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Biography

Dr. Chaoqun Liu received his BS in 1968 and MS in 1981 from Tsinghua University, Beijing, China and PhD in 1989 from University of Colorado at Denver, Colorado, USA. He is currently the Distinguished Professor and Director of Center for Numerical Simulation and Modeling at University of Texas at Arlington, Arlington, Texas, USA. He has worked on high order direct numerical simulation (DNS) and large eddy simulation (LES) for flow transition and turbulence since 1990. As PI, he has been awarded with 50 federal research grants of over 5.7 million US dollars since 1990 in the United States. He has published 11 books, 109 journal papers and 144 conference papers. He also chaired first and third US AFOSR International Conference on DNS/LES in 1997 and 2001. He is a well established expert in high order DNS/LES for flow transition, turbulence, and shock and boundary layer interaction.

Education

    • 1989 PhD in Mathematics
      University of Colorado Boulder, 1989
    • 1981 MS in Comp Fluid Dynamics
      Tsinghua University, 1981
    • 1967 BS in Comp Fluid Dynamics
      Tsinghua University, 1967

Appointments

    • Aug 2000 to Present Professor and CNSM Center Director
      Math ,University of Texas at Arlington (Arlington, TX, United States)
    • Feb 1996 to Aug 2000 Associate Professor and then Full Professor (from 1998)
      Math ,Louisiana Tech University (Ruston, LA, United States)
    • Jan 1990 to Feb 1998 Adjunct Associate Professor
      Math ,University of Colorado at Denver (Denver, CO, United States)
    • Jan 1981 to May 1986 Assistant Professor
      Thermal Dynamics ,Nanjing University of Aero & Astro (Nanjing, China)

Memberships

    • Jan 1990 to Present American Institute of Aeronautics and Astronautics
      Associate Fellow

Awards and Honors

    • Apr  2015 UTA Arlington Academy of Distinguished Scholars sponsored by UTA
    • Apr  2008 UTA Distinguished Record of Research or Creative Activity Award sponsored by UTA

Publications

      Journal Article 2017 2017
      • New Theory on Turbulence Generation and Structure
        DNS and Experiment, SCIENCE CHINA, Physics, Mechanics & Astronomy
        [Liu, Chaoqun]. DNS and Experiment, SCIENCE, CHINA, Physics, Mechanics & Astronomy, News and View. 60(8), DOI http://dx.doi.org/10.1007/s11433- 017 -9047 -2
      2017
      • Simulation of natural convection in an inclined polar cavity using a finite -difference lattice Boltzmann ethod
        International Journal of Numerical Methods for Heat and Fluid Flow
        [Liu, Chaoqun]. Int'l Jornal of Numerical Methods for Heat and Fluid Flow. 31(6), 3053-3065.
      2017
      • DNS Study on Vortex and Vorticity in Late Boundary Layer Transition
        [Liu, Chaoqun]. Communication in Computational Physics. DOI http://dx.doi.org/10.4208

      Book 2016
      • New Perspectives in Fluid Dynamics
        [Liu, Chaoqun].

      Journal Article 2016
      • 12) New Visualization Method for Vortex Structure in Turbulence, by Lambda 2 and Vortex Filaments e
        [Liu, Chaoqun]. Journal of Applied Mathematical Modelling. 40, 500-509.
      2016
      • 8) Physics of multiple level hairpin vortex structures in turbulence
        [Liu, Chaoqun]. Science China Physics, Mechanics & Astronomy. 59(2), 1-11.
      2016
      • 9) DNS Study on the Formation of Lambda Rotational Core and the Role of TS Wave in Boundary Layer Transition
        9)
        [Liu, Chaoqun]. Journal of Turbulence. 17(6), 572-601.
      2016
      • ILES for mechanism of ramp -type MVG reducing shock induced flow separation
        Science China, Physics, Mechanics & Astronomy
        [Liu, Chaoqun]. Science China, Physics, Mechanics & Astronomy. 59, DOI http://dx.doi.org/10.1007/s11433- 016- 0348 -2
      2016 2016
      • DNS study on volume vorticity increase in boundary layer transition
        [Liu, Chaoqun]. Transactions of Nanjing University of Aeronautics and Astronautics. 33(3), 252-259.
      2016
      • 13) Physics of multiple level hairpin vortex structures in turbulence
        [Liu, Chaoqun]. Journal Of Science China, Physics, Mechanics and& Astronomy. 59,

      Journal Article 2015
      • DNS Study on Mechanism of Flow Chaos in Late Boundary Layer Transition
        [Liu, Chaoqun]. CMSIM International Journal of Nonlinear Science. 157-168.
      2015
      • Separation Topology of Microramp Vortex Generator Controlled Flow at Mach Number 2.5
        [Liu, Chaoqun]. Journal of Aircraft Co33280. 52(6), 2095-2100. DOI http://dx.doi.org/10.2514/1.CO33280

      Book Review 2014
      Journal Article 2014 2014
      • 17) Physics of turbulence generation and sustenance in a boundary layer
        [Liu, Chaoqun]. Computers and Fluids. 102, 353-384.
      2014
      • 18) 18. Study on the ring like vortical structure in MVG controlled supersonic ramp flow with different inflow conditions
        [Liu, Chaoqun]. Aerospace Science and Technology. 35(106-115),
      2014 2014
      • 22) Modified Weighted Compact Scheme for Shock Capturing
        [Liu, Chaoqun]. J. of Computers and Fluids, Computers and Fluids 96. 165-176.
      2014 2014
      • 19)Numerical Investigation on Chaos in Late Boundary Layer Transition to Turbulence
        [Liu, Chaoqun]. J of Computer and Fluids. 91, 68-76.

