導(dǎo)師詳細(xì)信息

姓名：劉鐵鋼

性別：男

出生年份：1964

職稱：教授

院系：數(shù)學(xué)與系統(tǒng)科學(xué)學(xué)院

首次聘任導(dǎo)師時(shí)間：2008

現(xiàn)聘任導(dǎo)師一級(jí)學(xué)科名稱：數(shù)學(xué)

現(xiàn)聘任導(dǎo)師二級(jí)學(xué)科名稱：應(yīng)用數(shù)學(xué)

聘任在第二學(xué)科培養(yǎng)博士生專業(yè)名稱：無

聘任在自主設(shè)置學(xué)科培養(yǎng)博士生專業(yè)名稱：無

主要研究方向及特色：主要從事1）可壓縮空氣動(dòng)力學(xué)的高精度算法研究；2）可壓縮多介質(zhì)流特別是大密度比、高壓比多介質(zhì)流的算法研究和數(shù)值模擬；3）水下空化流、超空化流的物理模型建立及相應(yīng)的算法研究和數(shù)值計(jì)算；4）移動(dòng)邊界問題數(shù)值方法。所研究領(lǐng)域大多屬世界前沿包括可壓縮流非線性流固耦合數(shù)值技術(shù)、水下爆炸沖擊數(shù)值模擬、水下空化及超空化模擬、動(dòng)邊界捕捉技術(shù)、多介質(zhì)Riemann問題解及其解算器、可壓縮多介質(zhì)流高精度數(shù)值算法。于2003年發(fā)展了自己的modified ghost fluid method。2004年發(fā)展了等熵空化流模型(isentropicone-fluid cavitation model)。本人在大密度比、高壓高溫比多介質(zhì)流的算法研究已進(jìn)入世界前沿。本人的研究跟實(shí)際應(yīng)用緊密相連，在工業(yè)、國防和能源領(lǐng)域有著廣泛的應(yīng)用。近5年發(fā)表SCI論文20余篇，單篇引用最高達(dá)100次。20多次被國際、國內(nèi)著名大學(xué)和研究所邀請(qǐng)作學(xué)術(shù)報(bào)告。2007年中國數(shù)學(xué)大會(huì)特邀報(bào)告人之一。

電子信箱：liutg@buaa.edu.cn

辦公電話：010-82316470

辦公地點(diǎn)：北航新主樓F914

通信地址：北京市海淀區(qū)學(xué)院路37號(hào)

個(gè)人簡介：

個(gè)人簡歷

劉鐵鋼分別于1986和1989年獲得北京大學(xué)數(shù)學(xué)系學(xué)士和碩士。從1989至1995年，在中國科學(xué)院計(jì)算數(shù)學(xué)研究所工作。于2001獲新加坡國立大學(xué)機(jī)械系工學(xué)博士。從1999年至2007年，在新加坡國立大學(xué)和新加坡科技局高性能計(jì)算研究所工作和教學(xué)。于2007年八月回國任教，現(xiàn)為北京航空航天大學(xué)數(shù)學(xué)與系統(tǒng)科學(xué)學(xué)院教授、博士生導(dǎo)師、藍(lán)天學(xué)者。主要研究興趣有可壓縮計(jì)算流體動(dòng)力學(xué)、可壓縮多介質(zhì)流體數(shù)值方法、多介質(zhì)Riemann問題解及解算器、空化流模型及數(shù)值方法、非線性流固耦合、動(dòng)邊界問題及LevelSet方法。

詳細(xì)情況:

教育情況:

1982-1986理學(xué)學(xué)士，北京大學(xué)數(shù)學(xué)系計(jì)算數(shù)學(xué);1986-1989理學(xué)碩士，北京大學(xué)數(shù)學(xué)系計(jì)算流體力學(xué);1995-1999工學(xué)博士，新加坡國立大學(xué)機(jī)械系計(jì)算流體力學(xué).

獲獎(jiǎng)情況:

新1995-1999加坡國立大學(xué)獎(jiǎng)學(xué)金;1997中國科學(xué)院自然科學(xué)一等獎(jiǎng)（團(tuán)體.

