油藏数值模拟中复杂网格系统生成技术研究
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摘要
网格是油藏数值模拟的基础,网格质量的好坏直接影响着数值模拟结果的精确度,基于非结构网格系统的数值模拟技术目前已成为油藏模拟领域中的一个重要发展方向。角点网格、PEBI网格和CVFE网格具有非常灵活的特性,能够精确描述油藏的复杂形态(边界、断层、裂缝等),模拟效果更加真实。这三种网格都可以在三角形网格的基础上生成,因此高质量的三角形网格的生成方法研究显得尤为重要。本文提出了一种满足Delaunay条件的三角形网格系统生成方法——控制子域Delaunay三角化方法,与经典三角化方法的对比研究表明,该方法节省了网格点数、提高了运算速度,且生成的网格质量更高。在生成的Delaunay三角网基础上,将相邻三角形的公共边去掉就形成四边形网格系统,将相邻三角形的外心连接起来就形成PEBI网格系统,将三角形重心和各边中点连接起来就形成CVFE网格系统,另外还需要对边界进行特殊处理。平面四边形网格通过引出纵向坐标线和定义每个层面上的角点深度,可以生成三维角点网格系统,该网格系统是目前应用最多的非结构网格系统。应用PEBI网格系统和CVFE网格系统,对具有复杂边界形状、裂缝和断层不规则分布的油藏进行了网格剖分,使网格沿不规则边界及裂缝、断层走向分布,与笛卡尔网格和角点网格相比,剖分过程更加灵活,剖分结果更加接近油藏实际。基于几种优选的网格生成方法,特别针对具有不规则形状的复杂油藏编制了涵盖D-三角形网格系统、角点网格系统、PEBI网格系统和CVFE网格系统的网格生成软件。基于PEBI网格建立了二维两相油藏数值模型,并进行了求解,编制了数值模拟器,验证了模拟器的正确性。应用该模拟器建立了三个数值模拟实例,实例1表明PEBI网格有效降低了网格取向效应;实例2表明PEBI网格可以更加精确地模拟复杂油藏中断层、高渗透条带对渗流的影响;在实例3中,成功的将PEBI网格应用于五点法井网的油藏数值模拟,进一步验证了模拟器的正确性和可靠性。
Grid generation is the base of simulation and the quality of gird has direct influence upon the precision of simulation. At present, numerical simulation based on unstructed grid system is an important tendency of reservoir simulation and an indispensable functional module of simulation software. Corner Point Geometry, PEBI Grid, CVFE Grid are so flexible that they can exactly describe reservoirs with complex configuration (boundary, fault, fracture). It is important to research the method of creating high quality triangular grid because these three kinds of gird can be created on the basis of triangular gird. This paper presents a creating method meeting Delaunay condition-Controlled Subdomain Delaunay Triangulation Method. This method can save grid number, speed computation and create better grid in contrast with other methods. PEBI grid system is formed by connecting circumcenters of adjacent triangles and link the barycenter with midpoints of each edge to shape CVFE grid system, furthermore, the edges should be specially disposed. Three-dimensional Corner Point Geometry grid system is the most mature unstructed grid system and it can be created directly from quadrilateral grid system. PEBI and CVFE grid system are utilized in this paper to the reservoirs with complex shaped boundary, fractures and faults. The results demonstrate that it is more accurate than Cartesian grid and corner point geometry. The method of generating corner point geometry system is studied in this paper which is also evaluated through comparison with corner point geometry modular of the existing commercial simulation software. Furthermore, grid generation software covering Delaunay triangulation, PEBI grid, CVFE grid and corner point geometry is programmed especially for complex reservoirs with irregular boundaries. Three simulation examples are erected with this simulator: example 1 shows that PEBI gird system effectively reduces grid orientation effects; example 2 demonstrates PEBI grid can exactly simulate the effect of fault and high permeable strip to flow in complex reservoir; example 3 successfully used PEBI grid in five-spot pattern which verified the validity and reliability of this simulator.