      Journal Article 2013
      • 23) Study on Shock Wave -Vortex Ring Interaction by the Micro Vortex Generator Controlled Ramp Flow with Turbulent Inflow
        [Liu, Chaoqun]. Aerospace Science and Technology. 30, 226-231.
      2013 2013 2013
      • 28) Numerical Investigation on Mechanism of Multiple Vortex Rings Formation in Late Boundary-Layer Transition
        [Liu, Chaoqun]. J. of Computers and Fluids. 71, 156-158.
      2013
      • 38) Study on Multiple Ring -Like Vortex Formation and Small Vortex Generation in Late Flow Transition on a flat Plate
        [Liu, Chaoqun]. Theoretical and Numerica l Fluid Dynamics. 27(1), 41-70. DOI http://dx.doi.org/10.1007/s00162- 0110247-5,
      2013
      • 39) High Order Implicit Compact Method for Ordinary Differential Equationss
        [Liu, Chaoqun]. Journal of Current Applied Mathematics. 27(1), 41-70.
      2013
      • DNS Study for the Origin of the Flow Randomization in Late Boundary Layer Transition”
        [Liu, Chaoqun]. Special Issue of Global Journal of Mathematical Science.
      2013
      • High -order Mixed Weighted Compact and Non- Compact Scheme for Shock and Small Length Scale Interaction, International Journal of Computer Mathematics
        [Liu, Chaoqun]. 90(2), 376-407.

      Journal Article 2012
      • 33) Micro Vortex Generators in High -Speed Flow
        [Liu, Chaoqun]. Journal of Progress in Aerospace Science. 53, 30-45.
      2012
      • 34)Numerical study on U -shaped vortex formation in late boundary layer transition
        [Liu, Chaoqun]. Journal of Computers and Fluid. 55, 36-47.
      2012
      • 35) New shock detector and improved control function for shock -boundary layer interaction
        [Liu, Chaoqun]. International Journal of Numerical Analysis and Modeling. 9, 460-478.
      2012
      • 36) A Modified Fourier Spectral MMethod for Non-Periodic PDE
        [Liu, Chaoqun]. International Journal of Numerical Analysis and Modeling. 9(2), 460-478.
      2012
      • 37) DNS Study on Mechanism of Small Length Scale Vortex Generation in Late Boundary Layer Transition
        [Liu, Chaoqun]. Physica D. 241, 11-24.
      2012
      • 38) Study on Multiple Ring -Like Vortex Formation and Small Vortex Generation in Late Flow Transition on a Flat Plate
        [Liu, Chaoqun]. Theoretical and Numerical Fluid Dynamics.
      2012
      • New theories on boundary layer transition and turbulence formation, J. of Modeling and Simulation in Engineering
        [Liu, Chaoqun]. 2012, "Hindawi Publishing Corp. ".
      2012
      • Surface Friction and Boundary Layer Thickeningin Transitional Flow
        [Liu, Chaoqun]. "InTech Publisher ".
      2012
      • 3 2) Numerical discovery and experimental confirmation of vortex ring generation by microramp vortex generator
        [Liu, Chaoqun]. , J. of Applied Mathematical Modeling. 36(11),
      2012
      • Computational Fluid Dynamics and its Applications
        [Liu, Chaoqun, Yeoh, G, Tu, J, Timchenko, V]. "Hindawi Publishing Corp.".
      2012
      • 53)Numerical studies on evolution of secondary streamwise vortices in transitional
        [Liu, Chaoqun]. Applied Mathematics and Mechanics. 4, 449-458.
      2012
      • Modified Upwinding Compact Scheme for Shock and Shock Boundary Layer Interaction
        Communication in Computational Physics
        [Liu, Chaoqun]. CICP(Communication in Computational Physics). 11(3), 1022-1042.

      Book 2012
      • 6) Computational Fluid Dynamics
        A Practical Tool, Second Edition
        [Liu, Chaoqun, Tu, Yeoh]. "Elsevier ".
      2012
      • 2) Advances in Modeling of Fluid Dynamics
        [Liu, Chaoqun]. "InTech Publisher ".

      Journal Article 2011
      • 4) Advances in Computational Fluid Dynamics and Its Applications
        [Liu, Chaoqun, Yeoh, G, Tu, J, Timchenko, V]. "Hindawi Publishing Corp.".
      2011
      • 42) Implicit LES for Supersonic Micro ramp Vortex Generator - New Discoveries and New Mechanisms Advances in Computational Fluid Dynamics and Its Applications
        [Liu, Chaoqun]. 2011, "Hindawi Publishing Corp.".
      2011
      • 43)New Findings by High Order DNS for Late Flow Transition in a Boundary Layer
        [Liu, Chaoqun]. Special Issue, of J of Modeling and Simulation in Engineering. 2011, "Hindawi Publishing Corp.".
      2011
      • 45)Parallel DNS for vortex structure of late stages of flow transition
        [Liu, Chaoqun]. J. of Computers and Fluids. 45, 129-137.
      2011
      • 46)Numerical Investigations on the Effects of the Declining Angle of the Trailling-Edge of MVG -Edge
        [Liu, Chaoqun]. AIAA Journal. 47(6), 2086-2095.
      2011
      • 47) Numerical Study on Mechanisms of Second Sweep and Positive Spikes in Transitional Flow on a Flat Plate
        [Liu, Chaoqun]. Journal of Computers and Fluids. 40, 28-41.
      2011
      • 52) Numerical simulation on evolution of secondary streamwise vortices in transition al
        [Liu, Chaoqun]. Applied Mathematics and Mechanics. 4, 449-458.
      2011
      • 54) New properties of streamwise streaks in transitional boundary layers
        [Liu, Chaoqun]. Acta Physica Sinica. 60(9),
      2011
      • Evolution of the vortex structures and turbulent spots at the late -stage of transitional boundary layers
        [Liu, Chaoqun]. Science of China, Physics, Mechanics & Astronomy. 54(5), 986-990.
      2011
      • Numerical and Theoretical Study on “Vortex Breakdown"
        [Liu, Chaoqun]. International Journal of Computer Mathematics. 88(17), 3702-3708.