工作經(jīng)歷:

1989.9-1992.5工程師，中國科學(xué)院計(jì)算中心（現(xiàn)中科院計(jì)算數(shù)學(xué)研究所）

1992.6-1995.8助理研究員，中國科學(xué)院計(jì)算中心（現(xiàn)中科院計(jì)算數(shù)學(xué)研究所）

1999.2-2007.7高級(jí)研究員，新加坡科技局高性能計(jì)算研究所

2007.7-現(xiàn)在教授，博士生導(dǎo)師，北京航空航天大學(xué)數(shù)學(xué)系

研究領(lǐng)域:

1.空化流和超空化流的建模與數(shù)值模擬;2.可壓縮多相流多介質(zhì)流的建模與數(shù)值模擬;3.可壓縮多相流多介質(zhì)流Riemann問題解及解算器;4.動(dòng)邊界、動(dòng)體問題數(shù)值解法;5.超音速和高超音速流的數(shù)值解法;6.流－固耦合數(shù)值解法;7.流體與柔性壁相互作用的穩(wěn)定性分析.

已完成和承擔(dān)的項(xiàng)目:

1.民用客機(jī)xxxxx技術(shù)研究，2013-2017，工信部，1200萬，項(xiàng)目負(fù)責(zé)人之一

2.中俄大型xxxxx核心技術(shù)合作研究，2010-2014，科技部，2000萬，子項(xiàng)目負(fù)責(zé)人

3.飛行器高雷諾數(shù)下氣動(dòng)優(yōu)化及動(dòng)邊界問題高精度快速算法，2011-2014，國家自然科學(xué)基金，75萬，主持

4.高分辨率數(shù)值方法及其在三維復(fù)雜流體中的應(yīng)用.2010-2013，國家自然科學(xué)基金,160萬,主要參與者.

5.可壓縮大密度比多介質(zhì)無粘流的MGFM算法研究與應(yīng)用.2009-2011,國家自然科學(xué)基金,25萬,主持.

研究生培養(yǎng):

博士后2名（在國外完成）

博士生1名（在國外完成）+8名（北航）

碩士生4名（在國外完成）＋9名（北航）

教學(xué)情況:

Sympolic Computing;數(shù)值分析；并行算法；偏微分方程數(shù)值解、計(jì)算流體力學(xué)、科技論文寫作。

發(fā)表學(xué)術(shù)論文及出版專著情況:

已發(fā)表的SCI論文

--Liang Xu, Tiegang Liu.Modified Ghost Fluid Method as Applied to Fluid-Plate Interaction.Adv.Appl.Math.Mech., 26:24-48, 2014

--Jian Chen, Yaowen Lu, Tiegang Liu, Multidomain hybrid RKDG and WENO methods for hyperbolic conservation laws, SIAM J Sci Comput.Vol.35, No.2, pp.1049–1072, 2013.

--Zhen Wang, Shengjiao Yu, Tiegang Liu.Effect of Shape Parameterization on Aerodynamic Shape Optimization with SPSA Algorithm.Procedia Engineering.61:393-402, 2013

--Xiaofeng He, Zheng Wang, Tiegang Liu.Solving Two-Dimensional Euler Equations on GPU.Procedia Engineering.61:57-62, 2013

--Jun Zhu, Tiegang Liu, Jianxian Qiu, Boo Cheong Khoo, RKDG methods with WENO limiters for unsteady cavitating flow.Computers & Fluids 57:52–65, 2012.

--Liang Xu and Tiegang Liu, Accuracies and conservation errors of various ghost fluid methods for multi-medium Riemann problem.J.Comput.Phys., 230:4975-4990, 2011

--Jun Zhu, Jianxian Qiu, Tiegang Liu and Boo Cheong Khoo, RKDG methods with WENO type limiters and conservative interfacial procedure for one-dimensional compressible multi-medium flow simulations.Applied Numerical Mathematics.61:554-580, 2011.

--Liang Xu and Tiegang Liu, Optimal Error Estimation of the Modified Ghost Fluid Method.Commun.Comput.Phys., 8:403-426, 2010

--Jiequan Li, Tiegang Liu and Zhongfeng Sun, Implementation of the GRP scheme for computing radially symmetric compressible fluid flows.J.Comput.Phys., 228:5867-5887, 2009

--Wenfeng Xie, Tiegang Liu and Yin-Lu Young, The effect of surface curvature on undex-induced hull cavitation.Modern Physics Letters B, vol 23, 253-256, 2009.