Grid generation is the base of simulation and the quality of gird has direct influence upon the precision of simulation. At present, numerical simulation based on unstructed grid system is an important tendency of reservoir simulation and an indispensable functional module of simulation software. Corner Point Geometry, PEBI Grid, CVFE Grid are so flexible that they can exactly describe reservoirs with complex configuration (boundary, fault, fracture). It is important to research the method of creating high quality triangular grid because these three kinds of gird can be created on the basis of triangular gird. This paper presents a creating method meeting Delaunay condition-Controlled Subdomain Delaunay Triangulation Method. This method can save grid number, speed computation and create better grid in contrast with other methods. PEBI grid system is formed by connecting circumcenters of adjacent triangles and link the barycenter with midpoints of each edge to shape CVFE grid system, furthermore, the edges should be specially disposed. Three-dimensional Corner Point Geometry grid system is the most mature unstructed grid system and it can be created directly from quadrilateral grid system. PEBI and CVFE grid system are utilized in this paper to the reservoirs with complex shaped boundary, fractures and faults. The results demonstrate that it is more accurate than Cartesian grid and corner point geometry. The method of generating corner point geometry system is studied in this paper which is also evaluated through comparison with corner point geometry modular of the existing commercial simulation software. Furthermore, grid generation software covering Delaunay triangulation, PEBI grid, CVFE grid and corner point geometry is programmed especially for complex reservoirs with irregular boundaries. Three simulation examples are erected with this simulator: example 1 shows that PEBI gird system effectively reduces grid orientation effects; example 2 demonstrates PEBI grid can exactly simulate the effect of fault and high permeable strip to flow in complex reservoir; example 3 successfully used PEBI grid in five-spot pattern which verified the validity and reliability of this simulator.
引文
[1]哈利德·阿齐兹,安东尼·塞特瑞著.袁士义,王家禄译.油藏数值模拟[M].北京:石油工业出版社,2004:7~29
[2]陈月明.油藏数值模拟基础[M].东营:石油大学出版社,1988:1~280
[3]姜汉桥,姚军,姜瑞忠.油藏工程原理与方法[M].东营:石油大学出版社, 2003: 1~202
[4]谢海兵,马远乐,恒冠仁,等.非结构网格油藏数值模拟方法研究[J].石油学报, 2001, 22(1):63~66
[5] K.Aziz.Reservoir simulation grids:opportunities and problems[J].JPT, 1993(7):658~663
[6] Kleinstreuer C, Holdeman J T. A triangular finite element mesh generator for fluid dynamics ystems of arbitrary geometry[J].Int. J. Num. Meth. Eng.1990, 15(1):325~334
[7] Buratynski E K. A fully automatic three-dimensional mesh genertor for complex geometries[J]. Int. J. Num. Meth. Eng. 1990, 30(5):931~952
[8] Bowyer A. Computing dirichlet tessellations[J]. the Computer. Journal, 1981, 24(12):162~167
[9] Watson D F. Computing the n-dimensional delaunay tessellation with application to voronoi polytopes[J]. the Computer Journal,1981,24(2):167~172
[10] Lohner R, Parikh P. Generation of three-dimensional unstructured grids by advancing front method[J]. Int. J. Num. Meth. in Fluids, 1988,8(5):1135~1149
[11] Pirzadeh S. Three dimensional unstructured viscous grids by advancing Layer method[J]. AIAA Journal, 1996, 34(1):189~195
[12] Dmitri Sharov, Kazuhiro Nakahashi. Hybrid prismatic/tetrahedral grid generation for viscous flow applications[J]. AIAA Journal, 1998, 36(2):157~162
[13] Settari A, Aziz K.Use of irregular grid in reservoir simulation[J]. Society of Petroleum Engineers Journal, 1972, 103~114
[14] Settari A, Aziz K. Use of irregular grid in cylindrical coordinates[J]. Society of Petroleum Engineers Journal, 1974, 396~412
[15] Heinemann Z E, Brand C W. Gridding techniques in reservoir simulation[J]. First and Second Intl. Forum on Reservoir Simulation, 1988:404~415
[16] Nacu1 E C, Aziz K. Use of irregular grid in reservoir simulation[J]. SPE Annual Technical Conference and Exhibition, Dallas, 1989:6~9
