~donliu

Graduate Research Assistantship is available through my research grant for qualified graduate students who are well-motivated with good work ethics and a background in applied mathematics, computational mathematics, engineering, or something equivalent. Preference is given to students with research experience and programming skills in C or C++. Please contact me if you are qualified and seriously interested.

Academic Background

Don Liu received his Ph.D. (2004) and M.S. (2000) in applied mathematics from the Division of Applied Mathematics, Brown University, and his B.Sc. in thermal fluid engineering from Southeastern University. He accepted a joint appointment as Postdoctoral Research Associate at the University of Maryland Baltimore County and Research Fellow at NASA Goddard Space Flight Center in May 2004. Dr. Liu joined Louisiana Tech University as a tenure-track Assistant Professor in 2006.

Courses

Mechanics & Materials MEMT 312 [Syllabus]: Spring 2009
Mechanical Engineering MEEN 449 - Introduction to Computational Fluid Dynamics [syllabus]: Spring 2008
Mathematics MATH 414 - Numerical Analysis I [Syllabus]: Fall (2008, 2009)
Mathematics MATH 415 - Numerical Analysis II [Syllabus]: Winter (2009, 2010)
Mathematics MATH 407 - Partial Differential Equations [syllabus]: Fall (2006, 2007)
Mathematics MATH 405/505 - Linear Algebra [Syllabus]: Spring (2011)
Mathematics MATH 308 - Introduction to Linear Algebra [Syllabus]: Winter (2011, 2012)
Mathematics MATH 245 - Differential Equations (Engineering Mathematics) [syllabus]: Winter 2008, Summer (2009, 2010, 2011)
Mathematics MATH 244 - Mathematics for Engineering & Science V [syllabus]: Spring (2007, 2010), Fall (2010, 2011)
Mathematics MATH 243 - Mathematics for Engineering & Science IV [syllabus]: Fall (2006, 2007, 2008, 2009), Winter 2007, Summer (2008, 2009, 2010, 2011)
Mathematics MATH 242 - Mathematics for Engineering & Science III [syllabus]: Summer 2007

Awards

National Science Foundation award (PI), DMS-1115546, Oct. 1, 2011- Sept. 2014
Post-doctoral/Early career travel award from NSF & SIAM for Parallel Processing for Scientific Computing Conference, March 12-14, 2008, Atlanta, Georgia
Early career travel award from NSF & IMA for Seventh MS State - UAB Conference, November 1-3, 2007, Birmingham, AL
Board of Regents Research Competitive Award (PI), LEQSF2007-10-RD-A-22, 2007-2011
Dissertation Fellow Award from Brown University, 2004

Research Interests

Computational Fluid Dynamics, Scientific and Parallel Computing
Numerical Simulations of Disperse Flows, Two-Phase Flows
Numerical Simulations of Micro- and Nano-flows, Microelectromechanical Systems (MEMS), and Functional Nanodevices
Numerical Analysis and Solutions of Partial Differential Equations with Finite Element, Spectral, Spectral Element, Finite Difference, Finite Volume methods
Computational Heat and Mass Transfer
Stochastic Modeling and Data Assimilation using Kalman filters

Selected Publications

A Sixth-Order Accuracy Solution to Modified Boussinesq-Type Equations with Coupled Compact Methods, to be submitted, Jan. 2012
Finite Element and Spectral Element Solutions to Modified Boussinesq Equations, to be submitted Jan. 2012
GMR Sensors: Technologies and Medical Applications, Journal of Recent Patents on Nanomedicine, Vol. 1, No. 2, p1-8, 2011
Spectral Element Modeling of Sediment Transport in Shear Flows, Journal of Computer Methods in Applied Mechanics and Engineering, Vol. 200, p1691-1707, April 2011 [PDF]
Joint Simulations of Confined Diffusion inside Nanotubules, Journal of Computational and Theoretical Nanoscience, Vol. 8, No. 2, p1-11, 2011 [PDF]
Force-Coupling Method for Flows with Ellipsoidal Particles, Journal of Computational Physics, Vol. 228, p3559-3581, 2009 [PDF]
Spectral Element Simulations of Flow Past An Ellipsoid At Different Reynolds Numbers, Electronic Journal of Differential Equations, Proc. Conf. 17, p149-157, 2009 [PDF]
High order compact implicit difference methods for parabolic equations in geodynamo simulation, J. Advances in Mathematical Physics, Vol. 2009, Article ID 568296, doi:10.1155/2009/568296, 2009 [PDF]
MoSST_DAS: The First Generation Geomagnetic Data Assimilation Framework, Communications In Computational Physics, Vol. 3, NO. 1, p85-108, 2008 [PDF]
Spectral element simulation of flow past an ellipsoid at different Reynolds numbers, Proceedings of 9^th International Conference on Fluid Control, Measurement and Visualization, Tallahassee, Florida, September 16-19, 2007 [PDF]
Observing system simulation experiments in geomagnetic data assimilation, Journal of Geophysical Research, Vol. 112, B08103, doi:10.1029/2006JB004691, 2007 [PDF]
Simulations of dynamic self-assembly of paramagnetic microspheres in confined microgeometries, Journal of Micromechanics and Microengineering, Vol. 15, p2298-2308, 2005 [PDF]
Dynamic Self-Assembly in Micropipes: Effect of Net Flow, Proceedings of 2004 Engineering Conference International: Transport Phenomena in Micro and Nano-devices, Kona, Hawaii, October 17-21, 2004 [PDF]
New Advances in Force-Coupling Method: from Micro to Macro, Proceedings of 2004 International Union of Theoretical and Applied Mechanics Symposium, Argonne National Laboratory, Argonne, Illinois, October 4-7, 2004 [PDF]
Dynamic self-assembly in confined micro-domains, Proceedings of 2004 ASME International Mechanical Engineering Congress and RD & D Expo, Anaheim, California, November 13-19, 2004 [PDF]
Self-assembled particle structures for microflow systems, Symposiums of 5^th International Conference on Multiphase, ICMF'04, Yokohama, Japan, May 30-June 4, 2004 [PDF]
Spectral distributed Lagrange multiplier method: algorithm and benchmark tests, Journal of Computational Physics, Vol. 195, p695-717, 2004 [PDF]
Modeling and optimization of colloidal micro-pumps, Journal of Micromechanics and Microengineering, Vol. 14, 2004 [PDF]
Fast methods for colloidal microdevices, Proceedings of 41^st Aerospace Sciences Meeting & Exhibit, AIAA 2003-0437, Reno, Nevada, January 6-9, 2003 [PDF]
A fast method for particulate microflows, Journal of Microelectromechanical System, Vol. 11, NO. 6, December 2002 [PDF]
Numerical modeling of turbulent flow and heat transfer in a pin-finned convergent passage of gas turbine guiding vane, Journal of Aerospace Power, (in Mandarin) Vol. 13, No. 2, pp. 189-194, ISSN1000-8055, April 1998