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Two Phase Flow Simulation of Fractal Oil Reservoir Based on meshless method

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Energy Engineering 2022年第2期119卷 653-664页

作者： Xian Zhou Fei Wang Ziyu Wang Yunfeng Xu School of Petroleum Engineering Yangtze UniversityWuhan430100China China Oilfield Services Limited TianjinChina Xinmin Oil Production Plant of Jilin Oilfield Company PetroChinaSongyuan138000China

The reservoir is the networked rock skeleton of an oil and gas trap,as well as the generic term for the fluid contained within pore fractures and karst caves.Heterogeneity and a complex internal pore structure characterize the reservoir rock.By introducing the fractal permeability formula,this paper establishes a fractal mathematical model of oil-water two-phase flow in an oil reservoir with heterogeneity characteristics and numerically solves the mathematical model using the weighted least squares meshless method.Additionally,the method’s correctness is verified by comparison to the exact solution.The numerical results demonstrate that the fractal oil-water two-phase flow mathematical model developed using the meshless method is capable of more accurately and efficiently describing the flow characteristics of the oil-water two-phase migration process.In comparison to the conventional numerical model,this method achieves a greater degree of convergence and stability.This paper examines the effect of varying the initial viscosity of the oil,the initial formation pressure,and the production and injection ratios on daily oil production per well,water cut in the block,and accumulated oil in the block.For 10 and 60 cp initial crude oil viscosities,the water cut can be 0.62 and 0.80,with 3100 and 1900 m^(3)cumulative oil production.Initial pressures have little effect on production.In this case,the daily oil production of well PRO1 is 1.7 m^(3)at 7 and 10 MPa initial pressure.Block cumulative oil production is 3465.4 and 2149.9m^(3)when the production injection ratio is 1.4 and 0.8.The two-phase meshless method described in this paper is essential for a rational and effective study of production dynamics patterns in complex reservoirs and the development of reservoir simulations of oil-water flow in heterogeneous reservoirs.

关键词： Oil-water two-phase flow fractal theory weighted least square method meshless method

meshless method OF DUAL RECIPROCITY HYBRID RADIAL BOUNDARY NODE method FOR ELASTICITY

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Acta Mechanica Solida Sinica 2010年第5期23卷 447-458页

作者： Fei Yan Xiating Feng Hui Zhou 1(State Key Laboratory of Geomechanics and Geotechnical Engineering,Institute of Rock and Soil Mechanics,Chinese Academy of Science,Wuhan 430071,China) State Key Laboratory of Geomechanics and Geotechnical Engineering Institute of Rock and Soil Mechanics Chinese Academy of Science Wuhan China

Combining the radial point interpolation method （RPIM）, the dual reciprocity method （DRM） and the hybrid boundary node method （HBNM）, a dual reciprocity hybrid radial boundary node method （DHRBNM） is proposed for linear elasticity. Compared to DHBNM, RPIM is exploited to replace the moving least square （MLS） in DHRBNM, and it gets rid of the deficiency of MLS approximation, in which shape functions lack the delta function property, the boundary condition can not be applied easily and directly and it＇s computational expense is high. Besides, different approximate functions are discussed in DRM to get the interpolation property, in which the accuracy and efficiency for different basis functions are compared. Then RPIM is also applied in DRM to replace the conical function interpolation, which can greatly improve the accuracy of the present method. To demonstrate the effectiveness of the present method, DHBNM is applied for comparison, and some numerical examples of 2-D elasticity problems show that the present method is much more effective than DHBNM.

关键词： meshless method hybrid boundary node method dual reciprocity method radial point interpolation method elasticity

Independent cover meshless particle method for complex geotechnical engineering

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Frontiers of Structural and Civil Engineering 2018年第4期12卷 515-526页

作者： Jianqiu WU Yongchang CAI State Key Laboratory of Disaster Reduction in Civil Engineering College of Civil EngineeringTongji UniversityShanghai 200092China

A new Independent Cover meshless Particle (ICMP) method is proposed for the analysis of complex geotechnical engineering. In the ICMP method, the independent rectangular cover regardless of the shape of the analysis model is employed as the influence domain of each discrete node, the general polynomial is employed as the meshless interpolation function of the independent nodal cover, and the Cartesian Transformation method (CTM) is used for the numerical integration of the nodal covers cut by material interfaces, joints, cracks and faults. The present method has a simple formulation and a low computational cost, and is easy for the numerical analysis and modeling of complex geotechnical engineering. Several typical numerical examples are presented to demonstrate the accuracy and robustness of the proposed method.

