气相爆轰高阶中心差分-WENO组合格式自适应网格方法研究
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摘要
本文针对气相爆轰问题,主要研究采用高阶中心差分-WENO组合格式和自适应网格方法,数值模拟二维和三维气相爆轰波的结构.
高阶中心差分-WENO组合格式有效地将高阶中心差分格式和加权基本无振荡格式(WENO)组合起来,在间断区域使用WENO格式计算通量,在光滑区域使用中心差分格式计算通量,重点研究组合方法.在组合方法上通过数值试验比较了多种选择,并分析了不同数值实验结果产生的原因.本文最后选择了优化后的一组组合参数,并结合一种基于流场结构特征的自适应网格技术用于数值计算.通过计算一维,二维激波问题,研究了这种方法的精度和效率.数值试验表明,这种方法精度高,分辨率高,计算量小.
本文将高阶中心差分-WENO组合格式和自适应网格方法应用于气相爆轰数值计算.数值模拟二维和三维气相爆轰波非定常结构.数值模拟结果表明,本文发展的这种方法计算结果正确,清晰地反映了爆轰波面复杂的波系结构,以及周期性振荡过程,获得了较为满意的效果,计算结果表明本文的方法具有高精度,高分辨率和高效率的特点,在气相爆轰数值模拟中具有良好的应用前景.
In this thesis, a high order hybrid Central-WENO AMR method is presented for the numerical simulation of two- and three-dimensinal gaseous detonation structures.
The hybrid Central-WENO finite difference scheme composes the two schemes effectively where high gradients regions are computed with WENO scheme in order to capture the discontinuities while smooth regions are computed with more efficient and accurate central finite difference scheme. The thesis focuses on the composition mode, and chooses optimal transition function and parameters through numerical test cases. The adaptive mesh refinement grid is based on flow field structure.
In order to test the performance of the method, including accuracy, resolution and efficiency, one- and two-dimensional shock-dynamic examples are calculated. The results have proved that the hybrid scheme with AMR method has good property of high-order, high-resolution, and high-efficiency.
The hybrid method has been used in the numerical simulation of two- and three-dimensinal unsteady gaseous detonation. The numerical results have shown correctly and clearly the complex wave structures and dynamic physical processes. The method has good prospects for application in gaseous detonation.
高阶中心差分-WENO组合格式有效地将高阶中心差分格式和加权基本无振荡格式(WENO)组合起来,在间断区域使用WENO格式计算通量,在光滑区域使用中心差分格式计算通量,重点研究组合方法.在组合方法上通过数值试验比较了多种选择,并分析了不同数值实验结果产生的原因.本文最后选择了优化后的一组组合参数,并结合一种基于流场结构特征的自适应网格技术用于数值计算.通过计算一维,二维激波问题,研究了这种方法的精度和效率.数值试验表明,这种方法精度高,分辨率高,计算量小.
本文将高阶中心差分-WENO组合格式和自适应网格方法应用于气相爆轰数值计算.数值模拟二维和三维气相爆轰波非定常结构.数值模拟结果表明,本文发展的这种方法计算结果正确,清晰地反映了爆轰波面复杂的波系结构,以及周期性振荡过程,获得了较为满意的效果,计算结果表明本文的方法具有高精度,高分辨率和高效率的特点,在气相爆轰数值模拟中具有良好的应用前景.
In this thesis, a high order hybrid Central-WENO AMR method is presented for the numerical simulation of two- and three-dimensinal gaseous detonation structures.
The hybrid Central-WENO finite difference scheme composes the two schemes effectively where high gradients regions are computed with WENO scheme in order to capture the discontinuities while smooth regions are computed with more efficient and accurate central finite difference scheme. The thesis focuses on the composition mode, and chooses optimal transition function and parameters through numerical test cases. The adaptive mesh refinement grid is based on flow field structure.
In order to test the performance of the method, including accuracy, resolution and efficiency, one- and two-dimensional shock-dynamic examples are calculated. The results have proved that the hybrid scheme with AMR method has good property of high-order, high-resolution, and high-efficiency.
The hybrid method has been used in the numerical simulation of two- and three-dimensinal unsteady gaseous detonation. The numerical results have shown correctly and clearly the complex wave structures and dynamic physical processes. The method has good prospects for application in gaseous detonation.
