球坐标系下多介质混合物模型的数值模拟
|
摘要
利用多介质混合模型在求解球坐标系下的Riemann问题时,需要考虑界面处压力平衡性弱、奇点处理、状态方程复杂等多个难点。本文将原始基于体积分数的Mie-Grüneisen多介质混合模型扩展到球坐标系下,并对多个细节进行了修正和改进,包括:在界面处对热力学参数进行修正、采用质量分数导出新输送方程、利用质量分数加权计算偏导数、采用相邻网格点的物理量定义奇点等。经过改进后的计算模型,可以得到无振荡的数值解,而且可以准确捕捉到冲击波和界面的位置。另外,使用改进后的质量分数模型比原始的体积分数模型得到的计算结果更准确。
The aim of the paper is to extend the Mie-Grüneisen mixture model to spherical coordinate. As the multi-component mixture model is applied to the Riemann problem under spherical coordinate, many problems need to be taken into account: weak equilibrium, singular point treatment, complex equations of states and so on. In the article, the research work starts from the Mie-Grüneisen mixture model, then extend to the revision and modification about many details, include: revision of the thermo dynamical parameters at interface, deduction of new transport equation by mass fraction, weighting evaluation of partial derivatives by mass fraction, definition of physical parameters by the adjacent grid for singular point and other so on.The seriously modified numerical model, can not only obtain non-oscillation solutions, but also catch the positions of shock wave and interface clearly. In addition, the modified mass fraction model, can get more accurate results than the original model with mass fraction.
The aim of the paper is to extend the Mie-Grüneisen mixture model to spherical coordinate. As the multi-component mixture model is applied to the Riemann problem under spherical coordinate, many problems need to be taken into account: weak equilibrium, singular point treatment, complex equations of states and so on. In the article, the research work starts from the Mie-Grüneisen mixture model, then extend to the revision and modification about many details, include: revision of the thermo dynamical parameters at interface, deduction of new transport equation by mass fraction, weighting evaluation of partial derivatives by mass fraction, definition of physical parameters by the adjacent grid for singular point and other so on.The seriously modified numerical model, can not only obtain non-oscillation solutions, but also catch the positions of shock wave and interface clearly. In addition, the modified mass fraction model, can get more accurate results than the original model with mass fraction.
引文
[1]LIUT G,KHOOB C,YEOK S.Ghost fluid method for strong shock impacting on material interface[J].Journal of Computational Physics,2003,190(2):651-681.DOI:10.1016/S0021-9991(03)00301-2.
[2]SHYUE K M.A fluid-mixture type algorithm for compressible multicomponent flow with Mie-Grüneisen equation of state[J].Journal of Computational Physics,2001,171(2):678-707.DOI:10.1006/jcph.2001.6801.
[3]张宝銔,张庆民,黄风雷.爆轰物理学[M].北京:北京理工大学出版社,2001:160,377-383.
[4]ABGRALL R.How to prevent pressure oscillations in multicomponent flow calculations:a quasi conservative approach[J].Journal of Computational Physics,1996,125(1):150-160.DOI:10.1006/jcph.1996.0085.
[5]SAUREL R,ABGRALL R.A simple method for compressible multifuid flows[J].SIAM Journal on Scientific Computing,1999,21(3):1115-1145.DOI:10.1137/S1064827597323749.
[6]ABGRALL R,KARNI S.Computations of compressible multifluids[J].Journal of Computational Physics,2001,169(2):594-623.DOI:10.1006/jcph.2000.6685.
[7]SAUREL R,ABGRALL R.A multiphase Godunov method for compressible multifluid and multiphase flows[J].Journal of Computational Physics,1999,150(2):425-467.DOI:10.1006/jcph.1999.6187.
[8]柏劲松,陈森华,李平.多介质流体非守恒律欧拉方程组的数值计算方法[J].爆炸与冲击,2001,21(4):265-271.BO Jinsong,CHEN Senhua,LI Ping.Numerical methods of multicomponent flows of non-conservative Euler equations[J].Explosion and Shock Waves,2001,21(4):265-271.