--Chunwu Wang, Huazhong Tang and Tiegang Liu, An adaptive ghost fluid finite volume method for compressible gas–water simulations.J.Comput.Phys., 227:6383-6409, 2008.

--Liu TG, Xie WF and Khoo BC, The Modified Ghost Fluid Method for Coupling of Fluid and Structure Constituted with Hydro-Elasto-Plastic Equation of State.SIAM J.Sci.Comput., 33/3:1105-1130, 2008.

--Xie W.F., Y.L.Young and T.G.Liu, Multiphase Modeling of Dynamic Fluid-Structure Interaction during Close-in Explosion.International Journal for Numerical Methods in Engineering, 70:1019-1043, 2008.

--TG Liu, JY Ho, BC Khoo and AW Chowdhury, Numerical Simulation of Fluid-Structure Interaction Using Modified Ghost Fluid Method and Naviers Equations.J.Sci.Comput., 36: 45–68, 2008.

--Jianxian Qiu, Tiegang Liu and Boo Cheong Khoo, Simulations of compressible two-medium flow by Runge-Kutta discontinuous Galerkin methods with the ghost fluid method, Communications in Computational Physics, 3:479-502, 2008

--Xie W.F., Y.L.Young, T.G.Liu and B.C.Khoo, Dynamic response of deformable structures subjected to shock load and cavitation reload, Computational Mechanics.44:667-681,2007.

--Xie WF, Liu TG and Khoo BC.The Simulation of Cavitating Flows Induced by Underwater Shock-Free Surface Interaction.Applied Numerical Mathematics.57:734-745, 2007.

--Liu TG and Khoo BC, The Accuracy of the Modified Ghost Fluid Method for Gas-Gas Riemann Problem, Applied Numerical Mathematics.57:721-733, 2007.

--Qiu Jianxian, Liu Tiegang and Khoo Boo Cheong.Runge-Kutta discontinuous Galerkin methods for two-medium flow simulations: one-dimensional case, J.Comput.Phys., 222:353-373, 2007.

--Huazhong Tang and Tiegang Liu, A Note on the Conservative Schemes for the Euler Equations.J.Comput.Phys.218:451-459, 2006.

--Liu TG, Khoo BC, and Xie WF, The Modified Ghost Fluid Method as applied to extreme Fluid-Structure Interaction in the Presence of Cavitation, Communications in Computational Physics, Vol.1 No.5, pp 898-919, 2006.

--E Klaseboer, CK Turangan, SW Fong, TG Liu, KC Hung, BC Khoo, Simulations of pressure pulse–bubble interaction using boundary element method.Computer methods in applied mechanics and engineering, Vol.195, pp4287-4302, 2006.

--Wang CW, Liu TG, Khoo BC.A Real-Ghost Fluid Method for the Simulation of Multi-Medium Compressible Flow.SIAM J.Sci.Comput.Vol 28, No 1, pp278-302, 2006.

--Xie WF, Liu TG and Khoo BC, Application of a One-fluid Model for Large Scale Homogeneous Unsteady Cavitation: the modified Schmidt’s model.Comput.& Fluids.Vol 35, pp1177-1192, 2006.

--Liu TG, Xie WF and Khoo BC, Ghost fluid method applied to compressible multi-phase flows.Morden Physics Letters B, Vol 19, pp1475-1478, 2005.

--Liu TG, Khoo BC and Wang CW.The Ghost Fluid Method for Compressible Gas-Water Simulation.J.Comput.Phys.Vol.204, pp193-221, 2005.(cited by in scopus 19)

--Liu TG, Khoo BC and Xie WF.Isentropic One-Fluid Modelling of Unsteady Cavitating Flow.J.Comput.Phys.Vol 201, pp80-108, 2004.

--Liu TG, Khoo BC and Yeo KS.Ghost Fluid Method for strong shock impacting on material interface.J.Comput.Phys.Vol.190, pp651-681, 2003.(cited by in scopus 48)

--Liu T.G., B.C.Khoo, K.S.Yeo and Wang C.Underwater shock-free surface-structure interaction.Inter.J.Numer.Method Eng.Vol.58/4 pp609-630, 2003.

--Liu T.G., B.C.Khoo and K.S.Yeo, The simulation of compressible multi-medium flow.Part I: A new methodology with test applications to 1D gas-gas and gas-water cases.Comput.& Fluids.Vol.30/3, pp291-314, 2001.

