Jian-Guo Liu, Professor

Contact Info:

Office Location:	285 Physics
Office Phone:	919-660-2546
Email Address:
Web Page:	http://www.math.duke.edu/~jliu

Teaching (Spring 2012):

• PHYSICS 176.01, THERMAL PHYSICS Synopsis

  Physics 154, TuTh 11:40 AM-12:55 PM

  (also cross-listed as ECE 176.01)

Office Hours:

Tuesday, Thursday, 9am-10am

Education:

PhD	University of California, Los Angeles	1990
MS	Fudan University	1985
BS	Fudan University	1982

Specialties:

Applied Math

Research Interests: Numerical Analysis, Partial Differential Equations, Computational Fluid Dynamics

Areas of Interest:

Numerical Analysis
Partial Differential Equations
Computational Fluid Dynamics

Curriculum Vitae

Current Ph.D. Students   (Former Students)

Representative Publications   (More Publications)

1. P. Degond and J.-G. Liu, Hydrodynamics of self-alignment interactions with precession and derivation of the Landau-Lifschitz-Gilbert equation, Math. Models Methods Appl. Sci. (Accepted, 2011)
2. M. Acheritogaray, P. Degond, A. Frouvelle, and J.-G. Liu, Kinetic formulation and global existence for the Hall-Magneto-hydrodynamics system, Kinetic and Related Models, vol. 4 (2011), pp. 901-918
3. J.-G. Liu, Jie Liu and R. Pego, Stable and accurate pressure approximation for unsteady incompressible viscous flow, J. Comput. Phys., vol. 229 (2010), pp. 3428-3453
4. S.-Y. Ha and J.-G. Liu, A simple proof of the Cucker-Smale flocking dynamics and mean-field limit, Commun. Math. Sci., vol. 7 (2009), pp. 297-325
5. J.-G. Liu, J. Liu and R. Pego, Stability and convergence of efficient Navier-Stokes solvers via a commutator estimate via a commutator estimate, Comm. Pure Appl. Math., vol. 60 (2007), pp. 1443-1487
6. P. Degond, J.-G. Liu, and L. Mieussens, Macroscopic fluid models with localized kinetic upscaling effects, Multiscale Model. Simul., vol. 5 (2006), pp. 940--979
7. H. Johnston and J.-G. Liu, Accurate, stable and efficient Navier-Stokes solvers based on explicit treatment of the pressure term, J. Comput. Phys., vol. 188 (2004), pp. 221-259
8. J.-G. Liu and W.-C. Wang, Energy and helicity preserving schemes for hydro- and magneto-hydrodynamics flows with symmetry, J. Comput. Phys., vol. 200 (2004), pp. 8-33
9. Weinan E and J.-G. Liu, Gauge method for viscous incompressible flows, Comm. Math. Sci., vol. 1 (2003), pp. 317--332
10. Weinan E and J.-G. Liu, Essential compact scheme for unsteady viscous incompressible flows, J. Comput. Phys., vol. 126 (1996), pp. 122-138
11. Weinan E and J.-G. Liu, Vorticity boundary condition and related issues for finite difference schemes, J. Comput. Phys., vol. 124 (1996), pp. 368-382
12. J.-G. Liu and Z. Xin, Convergence of vortex methods for weak solutions to the 2-D Euler equations with vortex sheets data, Comm. Pure Appl. Math., vol. 48 (1995), pp. 611-628
13. J.-G. Liu and Z. Xin, Nonlinear stability of discrete shocks for systems of conservation laws, Arch. Rat. Mech. Anal., vol. 125 (1993), pp. 217-256

Selected Invited Lectures

1. Pressure boundary condition and projection method, September, 2011, ``Modern Techniques in the Numerical Solution of Partial Differential Equations'', Crete, Greece    
2. Asymptotic-preserving schemes for some kinetic equations, January, 2011, Workshop on "Numerical Methods for stiff problems in Hamiltonian systems and kinetic equations", Saint-Malo, France    
3. Dynamics of orientational alignment and phase transition, October, 2010, 2010 NIMS Thematic Program Workshop on Conservation Laws, Plasma and Related Fields, Seoul National University, South Korea    
4. Analysis of Dynamics of Doi-Onsager Phase Transition, September 6, 2010, Isaac Newton Institute for Mathematical Sciences, Cambridge, UK    
5. A simple proof of the Cucker-Smale flocking dynamics and mean-field limit, July, 2009, ICMS Workshop on Kinetic and Mean-field models in the Socio-Economic Sciences, Edinburgh, UK,    
6. A simple proof of the Cucker-Smale flocking dynamics and mean-field limit, July, 2009, Workshop on Kinetics and statistical methods for complex particle systems, Lisbon, Portugal    
7. All speed asymptotic-preserving schemes for compressible flows, August, 2008, Recent Developments in Numerical Methods for Nonlinear Hyperbolic Partial Differential Equations and their Applications, Banff Int'l Research Station for Math Innovation and Discovery, Canada    
8. On incompressible Navier-Stokes dynamics: a new approach for analysis and computation, May, 2007, The second MINNHOKEE memorial lecturer, Seoul National University    
9. Stability and convergence of efficient Navier-Stokes solvers via a commutator estimate, January, 2006, Kyoto Conference on the Navier-Stokes equations and their Applications , Kyoto, Japan    
10. On incompressible Navier-Stokes dynamics: a new approach for analysis and computation, September, 2004, Plenary Lecturer, The Tenth International Conference on Hyperbolic Problems: Theory, Numerics and Applications, Osaka, Japan    
11. Efficient numerical methods for incompressible flows, March, 2002, keynote Speaker, The Tenth South Eastern Approximation Theory Conference, Athens, Georgia    

Recent Grant Support

• Efficient Numerical Methods for Viscous Incompressible Flows, National Science Foundation, 1011738, 2009/07-2012/06.      
• Efficient numerical methods for viscous incompressible flows, National Science Foundation, DMS11177, 2008/07-2011/06.      

Conferences Organized

• IMA Workshop on Analysis and Computation of Incompressible Fluid Flow, Organizer Committee, February, 2010  
• Two Month Program on Mathematical Theory and Numerical Methods for Computational Materials Simulation and Design, Organizer Committee, Singapore, July, 2009 - August, 2009  
• "Twelfth International Conference on Hyperbolic Problems Theory, Numerics, Applications'', Maryland, Co-Chair, June, 2008  
• CSCAMM Workshop on Analytical and Computational Challenges of Incompressible Flows at High Reynolds Number, Organizer Committee, Maryland, October 23, 2006 - October 26, 2006  
• The Nonlinear Partial Differential Equations: Analysis, Numerics and Applications, Organizing Committee, Singapore, May, 2005  
• Two month program on ``Nanoscale Material Interfaces: Experiment, Theory and Simulation'', Co-Chair, Singapore, November 24, 2004 - January 23, 2005  
• First Singapore Workshop on PDE and Scientific Computing, Co-Chair, December, 2004