      Journal Article 2010
      • 51)New Shock/Discontinuity Detector
        [Liu, Chaoqun]. International Journal of Computer Mathematics.
      2010
      • 55) High Order Compact Scheme for Boundary Points
        [Liu, Chaoqun]. International Journal of C omputer Mathematics. 87(8), 1795-1819.
      2010
      • 48) New Shock Detector for Shock Boundary Layer Interaction
        [Liu, Chaoqun]. Lecture Notes in Computer Science, High Performance Computing and Applic ations. 78-87.
      2010
      • Evolution in the ring -like vortices and spike structure in transitional boundary
        [Liu, Chaoqun]. Science of China, Physics, Mechanics & Astronomy. 53(3), 514-520.
      2010
      • 56) Truncation Error, Dissipation and Dispersion Terms of 5th Order WENO and of WCS
        [Liu, Chaoqun]. International Journal of Computer Mathematics. 887(2), 339-352.

      Journal Article 2008
      • 58) Numerical study of passive and active flow separation control over a NACA0012 airfoil
        [Liu, Chaoqun]. Computers and Fluids. 37(8), 975-992.
      2008
      • 57. High Order Compact Schemes for Dirichlet Boundary
        [Liu, Chaoqun]. J. of Neural, Parallel & Scientific Computation. 16(2), 273-282.
      2008
      • 59) Large Eddy Simulation of Wing Tip Vortex in the Near Field
        [Liu, Chaoqun]. International Journal of CFD. 22(5), 289-330.

      Journal Article 2007
      • 61)DNS for flow separation control around an airfoil by pause jets
        [Liu, Chaoqun]. J. of Computers and Fluids. 36, 1040-1060.

      Book 2007
      • 5) Computational Fluid Dynamics
        [Liu, Chaoqun, Tu, Yeoh]. Elsevier .

      Journal Article 2006
      • 64)High performance computation for DNS/LES
        [Liu, Chaoqun]. J. of Applied Mathematical Modeling. 30(10), 1143-1165.

      Journal Article 2005
      • 62) Truncation error reduction method for Poisson equation
        [Liu, Chaoqun]. Modern Physics Letters B. 19(28-29), 1555-1558.
      2005
      • 63)Direct numerical simulation of flow separation around a NACA 0012 airfoil
        [Liu, Chaoqun]. J. of Computers and Fluids. 34, 1096-1114.

      Journal Article 2004
      • 65) Direct Numerical Simulations of Crossflow Disturbances in Supersonic Boundary Layers
        [Liu, Chaoqun]. Journal of Mathematics and Computers in Simulation. 65, 469-487.

      Journal Article 2003
      • 66) Parallel DNS for Flow Separation and Transition around Airfoil
        [Liu, Chaoqun]. Parallel Computational Fluid Dynamics and Parallel CFD 2003 Conference. 205-212.

      Journal Article 2002
      • s of weighted compact scheme to curvilinear coordinate system
        [Liu, Chaoqun]. Numerical Methods Applicatons. "Springer ".

      Book 2001
      • 9) DNS/LES – Progress and Challenges
        [Liu, Chaoqun, Sakell, Len, Beutner, Tom]. "Greyden Press ".

      Journal Article 2001
      • 68)Weighted Compact Scheme for Shock Capturing
        [Liu, Chaoqun]. International Journal of Computational Fluid Dynamics. 15, 147-155.

      Journal Article 2000
      • 69) Numerical Investigation of Compressible Separated Flow around a NACA 0012 Airfoil at 12 Degree Angle of Attack
        [Liu, Chaoqun]. , International Journal of Computational Fluid Dynamics. 9(2), 84-92.

      Other 1999
      • 72)Study of flow transition in a supersonic flat -plate boundary layer: Large eddy simulation and validation
        [Liu, Chaoqun]. International Journal of Computational Fluid Dynamics. 8, 208-219.

      Journal Article 1999
      • 70)
        [Liu, Chaoqun]. International Journal of Computational Fluid Dynamics. 13, 25-41.
      1999
      • 71) Direct numerical simulation of leading edge receptivity in a flat -plate boundary layer
        [Liu, Chaoqun]. International Journal of Computational Fluid Dynamics. 3, 470-480.

      Other 1998
      • 73) Turbulent transition simulation using the k- omega model
        [Liu, Chaoqun]. International Journal for Numeric Methods in Engineering. 42, 907-926.

