717页

作者： Hung-En Chen Hui-Ping Lee Shih-Wei Chiang Tung-Lin Tsai Jinn-Chuang Yang Department of Civil Engineering National Chiao Tung University1001 Ta Hsueh RoadHsinchu 30010Taiwan Agricultural Engineering Research Center 196-1 Chung Yuan RoadChungli 32061Taiwan Department of Civil and Water Resources Engineering National Chiayi University 300 Syuefu RoadChiayi 60004Taiwan Department of Civil Engineering and Disaster Prevention and Water Environment Research Center National Chiao Tung University1001 Ta Hsueh RoadHsinchu 30010Taiwan

This study presents a numerical solution to the three-dimensional solute transport in heterogeneous media by using a layer-integrated approach.Omitting vertical spatial variation of soil and hydraulic properties within each layer,a threedimensional solute transport can be simplified as a quasi-three-dimensional solute transport which couples a horizontal two-dimensional simulation and a vertical onedimensional computation.The finite analytic numericalmethod was used to discretize the derived two-dimensional governing equation.A quadratic function was used to approximate the vertical one-dimensional concentration distribution in the layer to ensure the continuity of concentration and flux at the interface between the adjacent layers.By integration over each layer,a set of system of equations can be generated for a single column of vertical cells and solved numerically to give the vertical solute concentration profile.The solute concentration field was then obtained by solving all columns of vertical cells to achieve convergence with the iterative solution procedure.The proposed model was verified through examples from the published literatures including four verifications in terms of analytical and experimental cases.Comparison of simulation results indicates that the proposed model satisfies the solute concentration profiles obtained from experiments in time and space.

关键词： Layer-integrated model groundwater solute transport finite analytic method heterogeneous media

Numerical simulation of seismic wave propagation in complex media by convolu-tional differentiator

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Earthquake Science 2008年第4期21卷 380-385+442页

作者：李信富李小凡 State Key Laboratory of Geological Processes and Mineral Resources China University of Geosciences State Key Laboratory of Lithospheric Evolution Institute of Geology and Geophysics Chinese Academy of Sci-ences

We apply the forward modeling algorithm constituted by the convolutional Forsyte polynomial differentiator pro-posed by former worker to seismic wave simulation of complex heterogeneous media and compare the efficiency and accuracy between this method and other seismic simulation methods such as finite difference and pseudospec-tral method. Numerical experiments demonstrate that the algorithm constituted by convolutional Forsyte polyno-mial differentiator has high efficiency and accuracy and needs less computational resources, so it is a numerical modeling method with much potential.

关键词： seismic wave numerical simulation heterogeneous media differential operator

Seismic scalar wave equation with variable coefficients modeling by a new convolutional differentiator

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Seismic scalar wave equation with variable coefficients mode...