关键词： meshless method particle method independent cover CTM geotechnical engineering Cataract, zonular Geotechnical engineering ANALYSIS MODELS Engineering geology meshfree methods

An Efficient meshless method for Hyperbolic Telegraph Equations in (1 + 1) Dimensions

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Computer Modeling in Engineering & Sciences 2021年第8期128卷 687-698页

作者： Fuzhang Wang Enran Hou Imtiaz Ahmad Hijaz Ahmad Yan Gu College of Mathematics and Statistics Xuzhou University of TechnologyXuzhou221018China College of Mathematics Huaibei Normal UniversityHuaibei235000China Department of Mathematics University of SwabiSwabi25000Pakistan Department of Basic Sciences University of Engineering and TechnologyPeshawar25000Pakistan College of Mathematics Qingdao UniversityQingdao266071China

Numerical solutions of the second-order one-dimensional hyperbolic telegraph equations are presented using the radial basis functions.The purpose of this paper is to propose a simple novel direct meshless scheme for solving hyperbolic telegraph equations.This is fulfilled by considering time variable as normal space variable.Under this scheme,there is no need to remove time-dependent variable during the whole solution process.Since the numerical solution accuracy depends on the condition of coefficient matrix derived from the radial basis function method.We propose a simple shifted domain method,which can avoid the full-coefficient interpolation matrix easily.Numerical experiments performed with the proposed numerical scheme for several second-order hyperbolic telegraph equations are presented with some discussions.

关键词： Radial basis functions telegraph equation shifted domain method meshless method

meshless method with Domain Decomposition for Submerged Porous Breakwaters in Waves

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Journal of Ocean University of China 2021年第6期20卷 1325-1340页

作者： CHIOUKH Nadji YÜKSEL Yalçın Department of Hydraulics University of Sidi Bel-AbbesSidi Bel-Abbes 22000Algeria Laboratory of Civil Engineering and Environment University of Sidi Bel-AbbesSidi Bel-Abbes 22000Algeria Laboratory of Hydraulics and Coastal Engineering Yildiz Technical UniversityEsenler-Istanbul 34220Turkey

Based on the improved version of the meshless singular boundary method(ISBM)in multi domain(MD),a numerical method is proposed in this paper to study the interaction of submerged permeable breakwaters and regular waves at normal incidence.To account for fluid flow inside the porous breakwaters,the conventional model of Sollitt and Cross for porous media is adopted.Both single and dual trapezoidal breakwaters are examined.The physical problem is formulated in the context of the linear potential wave theory.The domain decomposition method(DDM)is employed,in which the full computational domain is decomposed into separate domains,that is,the fluid domain and the domains of the breakwaters.Respectively,appropriate mixed type boundary and continuity conditions are applied for each subdomain and at the interfaces between domains.The solution is approximated in each subdomain by the ISBM.The discretized algebraic equations are combined,resulting in an overdetermined full system that is solved using a least-square solution procedure.The numerical results are presented in terms of the hydrodynamic quantities of reflection,transmission,and wave-energy dissipation.The relevance of the results of the present numerical procedure is first validated against data of previous studies,and then selected computations are discussed for various structural conditions.The proposed method is demonstrated to be highly accurate and computationally efficient.

关键词： meshless method domain decomposition regular waves breakwaters porosity reflection transmission dissipation coastal environment

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基于无网格移动变形构件的结构拓扑优化方法

Acta Mechanica Sinica 2022年第5期38卷 72-87,I0002页

作者：李林远刘畅杜宗亮张维声郭旭 State Key Laboratory of Structural Analysis for Industrial Equipment Department of Engineering MechanicsInternational Research Center for Computational MechanicsDalian University of TechnologyDalian 116023China Ningbo Institute of Dalian University of Technology Ningbo 315016China

传统拓扑优化方法往往需引入人工弱材料来模拟孔洞,以避免整体刚度矩阵的奇异性,并使用固定的有限元网格进行分析和优化.然而,这种处理方法不仅会增加结构分析的计算成本,还会导致不利的数值不稳定性,尤其是当涉及大变形和动力/屈曲行为... 详细信息