[9]柏劲松,陈森华,李平,等.多介质可压缩流体动力学界面捕捉方法[J].爆炸与冲击,2004,24(1):37-43.BAI Jingsong,CHEN Senhua,LI Ping.Interface capturing method for compressible multi-fluid dynamics[J].Explosion and Shock Waves,2004,24(1):37-43.
[10]梁姗,刘伟,袁礼.七方程可压缩多相流模型的HLLC格式及应用[J].力学学报,2012,44(5):884-895.DOI:10.6052/0459-1879-12-022.LIANG Shan,LIU Wei,YUAN Li.An HLLC scheme for the seven-equation multiphase model and its application to compressible multicomponent flow[J].Chinese Journal of Theoretical and Applied Mechanics,2012,44(5):884-895.DOI:10.6052/0459-1879-12-022.
[11]LIANG S,LIU W,YUAN L.Solving seven-equation model for compressible two-phase flow using multiple GPUs[J].Computers and Fluids,2014,99(7):156-171.DOI:10.1016/j.compfluid.2014.04.021.
[12]刘娜,陈艺冰.多介质流体力学计算的谱体积方法[J].爆炸与冲击,2017,37(1):114-119.DOI:10.11883/1001-1455(2017)01-0114-06.LIU Na,CHEN Yibing.High order spectral volume method for multi-component flows[J].Explosion and Shock Waves,2017,37(1):114-119.DOI:10.11883/1001-1455(2017)01-0114-06.
[13]ELEUTERIO F T.Riemann solvers and numerical methods for fluid dynamics[M].3rd ed.Berlin Heidelberg:Springer,2009:1-40.DOI:10.1007/978-3-540-49834-6.
[14]师华强,宗智,贾敬蓓.水下爆炸冲击波的近场特性[J].爆炸与冲击,2009,29(2):125-130.DOI:10.11883/1001-1455(2009)02-0125-06.SHI Huaqiang,ZONG Zhi,JIA Jingbei.Short-range characters of underwater blast waves[J].Explosion and Shock Waves,2009,29(2):125-130.DOI:10.11883/1001-1455(2009)02-0125-06.
[15]LIU T G,KHOO B C,YEO K S.The numerical simulations of explosion and implosion in air:use of a modified Harten's TVD scheme[J].International Journal for Numerical Methods in Fluids,1999,31(4):661-680.DOI:10.1002/(SICI)1097-0363(19991030)31:4<661::AID-FLD866>3.0.CO;2-G.
[16]LIUT G,KHOOB C,YEOK S.The simulation of compressible multi-medium flow:I:A new methodology with test application to 1D gas-gas and gas-water cases[J].Computers and Fluids,2001,30(3):291-314.DOI:10.1016/S0045-7930(00)00022-0.
[17]FLORES J,HOLT M.Glimm’s method applied to underwater explosion[J].Journal of Computational Physics,1981,44(2):377-387.DOI:10.1016/0021-9991(81)90058-9.
[18]CHIESUM J E,SHIN Y S.Explosion gas bubbles near simple boundaries[J].Shock and Vibration,1997,4(1):11-25.
[19]LIU G R,LIU M B.光滑粒子动力学:一种无网格粒子法[M].韩旭,等译.长沙:湖南大学出版社,2005.
[20]ZAMYSHLYAYEV B V,YAKOVLEV Y S.Dynamic loads in underwater explosion:AD-757183[R].USA:Naval intelligence Support Center,1973.
[2]SHYUE K M.A fluid-mixture type algorithm for compressible multicomponent flow with Mie-Grüneisen equation of state[J].Journal of Computational Physics,2001,171(2):678-707.DOI:10.1006/jcph.2001.6801.
[3]张宝銔,张庆民,黄风雷.爆轰物理学[M].北京:北京理工大学出版社,2001:160,377-383.
[4]ABGRALL R.How to prevent pressure oscillations in multicomponent flow calculations:a quasi conservative approach[J].Journal of Computational Physics,1996,125(1):150-160.DOI:10.1006/jcph.1996.0085.
[5]SAUREL R,ABGRALL R.A simple method for compressible multifuid flows[J].SIAM Journal on Scientific Computing,1999,21(3):1115-1145.DOI:10.1137/S1064827597323749.