引文
[1]孙锦山,朱建士,理论爆轰物理,国防工业出版社,1995.
[2]李维新,一维不定常流与冲击波,国防工业出版社,北京,2003.
[3]水鸿寿,一维流体力学差分方法,国防工业出版社,北京,1998.
[4]S.K.Godunov,A finite difference method for computation of discontinuous solutions of the equations ofluid dynamics,Mat.Sb.,vol.47,pp.271-306,1959.
[5]A.Harten,High resolution schemes for hyperbolic conservation laws,J.Comp.Phys,vol.49,pp.357-393,1983.
[6]刘儒勋,舒其望,计算流体力学新方法.科学出版社,北京,2003.
[7]P.R.Woodward,P.Colena,The piecewise parabolic method(PPM)for gas-dynamical simulations,J.Comp.Phys,vol.54,pp.174-201,1984.
[8]P.R.Woodward,P.Colella,The numerical simulation of two-dimensional fluid flow with strong shck,J.Comp.Phys.,vol.54,pp.115-173,1984
[9]A.Harten,B.Engquist,S.Osher R.Chakravarthy,uniformly high-order accurate essentially non-oscillatory Schemes,J.Comp.Phys,vol.71,pp.231-303,1987.
[10]C-W.Shu,Essentially Non-Oscillatory and Weighted Essentially Non-Oscillatory Schemes for Hyperbolic Conservation Laws,ICASE Report NO.97-65.
[11]E.F.Toro,Riemann Solvers and Numerical Methods for Fluid Dynamics.Springer-Verlag.Second Edition.June 1999.
[12]V.N.Gamezo,E.S.Oran,Two-dimensional reactive flow dynamics in cellular detonation waves,Shock Waves,vol.9,pp.11-17,1999.
[13]V.Deledicque,M.V.Papalexandris,Computational study of three-dimensional gaseous detonation structures,Combustion and Flame,vol.144,pp.821-837,2006
[14]M.Arienti,J.E.Shepherd,A numerical study of detonation diffraction,J.Fluid Mech,vol.529,pp.117-146,2005.
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[17]A.M.Khokhlov,J.M.Austin,F.Pintgen,and J.E.Shepherd.Numerical study of the detonation wave structure in ethylene-oxvgen mixtures.42nd AIAA Aerospace Sciences Meeting and Exhibit,2004,AIAA 2004-0792.
[18]王昌建,徐胜利,矩形管内临界爆轰动力学数值分析,高压物理学报,vol.20,no.2,2006.
[19]胡宗民,孙宇峰,郭长铭,张德良,气相爆轰波传播特性的数值模拟及实验对照,空气动力学学报,vol.23,no.2,2005.
[20]王春,张德良,姜宗林,爆轰波平掠惰性气体界面及其解耦现象的数值研究,爆炸与冲击,vol.6.2006.
[21]Ralf Deiterding,Numerical structure analysis of regular hydrogen-oxygen detonations,WSSCI Fall 2003 Meeting:Session 03F-28.
[22]R.Deiterding,An adaptive Cartesian detonation solver for fluid-structure interaction simulation on distributed memory computers,In A.Deane et al,editors,Parallel Computational Fluid Dynamics-Theory and Application,Proc.Parallel CFD 2005 Conference,pages 333-340,Elsevier.2006.
[23]Z.C.Zhang,S.T.Yu John,H.Ye,S.C.Chang,Direct calculations of two-and three-dimensional detonations by an extended CE/SE method,AIAA 2001-0476.
[24]M.J.Berger,Joseph Oliger,Adaptive mesh refinement for hyperbolic partial differential equations,J.Comp.Phys,vol.53,pp.484-512,1984.
[25]M.J.Berger,P.Collella,Local adaptive mesh refinement for shock hydrodynamics.J.Comp.Phys,vol.82,pp.64-84,1989.
[26]J.Bell,M.J.Berger,J.Saltzman,M.Welcome,Three-dimensional adaptive mesh refinement for hyperbolic conservational laws.SIAM J.Sci.Comput,vol.15,pp.127.138,1994.
[27]M.J.Berger,Accuracy,Adaptive Methods and CompIex Geometry.Proc.1~(st) AFOSR Confcrence on Dynamic Motion CFD,Rutgers University,L.Sakell and D.Knight,editors,June,1996.