传统拓扑优化方法往往需引入人工弱材料来模拟孔洞,以避免整体刚度矩阵的奇异性,并使用固定的有限元网格进行分析和优化.然而,这种处理方法不仅会增加结构分析的计算成本,还会导致不利的数值不稳定性,尤其是当涉及大变形和动力/屈曲行为时.本文提出了一种新的基于无网格的移动可变形组件拓扑优化方法(ML-MMC),该方法只对组件占据的实体区域进行结构分析,并通过自适应构造无网格形函数的影响域来实现离散组件的耦合,可以在不引入人工弱材料的情况下自然地避免拓扑优化过程中刚度矩阵的奇异性问题.与传统拓扑优化方法相比,这种处理方法可以大大减少优化过程中结构分析的自由度(DOFs)数量.一些典型的二维和三维算例说明了该方法的有效性和高效性.

关键词： Topology optimization Moving morphable components(MMCs) meshless method Influence domain Numerical integration

A Novel Localized meshless method for Solving Transient Heat Conduction Problems in Complicated Domains

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Computer Modeling in Engineering & Sciences 2023年第6期135卷 2407-2424页

作者： Chengxin Zhang Chao Wang Shouhai Chen Fajie Wang College of Mechanical and Electrical Engineering National Engineering Research Center for Intelligent Electrical Vehicle Power SystemQingdao UniversityQingdao266071China Hisense(Shandong)Air Conditioner Co. Ltd.Qingdao266100China

This paper first attempts to solve the transient heat conduction problem by combining the recently proposed local knot method(LKM)with the dual reciprocity method(DRM).Firstly,the temporal derivative is discretized by a finite difference scheme,and thus the governing equation of transient heat transfer is transformed into a non-homogeneous modified Helmholtz equation.Secondly,the solution of the non-homogeneous modified Helmholtz equation is decomposed into a particular solution and a homogeneous solution.And then,the DRM and LKM are used to solve the particular solution of the non-homogeneous equation and the homogeneous solution of the modified Helmholtz equation,respectively.The LKM is a recently proposed local radial basis function collocationmethod with themerits of being simple,accurate,and free ofmesh and integration.Compared with the traditional domain-type and boundary-type schemes,the present coupling algorithm could be treated as a really good alternative for the analysis of transient heat conduction on high-dimensional and complicated domains.Numerical experiments,including two-and three-dimensional heat transfer models,demonstrated the effectiveness and accuracy of the new methodology.

关键词： Local knot method transient heat conduction dual reciprocity method meshless method

A new complex variable meshless method for transient heat conduction problems

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Chinese Physics B 2012年第12期21卷 42-50页

作者：王健菲程玉民 Shanghai Institute of Applied Mathematics and Mechanics Shanghai University Shanghai Key Laboratory of Mechanics in Energy Engineering Shanghai University

In this paper, based on the improved complex variable moving least-square （ICVMLS） approximation, a new complex variable meshless method （CVMM） for two-dimensional （2D） transient heat conduction problems is presented. The variational method is employed to obtain the discrete equations, and the essential boundary conditions are imposed by the penalty method. As the transient heat conduction problems are related to time, the Crank-Nicolson difference scheme for two-point boundary value problems is selected for the time discretization. Then the corresponding formulae of the CVMM for 2D heat conduction problems are obtained. In order to demonstrate the applicability of the proposed method, numerical examples are given to show the high convergence rate, good accuracy, and high efficiency of the CVMM presented in this paper.

关键词： meshless method improved complex variable moving least-square approximation com-plex variable meshless method transient heat conduction problem

A meshless Galerkin method with moving least square approximations for infinite elastic solids

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Chinese Physics B 2013年第8期22卷 245-252页

作者：李小林李淑玲 College of Mathematics Science Chongqing Normal University

Combining moving least square approximations and boundary integral equations, a meshless Galerkin method, which is the Galerkin boundary node method （GBNM）, for twoand three-dimensional infinite elastic solid mechanics problems with traction boundary conditions is discussed. In this numerical method, the resulting formulation inherits the symmetry and positive definiteness of variational problems, and boundary conditions can be applied directly and easily. A rigorous error analysis and convergence study for both displacement and stress is presented in Sobolev spaces. The capability of this method is illustrated and assessed by some numerical examples.

关键词： meshless method Galerkin boundary node method error estimates elasticity