利用level set方法捕捉气、水界面的三维数值研究
|
摘要
本文以高压比、高密度比气、水界面模拟为主要研究对象,基于level set方法捕捉界面,结合流场解算器,采用MGFM和RGFM思想描述气、水界面边界条件,主要开展了以下问题研究。
(1)水下运动激波和气泡(串)相互作用。
(2)初始形状为圆柱形、球形和“V形”圆锥状高温高压气泡在水中膨胀问题。
(3)复杂域高温高压气泡(串)膨胀的分块、并行计算。
主要内容为:
(1)第一章简要介绍了本文研究背景、国内外相关研究进展和本文主要特色。
(2)第二章给出了流场控制方程、界面捕捉level set方程以及外推方程。为满足复杂域计算,还给出了上述方程在任意正交坐标系下的形式。
(3)第三章主要介绍本文采用数值方法和并行计算方法。采用迎风TVD格式求解Euler方程、用五阶WENO格式求解level set方程及其重新初始化方程。在共享存储环境下引入OpenMP库,对计算程序中效率最低的循环迭代实现多核并行计算和通信。
(4)第四章主要给出水下运动激波和气泡(群)相互作用、水下各种初始形状的高温高压气泡膨胀等问题的数值解,共给出了10个算例,包含考核算例。
(5)第五章主要给出了本文主要结论和下一步需研究的工作。
主要创新和特色为:
(1)将二维直角坐标系下的level set方法推广到三维直角坐标系的含气泡、激波流场计算中。
(2)将直角坐标系下的流场控制方程、level set方程和外推方程推广到任意正交坐标系中,并编写了经过算例验证的计算程序。
(3)将MGFM和RGFM思想成功地推广到三维直角坐标系和任意正交坐标系的level set方法中。
(4)实现了任意正交坐标系下level set方法的分块、并行计算,为开展多爆源、水下爆炸场等工程问题计算奠定了坚实的基础。
In a complex domain, three dimensional computations were carried out to study moving shock interacted with gas-water interface and bubble expansion underwater at high pressure and temperature. Based on concept of MGFM (modified ghost fluid method) and RGFM (real ghost fluid method), an approximate Riemann problem was constructed to describe gas-water interface condition with strong discontinuity initially. Level set method was used to track the moving interfaces. Following topics were included in this thesis:
(1) A strong moving shock interacted with bubbles underwater.
(2) Bubble expansion underwater at high pressure and temperature, such as cylindrical, spherical and V-shaped conical bubbles.
(3) Paralleled computation on bubble expansion at high pressure and temperature based on multi-block method.
Some works are summarized as follows:
(1) Brief introduction, related progress on flow interface especially on gas-water and works in this thesis were presented in chapter 1.
(2) In chapter 2, governing equations of flow field, level set method and extrapolated variables were respectively illustrated in Cartesian and body fitted coordinate frames. Meanwhile, MGFM (modified ghost fluid method) and RGFM (real ghost fluid method) approaches are adopted to describe gas-water interface conditions.
(3) In chapter 3, second order TVD and fifth order WENO schemes were respectively introduced to solve Eulerian equations, level set and reinitialized equations for flow-field and gas-water interfaces. Also, parallel and multi-block methods were introduced briefly based on OPENMP methodology.
(4) In chapter 4, benchmark examples and numerical results were discussed on shock interaction with gas-water interface and expansion of bubble underwater at high pressure and temperature. Ten examples were carried out and analyzed in this chapter to show highly resolved gas-water interfaces.
(5) In chapter 5, some conclusions and future works were presented in this thesis.
(1)水下运动激波和气泡(串)相互作用。
(2)初始形状为圆柱形、球形和“V形”圆锥状高温高压气泡在水中膨胀问题。
(3)复杂域高温高压气泡(串)膨胀的分块、并行计算。
主要内容为:
(1)第一章简要介绍了本文研究背景、国内外相关研究进展和本文主要特色。
(2)第二章给出了流场控制方程、界面捕捉level set方程以及外推方程。为满足复杂域计算,还给出了上述方程在任意正交坐标系下的形式。
(3)第三章主要介绍本文采用数值方法和并行计算方法。采用迎风TVD格式求解Euler方程、用五阶WENO格式求解level set方程及其重新初始化方程。在共享存储环境下引入OpenMP库,对计算程序中效率最低的循环迭代实现多核并行计算和通信。
(4)第四章主要给出水下运动激波和气泡(群)相互作用、水下各种初始形状的高温高压气泡膨胀等问题的数值解,共给出了10个算例,包含考核算例。
(5)第五章主要给出了本文主要结论和下一步需研究的工作。
主要创新和特色为:
(1)将二维直角坐标系下的level set方法推广到三维直角坐标系的含气泡、激波流场计算中。
(2)将直角坐标系下的流场控制方程、level set方程和外推方程推广到任意正交坐标系中,并编写了经过算例验证的计算程序。
(3)将MGFM和RGFM思想成功地推广到三维直角坐标系和任意正交坐标系的level set方法中。
(4)实现了任意正交坐标系下level set方法的分块、并行计算,为开展多爆源、水下爆炸场等工程问题计算奠定了坚实的基础。
In a complex domain, three dimensional computations were carried out to study moving shock interacted with gas-water interface and bubble expansion underwater at high pressure and temperature. Based on concept of MGFM (modified ghost fluid method) and RGFM (real ghost fluid method), an approximate Riemann problem was constructed to describe gas-water interface condition with strong discontinuity initially. Level set method was used to track the moving interfaces. Following topics were included in this thesis:
(1) A strong moving shock interacted with bubbles underwater.