[17] Rosenberg D W. Local grid refinement for finite difference networks[J]. Annual Technical Conference and Exhibition, New Orleans,1982: 26~29
[18] Quandalle P and Besset P. The use of flexible gridding for improved reservoir modeling[J]. Symposium on Reservoir Simulation, 1983:15~18
[19] Pedrosa O A Jr, Aziz K. Use of hybrid grid in reservoir simulation[J]. SPE Reservoir Engineering, 1986:611~621
[20] Nghiem L, Collins D A and Sharma R Seventh SPE comparative solution project: modeling of horizontal wells in reservoir simulation[J]. SPE Symposium on Reservoir Simulation, 1991:17~20
[21] Quandalle P Eighth SPE comparative solution project: gridding techniques in reservoir simulation[J]. SPE Symposium on Reservoir Simulation, 1993:33~38
[22] Collins D A, Nghiem L X, Sharma R, et al. Field scale simulation of horizontal wells with hybrid grids[J]. SPE Symposium on Reservoir Simulation, 1991:17~20
[23] Hegre T M, Dalen V and Henriquez A. Generalized trasmissibilities for distorted grids in resewoir simulation[J]. SPE Annual Technical Conference and Exhibitin, 1986:25~30
[24] Rozon B J. A generalized finite volume discretization method for reservoir simulation[J]. SPE Symposium on Reservoir Simulation, 1989:6~8
[25] Aavatsmark I. Doscretization on non-orthogonal quadrilateral grids for inhomogeneous anisotropic media[J]. J. Comp. Phys. 1996, 127: 2~14
[26] Heinemann Z E, Brand C, Munka M et al. Modelling reservoir geometry with irregular grids[J]. SPE Symposium on Reservoir Simulation, 1989: 6~8
[27] Heinemann Z E, Brand C W, Munka M, et al. Modelling reservoir geometry with irregular grids[J]. SPE Reservoir Engineering, 1991: 225~232
[28] Aeirnbacher F X, Heinemann Z E. Time-dependent incorporation of locally irregular grids in large reservoir simulation models[J]. SPE Symposium on Reservoir Simulation, 1993:35~40
[29] Palagi C I, Aziz K. Use of voronoi grid in reservoir simulation[J]. SPE Annual Technical Conference and Exhibitin, 1991:6~9
[30] Palagi C L, Aziz K. The modeling of vertical and horizontal wells with voronoi grid[J]. Western Regional Meeting, 1992:2~8
[31] Paper SPE25259.Palagi C L, Ballin P R, Aziz K. The modeling of flow in heterogeneous reservoirs with voronoi grid[J]. SPE Symposium on Reservoir Simulation, 1993:35~37
[32] Palagi C L, Aziz K. Modeling vertical and horizontal wells with voronoi grid[J]. SPE Reservoir Engineering, 1994:15~21.
[33] Verma S. A flexible gridding scheme for reservoir simulation[J]. SPE Intl. Student Paper Contest, 1995: 657~672
[34] Economides M J, Deimbacher F X, Brand C W et al. Comprehensive simulation of horizontal wells performance[J]. SPE Annual Technical Conference and Exhibitin, 1990:23~26.
[35] Economides M J, Deimbacher F X, Brand C W et al. Comprehensive simulation of horizontal wells performance[J]. SPE Formation Evaluation, 1991:418~426
[36] Kocberber S, Collins R E. Gas well test analysis in complex heterogeneous reservoirs[J]. SPE Gas Technology Symposium, 1991:23~25
[37] Kocberber S. A finite-element black oil simulation system for heterogeneous reservoir with horizontal wells having vertical hydraulic fractures[J]. SPE Symposium on Reservoir Simulation, 1993:66~72
[38] Chavent G. Discontinuous and mixed finite elements for two-phase incompressible flow[J]. SPE Symposium on Reservoir Simulation, 1987:255~270
[39] Darlow B L, Ewing R E and Wheeler M F. Mixed finite element method for miscible displacement problems in porous media[J]. Society of Petroleum Engineers Journal, 1984:391~398
[40] Ewing R E, Wheeler M F. Computional aspects of mixed finite element methods[J]. Numerical Methods for Scientific Computing, 1983:302~320
[41]张烈辉,李允.裂缝性油藏水平井数值模拟的进展和展望[J].西南石油学院学报.1997,19(4):48~52
[42]尹定.不规则多边形有限差分网格方法及其在油藏数值模拟中的应用[J].石油学报,1990,11(3):82~86
[43]凌建军,吴敬轩.网格方向性对水驱油油藏数值模拟结果的影响[J].江汉石油学院学报.1990,12(1):40~45
[44]王经荣,李允.混合网格技术在低渗透油藏数值模拟中的应用方法研究[J].石油勘探与开发.1999,26(6):51~54
[45]张烈辉,杜志敏,代艳英.一个可靠的水平井混合网格模型[J].石油学报, 1997, 18(3):77~82
[46]刘立明,廖新维.混合PEBI网格精细油藏数值模拟应用研究[J].石油学报. 2003, 24(3):64~67
[47]向祖平,张烈辉,陈中华,等.油藏任意约束平面域PEBI网格的生成算法[J].西南石油学院学报[J].2006,28(2):32~35.