--Liu T.G., B.C.Khoo and K.S.Yeo, The simulation of compressible multi-medium flow.Part II: Applications to 2D underwater shock refraction.Comput.& Fluids.Vol.30/3, pp315-337, 2001.

--Liu T.G., Khoo, B.C.and Yeo, K.S.The numerical simulations of explosion and implosion in air: use of a modified Harten's TVD scheme.1999, Int.J.Numer.Meth.Fluids, Vol.31/4.pp661-680.

--Liu Tiegang, Wang Ruquan and Song Songhe.An implicit-explicit upwind algorithm for the parabolized Navier-Stokes equations.ACTA Mechanic Sinica, Vol.10.No.2.p.129-135.1994.

20 篇國際會(huì)議論文

1.Liu TG, Khoo BC and Ho JY, The Modified Ghost Fluid Method for Fluid-Elastic Structure Coupling.The 7th World Congress on Computational Mechanics, 16-22 July 2006, Los Angles, California, USA.

2.Xie WF, Young J, Khoo BC and Liu TG, A Ghost Fluid Method for Shock, Structure and Free Surface Interaction.The 7th World Congress on Computational Mechanics, 16-22 July 2006, Los Angles, California, USA.

3.Hung, K.C., Fong, S.W., Klaseboer, E., Turangan, C.K., Khoo, B.C., and Liu, T.G.Simulation of pressure pulse-bubble interaction using the boundary element method.In Computational Methods in Multiphase Flow III, (Ed.Mammoli, A.A.and Brebbia, C.A.), pp.83-92, WIT Press.Sept.2005

4.Liu TG, Xie WF and Khoo BC, Cavitation Modeling with Applications to Shock Cavitation Interaction.The 25th International Symposium on Shock Waves - ISSW25, 17 - 22 July,2005.Bangalore, India.

5.Hung KC, Klaseboer E, Turangan CK, Fong SW, Liu TG and Khoo BC, Computational mechanics of a shock wave and its effects on a cavitation bubble, The 25th International Symposium on Shock Waves - ISSW25, 17 - 22 July, 2005.Bangalore, India.

6.Liu TG, Xie WF and Khoo BC, Ghost fluid method applied to compressible multi-phase flows.International Symposium on Physics of Fluids, 2005.9-12 June, 2005, Huangshan, China.

7.Liu TG, On Accuracy of the Ghost Fluid Method Applied to Gas-Gas Riemann Problems.International Conference on Scientific Computing (ICSC05).4 – 8 June, Nanjing, China, 2005.

8.Xie WF, Liu TG and Khoo BC, Multidimensional Simulation of Homogeneous Unsteady Cavitation.International Conference on Scientific Computing (ICSC05).4 – 8 June, Nanjing, China, 2005.

9.Siew Wan Fong, E Klaseboer, CK Turangan, BC Khoo, TG Liu and KC Hung.Simulations of pressure pulse-bubble interaction using boundary element method.Boundary Element Methods (BEM 27), 15-17 March 2005.Orlando, Florida, USA.

10.Liu TG, Khoo BC, Ghost fluid method for compressible gas-liquid flow.The International Conference on Computational Method (ICCM 2004), December 15-17, 2004, Singapore.

11.Xie WF, Liu TG, Khoo BC.Homogeneous simulation of cavitating flow.Proceedings of the 5th International Conference on Multi-phase Fluid (ICMF).Yokohama, Japan, May 30 to June 4, 2004.

12.Liu TG, Hung KC, Khoo BC.Simulation of Strong Shock-Interface Interaction, The 24th International Symposium on Shock Wave (ISSW24) July 11-16, 2004, Beijing.

13.Liu TG, Xie WF, Khoo BC.Modeling unsteady compressible cavitation flow.Proceedings of the International Conference on Scientific and Engineering Computation (IC-SEC 2004).June 30 to 02 July, 2004.Grand Copthorne Waterfront Hotel, Singapore.

14.Liu, T.G., Khoo, B.C.and Hung, K.C.The Modified Ghost Fluid Method.Proceedings of the International Conference on Scientific and Engineering Computation (IC-SEC 2002).Raffles City Convention Centre, Singapore, from 3 to 5 December 2002.P122-125

15.Wang C.W., Liu, T.G., Khoo, B.C.and Hung, K.C.High Accuracy Simulation of Multimedium Fluid.Proceedings of the International Conference on Scientific and Engineering Computation (IC-SEC 2002).Raffles City Convention Centre, Singapore, from 3 to 5 December 2002.P118-121.