      Journal Article 1998
      • 74) . A contravarient velocity based implicit multilevel method for simulating the whole process of incompressible flow transition around Joukowsky airfoils
        [Liu, Chaoqun]. J. of Applied Mechanics and Engineering. 3(1), 111-161.
      1998
      • 75)Multigrid Methods for Steady and Time -Dependent Flow
        [Liu, Chaoqun, Hafez, Oshima ]. Computational Fluid Dynamics Review. 1, 512-535.
      1998
      • 78) Preconditioned multigrid methods for unsteady incompressible flows
        [Liu, Chaoqun]. J. of Computational Physics.(139), 35-37.

      Journal Article 1997
      • 77. Multigrid computation of incompressible flows using two- equation turbulent models
        [Liu, Chaoqun]. ASME Journal of Fluids Engineering. 119, 893-899.
      1997
      • Multigrid, multiblock computation of incompressible flows using two- equation turbulent models Part II: Applications
        [Liu, Chaoqun]. ASME Journal of Fluids Engineering. 119, 900-905.

      Book 1997
      • 8) Advances in DNS/LES
        [Liu, Chaoqun]. "Greyden Prress ".

      Journal Article 1996
      • 79) NOx Prediction in 3- D Turbulent Diffusion Flames By Using Implicit Multigrid
        [Liu, Chaoqun, Liao, C, Liu, Z, Zheng, X]. Combust. Sci. and Tech. V.. 119, 219.

      Book 1995
      • Multigrid Method and Its Applications in Computational Fluid Dynamics
        [Liu, Chaoqun]. "Tsinghua University Press".

      Journal Article 1995
      • 81) Multigrid mapping and box relaxation for simulation of the whole process of flow
        [Liu, Chaoqun, Liu, Z]. J of Computational Physics. 119, 325-341.
      1995
      • 80) A Mass Flux Based Implicit Multigrid Method for Modeling Multi- Dimensional Combustion
        [Liu, Chaoqun, Zheng, X, Liao, C, Liu, Z]. Joint Propulsion Conference and Exhibit.

      Journal Article 1994
      • #83) Fourth order finite difference and multigrid methods for modeling instability in flat
        [Liu, Chaoqun]. J Computers and Fluids. 23(7), 995-982.
      1994
      • 82)Multilevel methods for temporal and spatial f low transition simulation in a rough channel
        [Liu, Chaoqun, Liu, Z, Liu, ZX, McCormick, S]. International Journal for Numerical Methods in Fluids. 18,

      Journal Article 1993
      • 84) Multilevel adaptive methods for laminar diffusion flames
        [Liu, Chaoqun, Liu, Z, McCormick, S]. J. Computers and Fluids. 23(7), 995-982.
      1993
      • 86) High order finite difference and multigrid methods for spatially -evolving instabi lity
        [Liu, Chaoqun, Liu, Z]. Journal of Computational Physics. 106, 92-100.

      Journal Article 1992
      • Communications In Applied Numerical Methods
        [Liu, Chaoqun, McCormick, S, Liu, Z]. Communications In Applied Numerical Methods. 8, 621-631.
      1992
      • 85) Finite volume and multigrid methods for modeling instabilities in flat plate boundary layers
        J. of Wind Engineering
        [Liu, Chaoqun, Liu, Z].(52), 412-417.

      Journal Article 1991
      • 88) Multilevel adaptive methods for incompressible flow in grooved channels
        [Liu, Chaoqun, Liu, Z, McCormick, S]. J of Computational and Applied Mathematics. 38, 283-295.
      1991
      • 89) Multigrid methods for flow transition in a planar channel
        [Liu, Chaoqun, Liu, Z, McCormick, S]. Computer Physics Communications. 188-200.

      Journal Article 1987
      • 90) A code for solving 3- D full Navier -Stokes equations of step flows
        [Liu, Chaoqun, Ho, Tang]. Computational Physics (China).(4),
      1987
      • A calculation and analysis of the simplified flow field o f exhaust pipe with two outlets on oth sides
        [Liu, Chaoqun, Ho, Tang ]. Acta Aerodynamica Sinica. 5(4),

      Journal Article 1984
      • 92)The calculation of recirculating flow behind bluff body inside a pipe
        [Liu, Chaoqun, Qioufan, Zhen, Qian, Zhou]. J. of Combustion (China). 3,
      1984
      • 93) An improvement on the hybrid scheme of the transport equation
        [Liu, Chaoqun]. J. NAL (china).(4),
      1984
      • 94) A comment on artificial viscosity of the transport equation and a rotated alternate
        [Liu, Chaoqun]. Acta Aerodynamica Sinica.(3),
      1984
      • 95) A discussion on the finite difference theory of vorticity transport equations
        [Liu, Chaoqun]. J. NAI (China). 3,

      Journal Article 1983
      • 96) Asymptotic analysis of the flow field of viscous gas in a closed cylinder
        [Liu, Chaoqun, Aiming , Shi, Riefeng, Fu]. Acta Aerodynamica Sinica. 3,

      Journal Article Unknown
      • 7) Motion around Λ vortices and vortex rings in boundary layer transition
        [Liu, Chaoqun]. J of Computational Technology (1925). 15-18.
      Unknown
      • Numerical Study on Microramp Vortex Generator for Supersonic Ramp Flow Control at Mach
        [Liu, Chaoqun]. An International Journal on Shock Waves, Detonations and Explosions (1925).