[28]M.Berger,M.Aftosmis,Aspects and aspect ratios of artesian mesh methods,Proceedings of the 16~(th) International Conf.on Num.Meth.In Fluid Dynamics.Jul 1998.
[29]宫翔飞,张树道,江松,界面捕捉Level Set方法的AMR数值模拟,计算物理,vol.23,2006.
[30]T.Plewa Adaptive Mesh Refinement-Theory and Applications,Springer 2004.
[31]R.Liska,B.Wendroff,Comparisonof several difference schemes on 1D and 2D test problems for the Euler equations,SIAM J.Sci.Comput,vol.25,no.3,pp.995-1017,2003.
[32]R.Liska,B.Wendroff,Composite schemes for conservation laws.SIAM J.Num.Anal,vol.30,pp.2250-2271,1998.
[33]王泽晖等,关于气动声学数值计算的方法和进展,力学季刊,vol.24,pp.219-226,2003.
[34]D.J.Hill,D.I.Pullin,Hybrid tuned center-difference-WENO method for large eddy simulations in the presence of strong Shocks,J.Comp.Phys.vol.194,pp.435-450,2004
[35]C.Pantano,R.Deiterding,D.J.Hill,D.I.pullin,A low numerical dissipation patch-based adaptive mesh refinement method for large-eddy simulation of compressible flows,J.Comp.phys,vol.221,pp.63-87,2007.
[36]G.S.Jiang,C.W.Shu,Efficient implementation of Weighted ENO Schemes,J.Com.Phys,vol.126,pp.202-228,1996.
[37]C.K.Tam,J.C.Webb,Dispersion-relation-preserving finite difference schemes for computational acoustics.J.Com.Phys.vol.107,pp.262-281,1993
[38]J.Qiu,C-W.Shu,On the Construction,Comparison,and Local Characteristic Decomposition for High-Order Central WENO Schemes,J.Com.Phys,vol.183,pp.187-209,2002.
[39]G.J.Sharpe,Transverse waves in numerical simulations of cellular detonations,J.Fluid Mech,vol.447,pp.31-51,2001.
[40]W.J.Coirier,An adaptively-refined,Cartesian,cell-based scheme for the Euler and Navier-Stokes equations,NASA Report TM-106754,1994.
[41]Shengtai Li,J.Mac Hyman,Adaptive mesh refinement for finite difference WENO schemes,Los Alamos Laboratory Report LA-UR-03-8927.
[42]M.G.Edwards,J.T.Oden,L.Demkowicz,An h-r adaptive approximate Riemann solver for the Euler equations in two dimensions,SIAM J.Sci.Comput,vol.14,no.1,pp185-217,1993.
[43]R.Keppens,M.Nool,G.Toth,J.P.Goedboed,Adaptive mesh refinement for conservative systems:multi-dimensional efficiency evaluation.2002.
[44]C.A.Eckett,J.J.Quirk,J.E.Shepherd,The role of unsteadiness in direct initiation of gaseous detonations,J.Fluid Mech,vol 421,pp.147-183,2000.
[45]Bram van Leer,Upwind and high-resolution methods for compressible flow:from donor cell to residual-distribution Schemes,Communications in Comp.Phys,vol.1,no.2,pp.192-206,2006.
[46)D.W.Stamps,S.E.Slezak,Sheldon R.Tieszen,Observations of the cellular structure of fuel-air detonations,Combustion and Flame.vol.144,pp.289-298,2006.
[47]李沁,张涵信,高树椿,一种混合型四阶格式,基于特征的边界条件及其应用,空气动力学学报,vol.18,no.2,2000.
[48]P.Colella,D.T.Graves,B.J.Keen,D.Modiano,A Cartesian grid embedded boundary method for hyperbolic conservation laws,J.Comp.Phys,vol.211,pp.347-366,2006.
[49]Keith A.Gonthier,J.M.Powers,A high-resolution ntmrerical method for a two-phase model of deflagration-to,detonation transition,J.Comp.Phys,vol163,pp.376-433,2000
[50]O.V.Vasilev,T.S.Lund,P.Moin,A general class of commutative filners for LES in complex geometries,J.Comp.Phys,vol.146,pp.82-104,1998.