[6]ABGRALL R,KARNI S.Computations of compressible multifluids[J].Journal of Computational Physics,2001,169(2):594-623.DOI:10.1006/jcph.2000.6685.
[7]SAUREL R,ABGRALL R.A multiphase Godunov method for compressible multifluid and multiphase flows[J].Journal of Computational Physics,1999,150(2):425-467.DOI:10.1006/jcph.1999.6187.
[8]柏劲松,陈森华,李平.多介质流体非守恒律欧拉方程组的数值计算方法[J].爆炸与冲击,2001,21(4):265-271.BO Jinsong,CHEN Senhua,LI Ping.Numerical methods of multicomponent flows of non-conservative Euler equations[J].Explosion and Shock Waves,2001,21(4):265-271.
[9]柏劲松,陈森华,李平,等.多介质可压缩流体动力学界面捕捉方法[J].爆炸与冲击,2004,24(1):37-43.BAI Jingsong,CHEN Senhua,LI Ping.Interface capturing method for compressible multi-fluid dynamics[J].Explosion and Shock Waves,2004,24(1):37-43.
[10]梁姗,刘伟,袁礼.七方程可压缩多相流模型的HLLC格式及应用[J].力学学报,2012,44(5):884-895.DOI:10.6052/0459-1879-12-022.LIANG Shan,LIU Wei,YUAN Li.An HLLC scheme for the seven-equation multiphase model and its application to compressible multicomponent flow[J].Chinese Journal of Theoretical and Applied Mechanics,2012,44(5):884-895.DOI:10.6052/0459-1879-12-022.
[11]LIANG S,LIU W,YUAN L.Solving seven-equation model for compressible two-phase flow using multiple GPUs[J].Computers and Fluids,2014,99(7):156-171.DOI:10.1016/j.compfluid.2014.04.021.
[12]刘娜,陈艺冰.多介质流体力学计算的谱体积方法[J].爆炸与冲击,2017,37(1):114-119.DOI:10.11883/1001-1455(2017)01-0114-06.LIU Na,CHEN Yibing.High order spectral volume method for multi-component flows[J].Explosion and Shock Waves,2017,37(1):114-119.DOI:10.11883/1001-1455(2017)01-0114-06.
[13]ELEUTERIO F T.Riemann solvers and numerical methods for fluid dynamics[M].3rd ed.Berlin Heidelberg:Springer,2009:1-40.DOI:10.1007/978-3-540-49834-6.
[14]师华强,宗智,贾敬蓓.水下爆炸冲击波的近场特性[J].爆炸与冲击,2009,29(2):125-130.DOI:10.11883/1001-1455(2009)02-0125-06.SHI Huaqiang,ZONG Zhi,JIA Jingbei.Short-range characters of underwater blast waves[J].Explosion and Shock Waves,2009,29(2):125-130.DOI:10.11883/1001-1455(2009)02-0125-06.
[15]LIU T G,KHOO B C,YEO K S.The numerical simulations of explosion and implosion in air:use of a modified Harten's TVD scheme[J].International Journal for Numerical Methods in Fluids,1999,31(4):661-680.DOI:10.1002/(SICI)1097-0363(19991030)31:4<661::AID-FLD866>3.0.CO;2-G.
[16]LIUT G,KHOOB C,YEOK S.The simulation of compressible multi-medium flow:I:A new methodology with test application to 1D gas-gas and gas-water cases[J].Computers and Fluids,2001,30(3):291-314.DOI:10.1016/S0045-7930(00)00022-0.
[17]FLORES J,HOLT M.Glimm’s method applied to underwater explosion[J].Journal of Computational Physics,1981,44(2):377-387.DOI:10.1016/0021-9991(81)90058-9.
[18]CHIESUM J E,SHIN Y S.Explosion gas bubbles near simple boundaries[J].Shock and Vibration,1997,4(1):11-25.
[19]LIU G R,LIU M B.光滑粒子动力学:一种无网格粒子法[M].韩旭,等译.长沙:湖南大学出版社,2005.
[20]ZAMYSHLYAYEV B V,YAKOVLEV Y S.Dynamic loads in underwater explosion:AD-757183[R].USA:Naval intelligence Support Center,1973.