Support & Funding

This data is entered manually by the author of the profile and may duplicate data in the Sponsored Projects section.
    • Sept 2016 to Aug 2021 Next Generation Advances in Ionosphere Thermosphere Coupling at Multiple Scales for Environmental Specification and Prediction sponsored by  - $6145710.02
      (Funded)
    • Feb 2013 to Dec 2013 High Order Algorithms for Estimating Pressure Fluctuation behind Shock sponsored by  - $50000
      Chaoqun Liu (Funded)
    • Mar 2012 to Dec 2012 Higher Order CFD Alogorithms for Estimating Pressure Fluctuations behind Shock sponsored by  - $50000
      Chaoqun Liu (Funded)
    • Sept 2011 to Dec 2011 Higher Order CFD Algorithms for Estimating Pressure Fluctuations Behind Shock sponsored by  - $40000
      Chaoqun Liu (Funded)
    • Apr 2008 to Nov 2010 High-Order LES for Shock-Blunt Body Interaction - Numerical, Experimental, and Theoretical Study sponsored by  - $609919
      (Funded)
    • Mar 2005 to Dec 2007 High Order Weighted Compact Scheme for High Speed Flow sponsored by  - $180000
      (Funded)
    • Apr 2005 to Dec 2005 Numerical Simulation of Flow Separation Control with Dynamic Vortex Generator sponsored by  - $34999.30078125
      Chaoqun Liu (Funded)
    • Apr 2003 to July 2006 LES for Near Field Wakes Behind Juncture of Wing and Plate sponsored by  - $179997
      Chaoqun Liu (Funded)
    • May 2003 to June 2005 Laminar-Turbulent Transition in a Three-dimensional Supersonic Boundary Layer sponsored by  - $74999
      Chaoqun Liu (Funded)
    • Aug 2004 to Dec 2005 DG solver for CFD & MHD sponsored by  - $72828
      Chaoqun Liu (Funded)
    • June 2004 to Dec 2005 Laminar Turbulent Transition sponsored by  - $95000
      Chaoqun Liu (Funded)
    • Sept 2004 to Aug 2005 2-D Navier-Stocks Solver Based on Weighted-Compact Schemes sponsored by  - $31500
      (Funded)
    • June 2004 to Dec 2004 Numerucal Simulation of Flow control with Dynamic Vortex Generator. sponsored by  - $30000
      Chaoqun Liu (Funded)
    • May 2002 to Mar 2004 Numerical Simulation of Laminar-Turbulent Transition in a Compressible Boundary Layer sponsored by  - $74996.5
      Chaoqun Liu (Funded)
    • Nov 2002 to Oct 2003 2D Multigrid Solver for Electric Potential sponsored by  - $22499
      Chaoqun Liu (Funded)
    • Dec 2000 to Sept 2003 Parallel Multigrid DNS/LES Methods for Time-Dependent Compressible?Flow sponsored by  - $249998
      Chaoqun Liu (Funded)
    • Dec 2000 to Nov 2001 AFOSR Sponsorship of Third AFOSR Conference on DNS/LES sponsored by  - $15000
      Chaoqun Liu (Funded)
    • Sept 2000 to June 2001 Efficiency Improvement for IFLOW RANS Code sponsored by  - $60000
      Chaoqun Liu (Funded)
    • May 2001 to Apr 2002 Numerical Simulation of Laminar-Turbulent Transition in a Subsonic Boundary Layer sponsored by  - $24999
      Chaoqun Liu (Funded)