[51]A.K.Kapila,D.W.Schwendeman,J.B.Bdzil,W.D.Henshaw,A study of detonation diffraction in the ignition-and-growth model,20th Intemational colloquium on the Dynamics of Explosions and Reactive SyStems,2005.
[52]William H.Calhoon,Neeraj Sinha,Detonation wave propagation in concentration gradients,AIAA-2005-1167.
[53]B.Koren,M.R.Lewis,E.H.van Brummelen,B.van Leer,Riemann-problem and leve-set approaches for homentropc two-fnuid flow computations,J.Comp.Phys,vol.181,pp.654-674,2002.
[54]J.E.Reaugh,Macro-scale reactive flow model for high-explosive detonation in support of ASCI weapon safety milepost,Lawlrence Livermore National Laboratory Report,UCRL-ID-146735.2002.
[55]R.B.Pember,J.B.Bell,P.Colella,W.Y.Crutchfield,M.L.Welcome,An adaptive Cartesian grid method for unsteady compressible fiow in Irregular regions,J.Comp.Phys,vol.120,pp.278-304,1995.
[56]W.M.Howard,L.E.Fried,P.C.Souers,Kinetic modeling of non-ideal explosives,Lawrence Livermore National Laboratory Report,UCRL-JC-132512,1999.
[57]J.B.Bdzil,R.Menikoff,S.F.Son,A.K.Kapila,D.S.Stewart,Two-phase modeling of deflagration-to-detonation transition in granular materials:A critical examination of modeling issues,Physics of Fluid,vol,ll,no.2,1999.
[58]G.H.Schmidt,F.J.Jacobs,Adaptive local grid refinement and munlti-grid in numerical reservoir simulation,J.Comp.Phys,vol.77,pp.140-165,1988
[59]Nail K.Yamaleev,Mark H.Carpenter,ON accuracy of adaptive grid methods for captures Shocks,NASA Report,TM-2002-211415.
[60]Wildon Fickett,The polymorphic detonation,Los Alamos Laboratory Report,LA-6859-MS,1977.
[61]J.Nordstrom,M.H.Carpenter Boundary and interface conditions for high order finite difference methods applied to the Euler and Navier-Stokes equations,ICASE Report NO.98-19,1998.
[62]J.M.Austin,F.Pintgen,J.E.Shepherd,Reaction zones in highly unstable detonations,Proceedings of the 30th Combustion Symposium,vol2,pp.1849-1857,2005.
[2]李维新,一维不定常流与冲击波,国防工业出版社,北京,2003.
[3]水鸿寿,一维流体力学差分方法,国防工业出版社,北京,1998.
[4]S.K.Godunov,A finite difference method for computation of discontinuous solutions of the equations ofluid dynamics,Mat.Sb.,vol.47,pp.271-306,1959.
[5]A.Harten,High resolution schemes for hyperbolic conservation laws,J.Comp.Phys,vol.49,pp.357-393,1983.
[6]刘儒勋,舒其望,计算流体力学新方法.科学出版社,北京,2003.
[7]P.R.Woodward,P.Colena,The piecewise parabolic method(PPM)for gas-dynamical simulations,J.Comp.Phys,vol.54,pp.174-201,1984.
[8]P.R.Woodward,P.Colella,The numerical simulation of two-dimensional fluid flow with strong shck,J.Comp.Phys.,vol.54,pp.115-173,1984
[9]A.Harten,B.Engquist,S.Osher R.Chakravarthy,uniformly high-order accurate essentially non-oscillatory Schemes,J.Comp.Phys,vol.71,pp.231-303,1987.
[10]C-W.Shu,Essentially Non-Oscillatory and Weighted Essentially Non-Oscillatory Schemes for Hyperbolic Conservation Laws,ICASE Report NO.97-65.
[11]E.F.Toro,Riemann Solvers and Numerical Methods for Fluid Dynamics.Springer-Verlag.Second Edition.June 1999.
[12]V.N.Gamezo,E.S.Oran,Two-dimensional reactive flow dynamics in cellular detonation waves,Shock Waves,vol.9,pp.11-17,1999.
[13]V.Deledicque,M.V.Papalexandris,Computational study of three-dimensional gaseous detonation structures,Combustion and Flame,vol.144,pp.821-837,2006
[14]M.Arienti,J.E.Shepherd,A numerical study of detonation diffraction,J.Fluid Mech,vol.529,pp.117-146,2005.
