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基于高阶Taylor展开提出一种改进的光滑粒子流体动力学（CSPH_HT）方法，并试探性地应用于涉及界面变形的黏弹性聚合物熔体充模过程的模拟.首先，针对传统光滑粒子流体动力学（SPH）方法和已有改进SPH方法的缺点，基于高阶Taylor展开，建立了一种新的改进SPH格式.然后通过基准算例验证了新的改进SPH方法的优势.最后，运用改进SPH方法模拟了环形腔和方形腔内的聚合物熔体充模过程，展示了XPP熔体和FENE-P熔体充模过程中界面演化的不同之处，分析了型腔参数对流动的影响.数值结果表明：CSPH_HT方法具有较高的数值精度和较好的数值稳定性，XPP（extended pom-pom）熔体和有限拉伸非线性弹簧（FENE-P）熔体具有不同的流动特性，型腔参数的微小变化能够对流动造成很大影响.In this work, an improved smoothed particle hydrodynamics (SPH) method based on higher order Taylor expansion (CSPH_HT) is proposed and tentatively applied to the filling process of the viscoelastic fluid. Owing to the disadvantages of the traditional SPH method and the presented corrected SPH methods, the CSPH_HT method based on the higher order Taylor expansion is proposed and described in detail. In order to illustrate the validity and merits of the CSPH_HT method, two benchmark problems are simulated and discussed. The numerical results show that the proposed CSPH_HT method has higher numerical accuracy and better stability. Subsequently, the proposed improved SPH method is extended to simulate the filling processes of the viscoelastic fluid in the ring-shaped mold, for the purpose of exhibiting the capacity of the proposed method. The extended pom-pom (XPP) model and finitely extensible nonlinear elastic-Peterlin (FENE-P) model fluid are all considered in this case, in which the viscoelastic fluid flow and extra stress are shown. The differences in fluid flow between the XPP model and FENE-P model are also discussed. Finally, the filling process of the viscoelastic fluid in the square mold with single inlet or two inlets are tentatively simulated. The differences between the filling process of XPP fluid and the filling process of FENE-P fluid are shown, and the influences of the parameters of the mold on the flow are analyzed. Especially, the influences of locations and sizes of two inlets on the filling process of viscoelastic fluid are illustrated. The XPP model fluid and FENE-P model fluid show different characteristics in the filling process and small change of the size of the mold can lead to obvious change of the flow.
[1] Carvalho D M, Tomé M F, Cuminato J A, Castelo A, Ferreira V G 2004TEMA:Tendên. Matemá. Aplica. Comput. 5 195
[2] John D A (translated by Wu S P, Liu Z S) 2007Computational Fluid Dynamics:the Basics with Applications (Beijing:China Machine Press) (in Chinese)[约翰D安德森著(吴颂平, 刘赵森译) 2007计算流体力学基础及其应用(北京:机械工业出版社)]
[3] Liu R F, Wang Z F 2001The Capture of Moving Interface and the Numerical Methods (Hefei:University of Science and Technology of China Press)[刘儒勋, 王志峰2001运动界面追踪与数值方法(合肥:中国科学技术大学出版社)]
[4] Fu D X, Ma Y W 2002Computational Fluid Mechanics (Beijing:Higher Education Press) (in Chinese)[傅德薰, 马延文2002计算流体力学(北京:高等教育出版社)]
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[7] Li Q 2012Ph. D. Dissertation (Xi'an:Northwestern Polytechnical University) (in Chinese)[李强2012博士学位论文(西安:西北工业大学)]