[48]刘红卫,李爱华,赵国忠.角点网格传导率计算技术研究[J].大庆石油地质与开发[J], 2005,24(6):35~36
[49]李玉坤,姚军,黄朝琴.油水两相渗流问题的无网格伽辽金法[J].水动力学研究与进展A辑. 2006, 21(6):796~804
[50]李玉坤,姚军,黄朝琴,等.油藏渗流问题的无网格法分析[J].中国石油大学学报(自然科学版). 2007, 31(2):95~104
[51] Tsai V. J. Delaunay D. Triangulations in TIN Creation: an Overview and a Linear-time Algorithm[J]. Int. J. of GIS, 1993, 7(6):501~524
[52] Lawson C. L. Software for C’Surface Interpolation[M]. Mathematical Software III. J.Rice, Ed. New York,Academic Press,1977
[53] Lingas A. The Greedy and Delaunay Triangulations are not Bad in the Average Case[J]. Information Processing Letters, 1986(22) :25~31
[54] Green P. J. Sibson R. Computing Dirichlet Tessellations in the Plane[J]. The Computer Journal, 1978, 21(2):168~173
[55] Bowyer A. Computing Dirichlet Tessellations[J], Computer Journal, 1981,24,:162~166
[56] Watson D F. Computing the n-dimension Delaunay Tesselation with Application to Voronoi Polytopes[J]. Computer Journal, 1981(24):167~172
[57] Shamos M I. Hoey D. Closest point Problems[J], In: Proceedings of the 16th Annual Symposium on the Foundations of Computer Science, 1975, 151~162
[58] Avis D. Toassaint T. An efficient algorithm for decomposing a polygon into star-shaped polygons[J] J. Pattern Recognition, 1981, 13(6):395~398
[59] Lo S H. Generating quadrilateral elements on plane and over curved surfaces[J]. Computers & Structures, 1989, 31(3):421~426.
[60]李玉坤,姚军.复杂断块油藏Delaunay三角网格自动剖分技术[J].油气地质与采收率, 2006, 13(3):58~60
[61] Gordon W J, Hall C A. Construction of curvilinear coordinate systems and applications to mesh generation[J]. Int. J. Num. Meth. Eng., 1973, 7(5): 461~477
[62]闵卫东,唐泽圣.三角形网格转化为四边形网格[J].计算机辅助设计与图形学学报. 1996, 8(1):1~6
[63]韩大匡,陈钦雷,闫存章.油藏数值模拟基础[M].北京:石油工业出版社, 1993: 226~231
[2]陈月明.油藏数值模拟基础[M].东营:石油大学出版社,1988:1~280
[3]姜汉桥,姚军,姜瑞忠.油藏工程原理与方法[M].东营:石油大学出版社, 2003: 1~202
[4]谢海兵,马远乐,恒冠仁,等.非结构网格油藏数值模拟方法研究[J].石油学报, 2001, 22(1):63~66
[5] K.Aziz.Reservoir simulation grids:opportunities and problems[J].JPT, 1993(7):658~663
[6] Kleinstreuer C, Holdeman J T. A triangular finite element mesh generator for fluid dynamics ystems of arbitrary geometry[J].Int. J. Num. Meth. Eng.1990, 15(1):325~334
[7] Buratynski E K. A fully automatic three-dimensional mesh genertor for complex geometries[J]. Int. J. Num. Meth. Eng. 1990, 30(5):931~952
[8] Bowyer A. Computing dirichlet tessellations[J]. the Computer. Journal, 1981, 24(12):162~167
[9] Watson D F. Computing the n-dimensional delaunay tessellation with application to voronoi polytopes[J]. the Computer Journal,1981,24(2):167~172
[10] Lohner R, Parikh P. Generation of three-dimensional unstructured grids by advancing front method[J]. Int. J. Num. Meth. in Fluids, 1988,8(5):1135~1149
[11] Pirzadeh S. Three dimensional unstructured viscous grids by advancing Layer method[J]. AIAA Journal, 1996, 34(1):189~195
[12] Dmitri Sharov, Kazuhiro Nakahashi. Hybrid prismatic/tetrahedral grid generation for viscous flow applications[J]. AIAA Journal, 1998, 36(2):157~162
[13] Settari A, Aziz K.Use of irregular grid in reservoir simulation[J]. Society of Petroleum Engineers Journal, 1972, 103~114