[15]E.O.Morano,J.E.Shepherd,Effct of reaction rate periodicity on detonation propagaticn.12th APS Topical Group Conference on Shock Compression of Condensed Matter,Atlanta,GA,June 24-29.2001.
[16]V.N.Gamezo,D.Desbordes,E.S.Oran,Formation and Evolution of two-dimensional Cellular detonations.Combustion and Flame,vol.116,no.1,pp.154-165,1999.
[17]A.M.Khokhlov,J.M.Austin,F.Pintgen,and J.E.Shepherd.Numerical study of the detonation wave structure in ethylene-oxvgen mixtures.42nd AIAA Aerospace Sciences Meeting and Exhibit,2004,AIAA 2004-0792.
[18]王昌建,徐胜利,矩形管内临界爆轰动力学数值分析,高压物理学报,vol.20,no.2,2006.
[19]胡宗民,孙宇峰,郭长铭,张德良,气相爆轰波传播特性的数值模拟及实验对照,空气动力学学报,vol.23,no.2,2005.
[20]王春,张德良,姜宗林,爆轰波平掠惰性气体界面及其解耦现象的数值研究,爆炸与冲击,vol.6.2006.
[21]Ralf Deiterding,Numerical structure analysis of regular hydrogen-oxygen detonations,WSSCI Fall 2003 Meeting:Session 03F-28.
[22]R.Deiterding,An adaptive Cartesian detonation solver for fluid-structure interaction simulation on distributed memory computers,In A.Deane et al,editors,Parallel Computational Fluid Dynamics-Theory and Application,Proc.Parallel CFD 2005 Conference,pages 333-340,Elsevier.2006.
[23]Z.C.Zhang,S.T.Yu John,H.Ye,S.C.Chang,Direct calculations of two-and three-dimensional detonations by an extended CE/SE method,AIAA 2001-0476.
[24]M.J.Berger,Joseph Oliger,Adaptive mesh refinement for hyperbolic partial differential equations,J.Comp.Phys,vol.53,pp.484-512,1984.
[25]M.J.Berger,P.Collella,Local adaptive mesh refinement for shock hydrodynamics.J.Comp.Phys,vol.82,pp.64-84,1989.
[26]J.Bell,M.J.Berger,J.Saltzman,M.Welcome,Three-dimensional adaptive mesh refinement for hyperbolic conservational laws.SIAM J.Sci.Comput,vol.15,pp.127.138,1994.
[27]M.J.Berger,Accuracy,Adaptive Methods and CompIex Geometry.Proc.1~(st) AFOSR Confcrence on Dynamic Motion CFD,Rutgers University,L.Sakell and D.Knight,editors,June,1996.
[28]M.Berger,M.Aftosmis,Aspects and aspect ratios of artesian mesh methods,Proceedings of the 16~(th) International Conf.on Num.Meth.In Fluid Dynamics.Jul 1998.
[29]宫翔飞,张树道,江松,界面捕捉Level Set方法的AMR数值模拟,计算物理,vol.23,2006.
[30]T.Plewa Adaptive Mesh Refinement-Theory and Applications,Springer 2004.
[31]R.Liska,B.Wendroff,Comparisonof several difference schemes on 1D and 2D test problems for the Euler equations,SIAM J.Sci.Comput,vol.25,no.3,pp.995-1017,2003.
[32]R.Liska,B.Wendroff,Composite schemes for conservation laws.SIAM J.Num.Anal,vol.30,pp.2250-2271,1998.
[33]王泽晖等,关于气动声学数值计算的方法和进展,力学季刊,vol.24,pp.219-226,2003.
[34]D.J.Hill,D.I.Pullin,Hybrid tuned center-difference-WENO method for large eddy simulations in the presence of strong Shocks,J.Comp.Phys.vol.194,pp.435-450,2004
[35]C.Pantano,R.Deiterding,D.J.Hill,D.I.pullin,A low numerical dissipation patch-based adaptive mesh refinement method for large-eddy simulation of compressible flows,J.Comp.phys,vol.221,pp.63-87,2007.
[36]G.S.Jiang,C.W.Shu,Efficient implementation of Weighted ENO Schemes,J.Com.Phys,vol.126,pp.202-228,1996.