[8] Li S F, Liu W K 2002Appl. Mech. Rev. 55 1
[9] Liu G R, Liu M B 2003Smoothed Particle Hydrodynamics:A Mesh-free Particle Method (Singapore:World Scientific)
[10] Monaghan J J 1988Comput. Phy. Commun. 48 89
[11] Fan X J, Tanner R I, Zheng R 2010J. Non-Newton. Fluid Mech. 165 219
[12] Liu W K, Jun S, Zhang Y F 1995Int. J. Num. Meth. Flu. 20 1081
[13] Chen J K, Beraun J E 2000Comput. Meth. Appl. Mech. Eng. 190 225
[14] Batra R C, Zhang G M 2007Comput. Mech. 40 531
[15] Zhang G M, Batra R C 2009Comput. Mech. 43 321
[16] Liu M B, Xie W P, Liu G R 2005Appl. Math. Model. 29 1252
[17] Oishi C M, Martins F P, Tomé M F, Alves M A 2012J. Non-Newton. Fluid Mech. 169-170 91
[18] Ren J L, Lu W G, Jiang T 2015Acta Phys. Sin. 64 080202(in Chinese)[任金莲, 陆伟刚, 蒋涛2015 64 080202]
[19] Yang X F, Liu M B 2012Acta Phys. Sin. 61 224701(in Chinese)[杨秀峰, 刘谋斌2012 61 224701]
[20] Ren J L, Ouyang J, Jiang T 2012Comput. Mech. 49 643
[21] Tomé M F, Mangiavacchi N, Castelo A, Cuminato J A, McKee S 2002J. Non-Newton. Fluid Mech. 106 61
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[1] Carvalho D M, Tomé M F, Cuminato J A, Castelo A, Ferreira V G 2004TEMA:Tendên. Matemá. Aplica. Comput. 5 195
[2] John D A (translated by Wu S P, Liu Z S) 2007Computational Fluid Dynamics:the Basics with Applications (Beijing:China Machine Press) (in Chinese)[约翰D安德森著(吴颂平, 刘赵森译) 2007计算流体力学基础及其应用(北京:机械工业出版社)]
[3] Liu R F, Wang Z F 2001The Capture of Moving Interface and the Numerical Methods (Hefei:University of Science and Technology of China Press)[刘儒勋, 王志峰2001运动界面追踪与数值方法(合肥:中国科学技术大学出版社)]
[4] Fu D X, Ma Y W 2002Computational Fluid Mechanics (Beijing:Higher Education Press) (in Chinese)[傅德薰, 马延文2002计算流体力学(北京:高等教育出版社)]
[5] Harlow F H, Amsden A A 1970J. Comput. Phys. 6 322
[6] Hirt C W, Nichols B D 1981J. Comput. Phys. 39 201
[7] Li Q 2012Ph. D. Dissertation (Xi'an:Northwestern Polytechnical University) (in Chinese)[李强2012博士学位论文(西安:西北工业大学)]
[8] Li S F, Liu W K 2002Appl. Mech. Rev. 55 1
[9] Liu G R, Liu M B 2003Smoothed Particle Hydrodynamics:A Mesh-free Particle Method (Singapore:World Scientific)
[10] Monaghan J J 1988Comput. Phy. Commun. 48 89
[11] Fan X J, Tanner R I, Zheng R 2010J. Non-Newton. Fluid Mech. 165 219
[12] Liu W K, Jun S, Zhang Y F 1995Int. J. Num. Meth. Flu. 20 1081
[13] Chen J K, Beraun J E 2000Comput. Meth. Appl. Mech. Eng. 190 225
[14] Batra R C, Zhang G M 2007Comput. Mech. 40 531
[15] Zhang G M, Batra R C 2009Comput. Mech. 43 321
[16] Liu M B, Xie W P, Liu G R 2005Appl. Math. Model. 29 1252
[17] Oishi C M, Martins F P, Tomé M F, Alves M A 2012J. Non-Newton. Fluid Mech. 169-170 91
[18] Ren J L, Lu W G, Jiang T 2015Acta Phys. Sin. 64 080202(in Chinese)[任金莲, 陆伟刚, 蒋涛2015 64 080202]
[19] Yang X F, Liu M B 2012Acta Phys. Sin. 61 224701(in Chinese)[杨秀峰, 刘谋斌2012 61 224701]
[20] Ren J L, Ouyang J, Jiang T 2012Comput. Mech. 49 643
[21] Tomé M F, Mangiavacchi N, Castelo A, Cuminato J A, McKee S 2002J. Non-Newton. Fluid Mech. 106 61
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