Courses

      • MATH 4345-001 NUM ANLYS & CMPTR APPS II
        (Course Id: 108402)
        Spring - Regular Academic Session - 2020
      • MATH 5339-001 NUMERICAL ANALYSIS II
        (Course Id: 108453)
        Spring - Regular Academic Session - 2020
      • MATH 5399-002 RESEARCH IN MATHEMATICS
        (Course Id: 112022)
        Spring - Regular Academic Session - 2020
      • MATH 5699-001 RESEARCH IN MATHEMATICS
        (Course Id: 112023)
        Spring - Regular Academic Session - 2020
      • MATH 6699-007 DISSERTATION
        (Course Id: 110860)
        Fall - Regular Academic Session - 2019
      • MATH 5338-001 NUMERICAL ANALYSIS I
        (Course Id: 108452)
        Fall - Regular Academic Session - 2019 Download Syllabus
      • MATH 5399-007 RESEARCH IN MATHEMATICS
        (Course Id: 112022)
        Fall - Regular Academic Session - 2019
      • MATH 5699-005 RESEARCH IN MATHEMATICS
        (Course Id: 112023)
        Fall - Regular Academic Session - 2019
      • MATH 5999-005 RESEARCH IN MATHEMATICS
        (Course Id: 112024)
        Fall - Regular Academic Session - 2019
      • MATH 6699-005 DISSERTATION
        (Course Id: 110860)
        Summer - Eleven Week - 2019
      • MATH 5699-005 RESEARCH IN MATHEMATICS
        (Course Id: 112023)
        Summer - Eleven Week - 2019
      • MATH 6699-001 DISSERTATION
        (Course Id: 110860)
        Spring - Regular Academic Session - 2019
      • MATH 4345-001 NUM ANLYS & CMPTR APPS II
        (Course Id: 108402 | Xlist Coursepre: Math | Xlist Coursenum: 5339)
        Spring - Regular Academic Session - 2019 Download Syllabus
      • MATH 5339-001 NUMERICAL ANALYSIS II
        (Course Id: 108453 | Xlist Coursepre: Math | Xlist Coursenum: 4345)
        Spring - Regular Academic Session - 2019 Download Syllabus
      • MATH 5699-001 RESEARCH IN MATHEMATICS
        (Course Id: 112023)
        Spring - Regular Academic Session - 2019
      • MATH 5395-004 SPECIAL PROJECT
        (Course Id: 108489)
        Spring - Regular Academic Session - 2019
      • MATH 6699-001 DISSERTATION
        (Course Id: 110860)
        Fall - Regular Academic Session - 2018
      • MATH 5338-001 NUMERICAL ANALYSIS I
        (Course Id: 108452)
        Fall - Regular Academic Session - 2018 Download Syllabus
      • MATH 5399-004 RESEARCH IN MATHEMATICS
        (Course Id: 112022)
        Fall - Regular Academic Session - 2018
      • MATH 5399-006 RESEARCH IN MATHEMATICS
        (Course Id: 112022)
        Fall - Regular Academic Session - 2018
      • MATH 5699-002 RESEARCH IN MATHEMATICS
        (Course Id: 112023)
        Fall - Regular Academic Session - 2018
      • MATH 5699-005 RESEARCH IN MATHEMATICS
        (Course Id: 112023)
        Fall - Regular Academic Session - 2018
      • MATH 5391-020 SPECIAL TOPICS IN MATH
        (Topic: Computational fluid dynamics | Course Id: 108486)
        Fall - Regular Academic Session - 2018
      • MATH 5399-004 RESEARCH IN MATHEMATICS
        (Course Id: 112022)
        Summer - Five Week - Second - 2018
      • MATH 5699-004 RESEARCH IN MATHEMATICS
        (Course Id: 112023)
        Summer - Eleven Week - 2018
      • MATH 4345-001 NUM ANLYS & CMPTR APPS II
        (Course Id: 108402 | Xlist Coursepre: Math | Xlist Coursenum: 5339)
        Spring - Regular Academic Session - 2018 Download Syllabus
      • MATH 5339-001 NUMERICAL ANALYSIS II
        (Course Id: 108453 | Xlist Coursepre: Math | Xlist Coursenum: 4345)
        Spring - Regular Academic Session - 2018 Download Syllabus
      • MATH 5699-004 RESEARCH IN MATHEMATICS
        (Course Id: 112023)
        Spring - Regular Academic Session - 2018
      • MATH 5999-005 RESEARCH IN MATHEMATICS
        (Course Id: 112024)
        Spring - Regular Academic Session - 2018
      • MATH 5391-114 SPECIAL TOPICS IN MATH
        (Topic: High Order DNS for Turbulence | Course Id: 108486)
        Spring - Regular Academic Session - 2018
      • MATH 5338-001 NUMERICAL ANALYSIS I
        (Course Id: 108452)
        Fall - Regular Academic Session - 2017
      • MATH 5399-002 RESEARCH IN MATHEMATICS
        (Course Id: 112022)
        Fall - Regular Academic Session - 2017
      • MATH 5999-005 RESEARCH IN MATHEMATICS
        (Course Id: 112024)
        Fall - Regular Academic Session - 2017
      • MATH 5391-009 SPECIAL TOPICS IN MATH
        (Topic: computational fluid dynamics | Course Id: 108486)
        Fall - Regular Academic Session - 2017
      • MATH 7399-001 DOCTORAL DEGREE COMPLETION
        (Course Id: 111647)
        Summer - Five Week - First - 2017
      • MATH 7399-003 DOCTORAL DEGREE COMPLETION
        (Course Id: 111647)
        Summer - Eleven Week - 2017
      • MATH 6399-002 DISSERTATION
        (Course Id: 110859)
        Spring - Regular Academic Session - 2017
      • MATH 6699-004 DISSERTATION
        (Course Id: 110860)
        Spring - Regular Academic Session - 2017
      • MATH 7399-003 DOCTORAL DEGREE COMPLETION
        (Course Id: 111647)
        Spring - Regular Academic Session - 2017
      • MATH 5399-003 RESEARCH IN MATHEMATICS