[37]C.K.Tam,J.C.Webb,Dispersion-relation-preserving finite difference schemes for computational acoustics.J.Com.Phys.vol.107,pp.262-281,1993
[38]J.Qiu,C-W.Shu,On the Construction,Comparison,and Local Characteristic Decomposition for High-Order Central WENO Schemes,J.Com.Phys,vol.183,pp.187-209,2002.
[39]G.J.Sharpe,Transverse waves in numerical simulations of cellular detonations,J.Fluid Mech,vol.447,pp.31-51,2001.
[40]W.J.Coirier,An adaptively-refined,Cartesian,cell-based scheme for the Euler and Navier-Stokes equations,NASA Report TM-106754,1994.
[41]Shengtai Li,J.Mac Hyman,Adaptive mesh refinement for finite difference WENO schemes,Los Alamos Laboratory Report LA-UR-03-8927.
[42]M.G.Edwards,J.T.Oden,L.Demkowicz,An h-r adaptive approximate Riemann solver for the Euler equations in two dimensions,SIAM J.Sci.Comput,vol.14,no.1,pp185-217,1993.
[43]R.Keppens,M.Nool,G.Toth,J.P.Goedboed,Adaptive mesh refinement for conservative systems:multi-dimensional efficiency evaluation.2002.
[44]C.A.Eckett,J.J.Quirk,J.E.Shepherd,The role of unsteadiness in direct initiation of gaseous detonations,J.Fluid Mech,vol 421,pp.147-183,2000.
[45]Bram van Leer,Upwind and high-resolution methods for compressible flow:from donor cell to residual-distribution Schemes,Communications in Comp.Phys,vol.1,no.2,pp.192-206,2006.
[46)D.W.Stamps,S.E.Slezak,Sheldon R.Tieszen,Observations of the cellular structure of fuel-air detonations,Combustion and Flame.vol.144,pp.289-298,2006.
[47]李沁,张涵信,高树椿,一种混合型四阶格式,基于特征的边界条件及其应用,空气动力学学报,vol.18,no.2,2000.
[48]P.Colella,D.T.Graves,B.J.Keen,D.Modiano,A Cartesian grid embedded boundary method for hyperbolic conservation laws,J.Comp.Phys,vol.211,pp.347-366,2006.
[49]Keith A.Gonthier,J.M.Powers,A high-resolution ntmrerical method for a two-phase model of deflagration-to,detonation transition,J.Comp.Phys,vol163,pp.376-433,2000
[50]O.V.Vasilev,T.S.Lund,P.Moin,A general class of commutative filners for LES in complex geometries,J.Comp.Phys,vol.146,pp.82-104,1998.
[51]A.K.Kapila,D.W.Schwendeman,J.B.Bdzil,W.D.Henshaw,A study of detonation diffraction in the ignition-and-growth model,20th Intemational colloquium on the Dynamics of Explosions and Reactive SyStems,2005.
[52]William H.Calhoon,Neeraj Sinha,Detonation wave propagation in concentration gradients,AIAA-2005-1167.
[53]B.Koren,M.R.Lewis,E.H.van Brummelen,B.van Leer,Riemann-problem and leve-set approaches for homentropc two-fnuid flow computations,J.Comp.Phys,vol.181,pp.654-674,2002.
[54]J.E.Reaugh,Macro-scale reactive flow model for high-explosive detonation in support of ASCI weapon safety milepost,Lawlrence Livermore National Laboratory Report,UCRL-ID-146735.2002.
[55]R.B.Pember,J.B.Bell,P.Colella,W.Y.Crutchfield,M.L.Welcome,An adaptive Cartesian grid method for unsteady compressible fiow in Irregular regions,J.Comp.Phys,vol.120,pp.278-304,1995.
[56]W.M.Howard,L.E.Fried,P.C.Souers,Kinetic modeling of non-ideal explosives,Lawrence Livermore National Laboratory Report,UCRL-JC-132512,1999.
[57]J.B.Bdzil,R.Menikoff,S.F.Son,A.K.Kapila,D.S.Stewart,Two-phase modeling of deflagration-to-detonation transition in granular materials:A critical examination of modeling issues,Physics of Fluid,vol,ll,no.2,1999.
[58]G.H.Schmidt,F.J.Jacobs,Adaptive local grid refinement and munlti-grid in numerical reservoir simulation,J.Comp.Phys,vol.77,pp.140-165,1988
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