[14] Settari A, Aziz K. Use of irregular grid in cylindrical coordinates[J]. Society of Petroleum Engineers Journal, 1974, 396~412
[15] Heinemann Z E, Brand C W. Gridding techniques in reservoir simulation[J]. First and Second Intl. Forum on Reservoir Simulation, 1988:404~415
[16] Nacu1 E C, Aziz K. Use of irregular grid in reservoir simulation[J]. SPE Annual Technical Conference and Exhibition, Dallas, 1989:6~9
[17] Rosenberg D W. Local grid refinement for finite difference networks[J]. Annual Technical Conference and Exhibition, New Orleans,1982: 26~29
[18] Quandalle P and Besset P. The use of flexible gridding for improved reservoir modeling[J]. Symposium on Reservoir Simulation, 1983:15~18
[19] Pedrosa O A Jr, Aziz K. Use of hybrid grid in reservoir simulation[J]. SPE Reservoir Engineering, 1986:611~621
[20] Nghiem L, Collins D A and Sharma R Seventh SPE comparative solution project: modeling of horizontal wells in reservoir simulation[J]. SPE Symposium on Reservoir Simulation, 1991:17~20
[21] Quandalle P Eighth SPE comparative solution project: gridding techniques in reservoir simulation[J]. SPE Symposium on Reservoir Simulation, 1993:33~38
[22] Collins D A, Nghiem L X, Sharma R, et al. Field scale simulation of horizontal wells with hybrid grids[J]. SPE Symposium on Reservoir Simulation, 1991:17~20
[23] Hegre T M, Dalen V and Henriquez A. Generalized trasmissibilities for distorted grids in resewoir simulation[J]. SPE Annual Technical Conference and Exhibitin, 1986:25~30
[24] Rozon B J. A generalized finite volume discretization method for reservoir simulation[J]. SPE Symposium on Reservoir Simulation, 1989:6~8
[25] Aavatsmark I. Doscretization on non-orthogonal quadrilateral grids for inhomogeneous anisotropic media[J]. J. Comp. Phys. 1996, 127: 2~14
[26] Heinemann Z E, Brand C, Munka M et al. Modelling reservoir geometry with irregular grids[J]. SPE Symposium on Reservoir Simulation, 1989: 6~8
[27] Heinemann Z E, Brand C W, Munka M, et al. Modelling reservoir geometry with irregular grids[J]. SPE Reservoir Engineering, 1991: 225~232
[28] Aeirnbacher F X, Heinemann Z E. Time-dependent incorporation of locally irregular grids in large reservoir simulation models[J]. SPE Symposium on Reservoir Simulation, 1993:35~40
[29] Palagi C I, Aziz K. Use of voronoi grid in reservoir simulation[J]. SPE Annual Technical Conference and Exhibitin, 1991:6~9
[30] Palagi C L, Aziz K. The modeling of vertical and horizontal wells with voronoi grid[J]. Western Regional Meeting, 1992:2~8
[31] Paper SPE25259.Palagi C L, Ballin P R, Aziz K. The modeling of flow in heterogeneous reservoirs with voronoi grid[J]. SPE Symposium on Reservoir Simulation, 1993:35~37
[32] Palagi C L, Aziz K. Modeling vertical and horizontal wells with voronoi grid[J]. SPE Reservoir Engineering, 1994:15~21.
[33] Verma S. A flexible gridding scheme for reservoir simulation[J]. SPE Intl. Student Paper Contest, 1995: 657~672
[34] Economides M J, Deimbacher F X, Brand C W et al. Comprehensive simulation of horizontal wells performance[J]. SPE Annual Technical Conference and Exhibitin, 1990:23~26.