        (Course Id: 112022)
        Spring - Regular Academic Session - 2017
      • MATH 5395-002 SPECIAL PROJECT
        (Course Id: 108489)
        Spring - Regular Academic Session - 2017
      • MATH 5391-006 SPECIAL TOPICS IN MATH
        (Topic: Inverse Problems | Course Id: 108486)
        Spring - Regular Academic Session - 2017
      • MATH 6699-010 DISSERTATION
        (Course Id: 110860)
        Fall - Regular Academic Session - 2016
      • MATH 3345-001 NUMERICAL ANALYSIS & COMP APPS
        (Course Id: 108378)
        Fall - Regular Academic Session - 2016
      • MATH 5338-001 NUMERICAL ANALYSIS I
        (Course Id: 108452)
        Fall - Regular Academic Session - 2016
      • MATH 5699-005 RESEARCH IN MATHEMATICS
        (Course Id: 112023)
        Fall - Regular Academic Session - 2016
      • MATH 6699-006 DISSERTATION
        (Course Id: 110860)
        Summer - Five Week - First - 2016
      • MATH 6399-002 DISSERTATION
        (Course Id: 110859)
        Spring - Regular Academic Session - 2016
      • MATH 5339-001 NUMERICAL ANALYSIS II
        (Course Id: 108453)
        Spring - Regular Academic Session - 2016
      • MATH 5399-003 RESEARCH IN MATHEMATICS
        (Course Id: 112022)
        Spring - Regular Academic Session - 2016
      • MATH 5399-006 RESEARCH IN MATHEMATICS
        (Course Id: 112022)
        Spring - Regular Academic Session - 2016
      • MATH 5699-004 RESEARCH IN MATHEMATICS
        (Course Id: 112023)
        Spring - Regular Academic Session - 2016
      • MATH 5392-004 SELECTED TOPICS IN MATH
        (Topic: High Order DNS for Turbulance | Course Id: 108487)
        Spring - Regular Academic Session - 2016
      • MATH 5395-003 SPECIAL PROJECT
        (Course Id: 108489)
        Spring - Regular Academic Session - 2016
      • MATH 5338-001 NUMERICAL ANALYSIS I
        (Course Id: 108452)
        Fall - Regular Academic Session - 2015
      • MATH 5399-007 RESEARCH IN MATHEMATICS
        (Course Id: 112022)
        Fall - Regular Academic Session - 2015
      • MATH 5699-007 RESEARCH IN MATHEMATICS
        (Course Id: 112023)
        Fall - Regular Academic Session - 2015
      • MATH 5392-004 SELECTED TOPICS IN MATH
        (Topic: High Order Num Simulation | Course Id: 108487)
        Fall - Regular Academic Session - 2015
      • MATH 5699-006 RESEARCH IN MATHEMATICS
        (Course Id: 112023)
        Summer - Eleven Week - 2015
      • MATH 6999-006 DISSERTATION
        (Course Id: 110861)
        Spring - Regular Academic Session - 2015
      • MATH 4345-001 NUM ANLYS & CMPTR APPS II
        (Course Id: 108402)
        Spring - Regular Academic Session - 2015
      • MATH 5339-001 NUMERICAL ANALYSIS II
        (Course Id: 108453)
        Spring - Regular Academic Session - 2015
      • MATH 5395-003 SPECIAL PROJECT
        (Course Id: 108489)
        Spring - Regular Academic Session - 2015
      • MATH 5391-007 SPECIAL TOPICS IN MATH
        (Topic: Direct Num. Sim. for Turbulanc | Course Id: 108486)
        Spring - Regular Academic Session - 2015
      • MATH 7399-002 DOCTORAL DEGREE COMPLETION
        (Course Id: 111647)
        Fall - Regular Academic Session - 2014
      • MATH 5338-001 NUMERICAL ANALYSIS I
        (Course Id: 108452)
        Fall - Regular Academic Session - 2014
      • MATH 5391-004 SPECIAL TOPICS IN MATH
        (Topic: Introduction of High Order CFD | Course Id: 108486)
        Fall - Regular Academic Session - 2014
      • MATH 5391-003 SPECIAL TOPICS IN MATH
        (Topic: Introduction to CFD | Course Id: 108486)
        Summer - Eleven Week - 2014
      • MATH 4345-001 NUM ANLYS & CMPTR APPS II
        (Course Id: 108402)
        Spring - Regular Academic Session - 2014
      • MATH 5339-001 NUMERICAL ANALYSIS II
        (Course Id: 108453)
        Spring - Regular Academic Session - 2014
      • MATH 5395-005 SPECIAL PROJECT
        (Course Id: 108489)
        Spring - Regular Academic Session - 2014
      • MATH 5391-004 SPECIAL TOPICS IN MATH
        (Topic: Computational Fluid Dynamics | Course Id: 108486)
        Spring - Regular Academic Session - 2014
      • MATH 7399-001 DOCTORAL DEGREE COMPLETION
        (Course Id: 111647)
        Fall - Regular Academic Session - 2013
      • MATH 5338-001 NUMERICAL ANALYSIS I
        (Course Id: 108452)
        Fall - Regular Academic Session - 2013
      • MATH 5395-003 SPECIAL PROJECT
        (Topic: Data Proc of DNS Flow Trans | Course Id: 108489)
        Fall - Regular Academic Session - 2013
      • MATH 5395-007 SPECIAL PROJECT
        (Course Id: 108489)
        Fall - Regular Academic Session - 2013
      • MATH 6699-004 DISSERTATION
        (Course Id: 110860)
        Summer - Eleven Week - 2013
      • MATH 5391-002 SPECIAL TOPICS IN MATH
        (Topic: Intro Computational Fluid Dyn | Course Id: 108486)
        Summer - Five Week - Second - 2013
      • MATH 6699-007 DISSERTATION
        (Course Id: 110860)
        Spring - Regular Academic Session - 2013
      • MATH 4345-001 NUM ANLYS & CMPTR APPS II
        (Course Id: 108402)