(2) Bubble expansion underwater at high pressure and temperature, such as cylindrical, spherical and V-shaped conical bubbles.
(3) Paralleled computation on bubble expansion at high pressure and temperature based on multi-block method.
Some works are summarized as follows:
(1) Brief introduction, related progress on flow interface especially on gas-water and works in this thesis were presented in chapter 1.
(2) In chapter 2, governing equations of flow field, level set method and extrapolated variables were respectively illustrated in Cartesian and body fitted coordinate frames. Meanwhile, MGFM (modified ghost fluid method) and RGFM (real ghost fluid method) approaches are adopted to describe gas-water interface conditions.
(3) In chapter 3, second order TVD and fifth order WENO schemes were respectively introduced to solve Eulerian equations, level set and reinitialized equations for flow-field and gas-water interfaces. Also, parallel and multi-block methods were introduced briefly based on OPENMP methodology.
(4) In chapter 4, benchmark examples and numerical results were discussed on shock interaction with gas-water interface and expansion of bubble underwater at high pressure and temperature. Ten examples were carried out and analyzed in this chapter to show highly resolved gas-water interfaces.
(5) In chapter 5, some conclusions and future works were presented in this thesis.
引文
[1]傅德薰,汪翼云,马延文,等.计算空气动力学[M].北京:宇航出版社,1994.
[2]忻孝康,刘儒勋,蒋伯诚.计算流体动力学[M].长沙:国防科技大学出版社,1989.
[3]水鸿寿.一维流体力学差分方法[M].北京:国防工业出版社,1998.
[4]童秉纲,孔祥言,邓国华.气体动力学[M].北京:高等教育出版社,1999.
[5]刘儒勋,王志峰.数值模拟方法和运动界面追踪[M].合肥:中国科学技术大学出版社,2001.
[6]刘儒勋,舒其望.计算流体力学的若干新方法[M].北京:科学出版社,2003.
[7] Fedkiw Ronald,Aslam Tariq,Merriman Barry, et al. A Non-oscillatory Eulerian Approach to Interfaces in Multimaterial Flows (the Ghost Fluid Method)[J]. Journal of Computational Physics, 1999, 152: 457-492.
[8] Harten A. High resolution schemes for hyperbolic conservation laws [J]. Journal of Computational Physics, 1983, 49:357-393.
[9] Fedkiw Ronald,Marquina Antonio, Merriman Barry. An Isobaric Fix for the Overheating Problem in Multimaterial Compressible Flows[J]. Journal of Computational Physics, 1999, 148:545-578.
[10] Liu T.G, Khoo B.C, Yeo K.S. The simulation of compressible multi-medium flowⅠ.A new mechodology with test applications to 1D gas-gas and gas-water cases [J]. Computers & Fluids, 2001, 30:291-314.
[11] The simulation of compressible multi-medium flowⅡ. Applications to 2D underwater shock refraction [J]. Computers & Fluids, 2001, 30:315-337.
[12] Liu T.G, Khoo B.C,. The ghost fluid method for compressible gas-water simulation[J]. Journal of Computational Physics, 2005, 204:193-221.
[13] Liu T.G, Khoo B.C, Yeo K.S. Ghost fluid method for strong shock impacting on material interface[J]. Journal of Computational Physics, 2003, 190: 651-681.
[14] Wang C.W, Liu T.G Khoo B.C. A Real Ghost Fluid Method for the Simulation of Multimedium Compressible Flow[J]. J. Sci.Comput, 2005, 128:278-232.
[15]陈菲,张梦萍,徐胜利.运动激波和气泡相互作用的初步数值模拟[J].计算物理,2004,21(5): 443-448.
[16] Roose Dirk, Van Driessche Rafael.并行计算机和计算流体力学并行算法[J].力学进展,1998, 28(1):111-127.
[17]朱国林,徐庆新.计算流体力学并行计算技术研究综述[J].空气动力学学报, 2002,20:1-6.