16.Liu, T.G., Khoo, B.C., Yeo, K.S.and Wang C.Shook loading in the presence of free surface and cavitation.The 23rd International Symposium on Shock Waves (ISSW23), Arlington TX, USA, 23-27 July 2001.P.219.

17.Yeo, K.S., Zhao, H.Z., Liu, T.G.and Lim, T.B.Interaction of flow and compliant surfaces.Proceedings of Underwater Defence Technology (UDT) Pacific 2000, Sydney.February 7-9, 2000.Pp.306-310.

18.Liu, T.G., Khoo, B.C.and Yeo, K.S.Shock Structure Cavitation Interaction.Joint Conference between ONR-Singapore, Washington DC, USA.November 1-3, 2000.

19.Yeo, K.S., Zhao, H.Z., Liu, T.G.and Lim, T.B.Interaction of flow and compliant surface.1999, Naval Platform Technology Conference, Singapore.Oct, 15, 1999.

20.Liu, T.G., Khoo, B.C.and Yeo, K.S.The simulation of underwater explosion near a free surface.1998, The 3rd High Performance Computing Asia Conference.Singapore, Sept.23-25, pp.812-820

26次被邀請(qǐng)?jiān)L問和講學(xué)

1.The modified ghost fluid method.29 June 2007.Hunan University, Changsha, China.

2.The modified ghost fluid method.28 June 2007.Dept of Math., Hunan Normal University, Changsha, China.

3.The modified ghost fluid method.26 (25-29) June 2007.School of Astronautics and material Engineering, National University of Defence Technology.Changsha, China,

4.Isentropic One-Fluid Cavitation Modelling and Applications.25 (25-29) June 2007.School of Astronautics and material Engineering, National University of Defence Technology.Changsha, China

5.The Latest Development and Applications of the Modified Ghost Fluid Method.Dept of Mech.Eng., 20-22 June, 2007.University of Science and Technology of China.Hefei, China

6.The modified ghost fluid method.19 June 2007, Beijing Institute of Technology, Beijing

7.The Modified Ghost Fluid Method for Treating Moving Interfaces and its Applications.17 April 2007, Dept of Math.National University of Defence Technology.Changsha, China

8.Isentropic One-Fluid Cavitation Modelling and Applications, 13 April 2007.Dept of Math, Nanjing University of Aeronautics and Astronautics.Nanjing, China.

9.The Modified Ghost Fluid Method and its Applications, 12 March, 2007, Institute for Mathematical Science, National University of Singapore, Singapore

10.The Modified Ghost Fluid Method and its Applications to Fluid-Structure Interaction, 18-22 June 2006, Institute of Mechanics, Chinese Academy of Science.

11.The Modified Ghost Fluid Method, 11-16 June 2006.Dept of Mech.Eng., University of Science and Technology of China.

12.On Accuracy of Various Ghost Fluid Methods, 11-16 June 2006.Dept of Mech.Eng., University of Science and Technology of China.

13.The Modified Ghost Fluid Method Applied to Compressible Fluid-Deformable Structure Coupling, 11-16 June 2006.Dept of Mech.Eng., University of Science and Technology of China.

14.Isentropic One-Fluid Cavitation Modeling, 1-16 June 2006.Dept of Mech.Eng., University of Science and Technology of China.

15.The Modified Ghost Fluid Method Applied to Compressible Fluid-Deformable Structure Coupling.28 March 2006.Dept.of Math.National University of Singapore.

16.The Modified Ghost Fluid Method Applied to Compressible Fluid-Deformable Structure Coupling.27 Dec.2005, Institute of Applied Physics and Computational Mathematics, Beijing.

17.The Modified Ghost Fluid Method Applied to Compressible Fluid-Deformable Structure Coupling.The 2nd International Conference on Scientific Computing and Partial Differential Equations & the First East Asia SIAM Conference (CSCPDE05).12 – 16 December 2005.Hong Kong Baptist University.