[35] Economides M J, Deimbacher F X, Brand C W et al. Comprehensive simulation of horizontal wells performance[J]. SPE Formation Evaluation, 1991:418~426
[36] Kocberber S, Collins R E. Gas well test analysis in complex heterogeneous reservoirs[J]. SPE Gas Technology Symposium, 1991:23~25
[37] Kocberber S. A finite-element black oil simulation system for heterogeneous reservoir with horizontal wells having vertical hydraulic fractures[J]. SPE Symposium on Reservoir Simulation, 1993:66~72
[38] Chavent G. Discontinuous and mixed finite elements for two-phase incompressible flow[J]. SPE Symposium on Reservoir Simulation, 1987:255~270
[39] Darlow B L, Ewing R E and Wheeler M F. Mixed finite element method for miscible displacement problems in porous media[J]. Society of Petroleum Engineers Journal, 1984:391~398
[40] Ewing R E, Wheeler M F. Computional aspects of mixed finite element methods[J]. Numerical Methods for Scientific Computing, 1983:302~320
[41]张烈辉,李允.裂缝性油藏水平井数值模拟的进展和展望[J].西南石油学院学报.1997,19(4):48~52
[42]尹定.不规则多边形有限差分网格方法及其在油藏数值模拟中的应用[J].石油学报,1990,11(3):82~86
[43]凌建军,吴敬轩.网格方向性对水驱油油藏数值模拟结果的影响[J].江汉石油学院学报.1990,12(1):40~45
[44]王经荣,李允.混合网格技术在低渗透油藏数值模拟中的应用方法研究[J].石油勘探与开发.1999,26(6):51~54
[45]张烈辉,杜志敏,代艳英.一个可靠的水平井混合网格模型[J].石油学报, 1997, 18(3):77~82
[46]刘立明,廖新维.混合PEBI网格精细油藏数值模拟应用研究[J].石油学报. 2003, 24(3):64~67
[47]向祖平,张烈辉,陈中华,等.油藏任意约束平面域PEBI网格的生成算法[J].西南石油学院学报[J].2006,28(2):32~35.
[48]刘红卫,李爱华,赵国忠.角点网格传导率计算技术研究[J].大庆石油地质与开发[J], 2005,24(6):35~36
[49]李玉坤,姚军,黄朝琴.油水两相渗流问题的无网格伽辽金法[J].水动力学研究与进展A辑. 2006, 21(6):796~804
[50]李玉坤,姚军,黄朝琴,等.油藏渗流问题的无网格法分析[J].中国石油大学学报(自然科学版). 2007, 31(2):95~104
[51] Tsai V. J. Delaunay D. Triangulations in TIN Creation: an Overview and a Linear-time Algorithm[J]. Int. J. of GIS, 1993, 7(6):501~524
[52] Lawson C. L. Software for C’Surface Interpolation[M]. Mathematical Software III. J.Rice, Ed. New York,Academic Press,1977
[53] Lingas A. The Greedy and Delaunay Triangulations are not Bad in the Average Case[J]. Information Processing Letters, 1986(22) :25~31
[54] Green P. J. Sibson R. Computing Dirichlet Tessellations in the Plane[J]. The Computer Journal, 1978, 21(2):168~173
[55] Bowyer A. Computing Dirichlet Tessellations[J], Computer Journal, 1981,24,:162~166
[56] Watson D F. Computing the n-dimension Delaunay Tesselation with Application to Voronoi Polytopes[J]. Computer Journal, 1981(24):167~172
[57] Shamos M I. Hoey D. Closest point Problems[J], In: Proceedings of the 16th Annual Symposium on the Foundations of Computer Science, 1975, 151~162
[58] Avis D. Toassaint T. An efficient algorithm for decomposing a polygon into star-shaped polygons[J] J. Pattern Recognition, 1981, 13(6):395~398
[59] Lo S H. Generating quadrilateral elements on plane and over curved surfaces[J]. Computers & Structures, 1989, 31(3):421~426.
[60]李玉坤,姚军.复杂断块油藏Delaunay三角网格自动剖分技术[J].油气地质与采收率, 2006, 13(3):58~60
[61] Gordon W J, Hall C A. Construction of curvilinear coordinate systems and applications to mesh generation[J]. Int. J. Num. Meth. Eng., 1973, 7(5): 461~477
[62]闵卫东,唐泽圣.三角形网格转化为四边形网格[J].计算机辅助设计与图形学学报. 1996, 8(1):1~6
[63]韩大匡,陈钦雷,闫存章.油藏数值模拟基础[M].北京:石油工业出版社, 1993: 226~231
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