[18]张来平,徐庆新,张涵信.非结构网格及混合网格复杂无粘流场并行计算方法研究[J].空气动力学学报,2002,20:14-21.
[19]魏淑贤,沈跃,黄延军.计算流体力学的发展及应用[J].河北理工学院学报,2005, 27:115-122.
[20]唐维军,张景琳,李晓林,等.三维流体界面不稳定性的Ghost方法[J].计算物理,2001,18(2):164:169.
[21] Shu C W. Essentially Non-Oscillatory and Weighted Essentially Non-Oscillatory Schemes for Hyperbolic Conservation Laws [R]. New York: CASE Report, 1997.
[22]张涵信.无波动/无自由参数的耗散差分格式[J].空气动力学学报,1988, 6(2):143:165.
[23]陈菲,徐胜利.运动激波和气-气、气-水界面相互作用的数值研究[D].合肥:中国科学技术大学近代力学系, 2006.
[24]曹乐,徐胜利.运动激波和气-气界面相互作用的数值研究[D].合肥:中国科学技术大学近代力学系, 2006.
[2]忻孝康,刘儒勋,蒋伯诚.计算流体动力学[M].长沙:国防科技大学出版社,1989.
[3]水鸿寿.一维流体力学差分方法[M].北京:国防工业出版社,1998.
[4]童秉纲,孔祥言,邓国华.气体动力学[M].北京:高等教育出版社,1999.
[5]刘儒勋,王志峰.数值模拟方法和运动界面追踪[M].合肥:中国科学技术大学出版社,2001.
[6]刘儒勋,舒其望.计算流体力学的若干新方法[M].北京:科学出版社,2003.
[7] Fedkiw Ronald,Aslam Tariq,Merriman Barry, et al. A Non-oscillatory Eulerian Approach to Interfaces in Multimaterial Flows (the Ghost Fluid Method)[J]. Journal of Computational Physics, 1999, 152: 457-492.
[8] Harten A. High resolution schemes for hyperbolic conservation laws [J]. Journal of Computational Physics, 1983, 49:357-393.
[9] Fedkiw Ronald,Marquina Antonio, Merriman Barry. An Isobaric Fix for the Overheating Problem in Multimaterial Compressible Flows[J]. Journal of Computational Physics, 1999, 148:545-578.
[10] Liu T.G, Khoo B.C, Yeo K.S. The simulation of compressible multi-medium flowⅠ.A new mechodology with test applications to 1D gas-gas and gas-water cases [J]. Computers & Fluids, 2001, 30:291-314.
[11] The simulation of compressible multi-medium flowⅡ. Applications to 2D underwater shock refraction [J]. Computers & Fluids, 2001, 30:315-337.
[12] Liu T.G, Khoo B.C,. The ghost fluid method for compressible gas-water simulation[J]. Journal of Computational Physics, 2005, 204:193-221.
[13] Liu T.G, Khoo B.C, Yeo K.S. Ghost fluid method for strong shock impacting on material interface[J]. Journal of Computational Physics, 2003, 190: 651-681.
[14] Wang C.W, Liu T.G Khoo B.C. A Real Ghost Fluid Method for the Simulation of Multimedium Compressible Flow[J]. J. Sci.Comput, 2005, 128:278-232.
[15]陈菲,张梦萍,徐胜利.运动激波和气泡相互作用的初步数值模拟[J].计算物理,2004,21(5): 443-448.
[16] Roose Dirk, Van Driessche Rafael.并行计算机和计算流体力学并行算法[J].力学进展,1998, 28(1):111-127.
[17]朱国林,徐庆新.计算流体力学并行计算技术研究综述[J].空气动力学学报, 2002,20:1-6.
[18]张来平,徐庆新,张涵信.非结构网格及混合网格复杂无粘流场并行计算方法研究[J].空气动力学学报,2002,20:14-21.
[19]魏淑贤,沈跃,黄延军.计算流体力学的发展及应用[J].河北理工学院学报,2005, 27:115-122.
[20]唐维军,张景琳,李晓林,等.三维流体界面不稳定性的Ghost方法[J].计算物理,2001,18(2):164:169.
[21] Shu C W. Essentially Non-Oscillatory and Weighted Essentially Non-Oscillatory Schemes for Hyperbolic Conservation Laws [R]. New York: CASE Report, 1997.
[22]张涵信.无波动/无自由参数的耗散差分格式[J].空气动力学学报,1988, 6(2):143:165.
[23]陈菲,徐胜利.运动激波和气-气、气-水界面相互作用的数值研究[D].合肥:中国科学技术大学近代力学系, 2006.
[24]曹乐,徐胜利.运动激波和气-气界面相互作用的数值研究[D].合肥:中国科学技术大学近代力学系, 2006.