18.On Accuracy of the Ghost Fluid Method Applied to Gas-Gas Riemann Problems.International Conference on Scientific Computing (ICSC05).4 – 8 June, Nanjing, China, 2005

19.The Accuracy of Ghost Fluid Method.14 June 2005.Department of Math.Nanjing University of Aeronautics and Astronautics.Nanjing, China

20.On Accuracy of the Ghost Fluid Method.Workshop on nonlinear partial differential equations: analysis, computation and applications.3-6 May 2005.IMS, NUS.

21.Isentropic modelling of unsteady cavitating flow.The 1st Workshop on partial differential equation and scientific computing.December 23-24, 2004, NUS.

22.The Ghost Fluid Method for Compressible Multi-medium Flow, 9:00-10:00am, 03 (Wednesday) December 2003.Room 344, LNM, Institute of Mechanics, Chinese Academy of Sciences, Beijing.

23.The Ghost Fluid Method for Compressible Gas-Water Flow, 4:30-5:30pm, 18 (Tuesday) November 2003.Department of Computational Mathematics, School of Mathematical Sciences, Peking University, Beijing.

24.The Ghost Fluid Method, 3:00-4:00pm, 12 (Wednesday) November 2003, Institute of Computational Mathematics, Academy of Mathematical and System Sciences, Chinese Academy of Sciences, Beijing.

25.Ghost Fluid Method for Strong Shock Impacting on Material Interface, 10:00-11:00am, 10 (Monday) November 2003, Institute of Applied Physics and Computational Mathematics, Beijing.

26.Simulation of Underwater Explosion near a Free Surface and Structure, 2:00-3:00pm, 25 March 2002, CIM-IHPC Seminar, Department of Mathematics, National University of Singapore (NUS).

15 個(gè)技術(shù)報(bào)告

1.Zhao, H.Z., Liu T.G., Yeo, K.S.and Khoo, B.C.Interaction of flow with submerged compliant coating.Half-Year Report No.2, Nov.1999.Institute of High Performance Computing, Singapore.

2.Zhao, H.Z., Liu T.G., Yeo, K.S.and Khoo, B.C.Interaction of flow with submerged compliant coating.Half-Year Report No.3, Apr.2000.Institute of High Performance Computing, Singapore.

3.Liu T.G., Zhao, H.Z., Yeo, K.S.and Khoo, B.C.Interaction of flow with submerged compliant coating.Half-Year Report No.4, Nov.2000.Institute of High Performance Computing, Singapore.

4.Liu T.G., Khan S., Yeo, K.S.and Khoo, B.C.Interaction of flow with submerged compliant coating.Half-Year Report No.5, Apr.2001.Institute of High Performance Computing, Singapore.

5.Liu T.G., Khan S., Yeo, K.S.and Khoo, B.C.Interaction of flow with submerged compliant coating.Half-Year Report No.6, Nov.2001.Institute of High Performance Computing, Singapore.

6.Liu T.G., Khan S., Yeo, K.S.and Khoo, B.C.Interaction of flow with submerged compliant coating.Half-Year Report No.7 (Report for Exrtension), June 2002.Institute of High Performance Computing, Singapore.

7.Liu T.G., Khan S., Yeo, K.S.and Khoo, B.C.Interaction of flow with submerged compliant coating.Final Report, June 2002.Institute of High Performance Computing, Singapore.

8.Liu T.G.Evert C.Hung K.C.and Khoo B.C.Validation of Undex Research Code with selected test cases and study of underwater shock structure cavitation interaction.Half-Yearly Report No.1, July 2002.

9.Liu T.G.Evert C.Hung K.C.and Khoo B.C.Validation of Undex Research Code with selected test cases and study of underwater shock structure cavitation interaction.Half-Yearly Report No.2, December 2002.

10.Liu T.G.The development of advanced GFM solvers for compressible multi-medium/multi-phase flow.Half-Yearly Report No.1, May 2003.

11.Liu T.G.and Wang C.W.The development of advanced GFM solvers for compressible multi-medium/multi-phase flow.Half-Yearly Report No.2, January 2004.

12.Liu T.G.Turangan C.Numerical methods for cavitation problems.Half-Yearly Report NO 1.January 2005.

13.Liu T.G.Turangan C.Numerical methods for cavitation problems.Half-Yearly Report NO 2.July 2005.

14.Liu T.G.Turangan C.Numerical methods for cavitation problems.Half-Yearly Report NO 3.February 2006.

15.Liu T.G.Turangan C.Numerical methods for cavitation problems.Half-Yearly Report NO 4.December 2006.