        Spring - Regular Academic Session - 2013
      • MATH 5339-001 NUMERICAL ANALYSIS II
        (Course Id: 108453)
        Spring - Regular Academic Session - 2013
      • MATH 5391-010 SPECIAL TOPICS IN MATH
        (Topic: Math & Stats Analy/Ship Data | Course Id: 108486)
        Spring - Regular Academic Session - 2013
      • MATH 6999-009 DISSERTATION
        (Course Id: 110861)
        Fall - Regular Academic Session - 2012
      • MATH 5338-001 NUMERICAL ANALYSIS I
        (Course Id: 108452)
        Fall - Regular Academic Session - 2012
      • MATH 5391-006 SPECIAL TOPICS IN MATH
        (Topic: Math & Stat Analysis for Ship | Course Id: 108486)
        Fall - Regular Academic Session - 2012
      • MATH 6699-002 DISSERTATION
        (Course Id: 110860)
        Summer - Eleven Week - 2012
      • MATH 5391-001 SPECIAL TOPICS IN MATH
        (Topic: CPT | Course Id: 108486)
        Summer - Eleven Week - 2012
      • MATH 6399-001 DISSERTATION
        (Course Id: 110859)
        Spring - Regular Academic Session - 2012
      • MATH 6699-010 DISSERTATION
        (Course Id: 110860)
        Spring - Regular Academic Session - 2012
      • MATH 6999-001 DISSERTATION
        (Course Id: 110861)
        Spring - Regular Academic Session - 2012
      • MATH 5392-002 SELECTED TOPICS IN MATH
        (Topic: High Order CFD/High Speed Flow | Course Id: 108487)
        Spring - Regular Academic Session - 2012
      • MATH 5391-001 SPECIAL TOPICS IN MATH
        (Topic: Computational Hydrodynamics | Course Id: 108486)
        Spring - Regular Academic Session - 2012
      • MATH 6399-002 DISSERTATION
        (Course Id: 110859)
        Fall - Regular Academic Session - 2011
      • MATH 5392-004 SELECTED TOPICS IN MATH
        (Topic: Higher Order CFD | Course Id: 108487)
        Fall - Regular Academic Session - 2011
      • MATH 5391-006 SPECIAL TOPICS IN MATH
        (Topic: CFD Analysis Based/Marine Tech | Course Id: 108486)
        Fall - Regular Academic Session - 2011
      • MATH 6699-002 DISSERTATION
        (Course Id: 110860)
        Summer - Five Week - Second - 2011
      • MATH 5391-001 SPECIAL TOPICS IN MATH
        (Topic: High Order CFD/Supersonic Flow | Course Id: 108486)
        Summer - Five Week - Second - 2011
      • MATH 5391-006 SPECIAL TOPICS IN MATH
        (Topic: High Order LES/ Supersonic MVG | Course Id: 108486)
        Summer - Eleven Week - 2011
      • MATH 5391-008 SPECIAL TOPICS IN MATH
        (Topic: DNS for Transition | Course Id: 108486)
        Summer - Eleven Week - 2011
      • MATH 6999-007 DISSERTATION
        (Course Id: 110861)
        Spring - Regular Academic Session - 2011
      • MATH 5339-001 NUMERICAL ANALYSIS II
        (Course Id: 108453)
        Spring - Regular Academic Session - 2011
      • MATH 5395-006 SPECIAL PROJECT
        (Topic: High Order Scheme for SBLI | Course Id: 108489)
        Spring - Regular Academic Session - 2011
      • MATH 5391-013 SPECIAL TOPICS IN MATH
        (Topic: High Order Scheme for SBLI | Course Id: 108486)
        Spring - Regular Academic Session - 2011
      • MATH 6399-004 DISSERTATION
        (Course Id: 110859)
        Fall - Regular Academic Session - 2010
      • MATH 6999-001 DISSERTATION
        (Course Id: 110861)
        Fall - Regular Academic Session - 2010
      • MATH 5338-001 NUMERICAL ANALYSIS I
        (Course Id: 108452)
        Fall - Regular Academic Session - 2010
      • MATH 5391-004 SPECIAL TOPICS IN MATH
        (Topic: Lg Eddy Sim for High Spd Flow | Course Id: 108486)
        Fall - Regular Academic Session - 2010
      • MATH 6399-002 DISSERTATION
        (Course Id: 110859)
        Summer - Eleven Week - 2010
      • MATH 5391-001 SPECIAL TOPICS IN MATH
        (Topic: High Order Subgrid Models | Course Id: 108486)
        Summer - Five Week - Second - 2010
      • MATH 5391-002 SPECIAL TOPICS IN MATH
        (Topic: LES for Shock-Boundary Layer | Course Id: 108486)
        Summer - Five Week - Second - 2010
      • MATH 6399-003 DISSERTATION
        (Course Id: 110859)
        Spring - Regular Academic Session - 2010
      • MATH 5339-001 NUMERICAL ANALYSIS II
        (Course Id: 108453)
        Spring - Regular Academic Session - 2010
      • MATH 4391-005 SPECIAL TOPICS IN MATH
        (Topic: Numerical Analysis II | Course Id: 108404)
        Spring - Regular Academic Session - 2010
      • MATH 5391-007 SPECIAL TOPICS IN MATH
        (Topic: DNS for Flow Transition | Course Id: 108486)
        Spring - Regular Academic Session - 2010
      • MATH 6399-003 DISSERTATION
        (Course Id: 110859)
        Fall - Regular Academic Session - 2009
      • MATH 5338-001 NUMERICAL ANALYSIS I
        (Course Id: 108452)
        Fall - Regular Academic Session - 2009
      • MATH 4391-008 SPECIAL TOPICS IN MATH
        (Topic: Numerical Analysis I | Course Id: 108404)
        Fall - Regular Academic Session - 2009
      • MATH 5391-003 SPECIAL TOPICS IN MATH
        (Topic: Numerical Methods Viscous Flow | Course Id: 108486)
        Fall - Regular Academic Session - 2009