Zahir U. Warsi
Drawer A, Mississippi State, MS 39762
316 Walker Engineering Building
(601) 325-3623 or 325-7293
FAX: (601) 325-7730

warsi@ae.msstate.edu

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Education

University of Lucknow, Lucknow (India)

B.Sc., Physics, Mathematics, Mathematical Statistics and English, 1954

M.Sc., Mathematics: (Topics in Applied Mathematics with specialization in Fluid Dynamics), 1956

Ph.D., Mathematics: (Dissertation in Boundary Layer Theory), 1965

Ph.D. Dissertation Title: "On Some Problems in Unsteady Axially Symmetric and Three-Dimensional Boundary Layer Flow"

Dissertation Examiners:

Professor Shih-I Pai, University of Maryland, U.S.A.

Professor C.R. Illingworth, University of Manchester, U.K.

Professor R. Ballabh, University of Lucknow, India

Employment

1957-1958

Lecturer in mathematics and physics, H.M. College, Kanpur, India. (From August 1957 to December 1958, I taught all branches of mathematics and physics (both theory and experiments) to students in XIIth grade.

1958-1962

Research Supervisor, Irrigation Research Institute, Roorkee, India. The institute mentioned above arranged for my training in the photoelastic methods at the Central Water and Power Commission at Bombay and Poona. I worked on two-dimensional photoelastic problems pertaining to beams, plates, and earth dam foundations. In this period, the University of Lucknow allowed me to enroll as an off-campus student to work independently on my Ph.D. dissertation problem.

1962-1967

Scientist, Physics Division, Central Building Research Institute, Roorkee India (Under the Council of Scientific and Industrial Research, Govt. of India.) At CBRI, I worked on the problems of airflow, heat transfer, and ventilation, pertaining to the design of modern buildings. Here I also continued the work on my dissertation problem which was independent of the normal assigned program of the institute. Occasionally I attended and gave lectures at the nearby engineering university.

1967-1969

Visiting Assistant Professor, Department of Aerophysics and Aerospace Engineering, Mississippi State University.

1969-1973

Assistant Professor, Department of Aerospace Engineering, Mississippi State University.

1973-1980

Associate Professor, Department of Aerospace Engineering, Mississippi State University.

1980-Present

Professor, Department of Aerospace Engineering, Mississippi State University.

Professional Activities

Since coming to Mississippi State University, I have taught both the graduate and the undergraduate courses in fluid dynamics and engineering mechanics. My research projects have been supported by the Army Research Office, Air Force Office of Scientific Research, and the NASA. The research has invariably been in the fluid dynamics areas, including boundary layers, Navier-Stokes solutions, and in the mean turbulent flow modeling. Besides fluid dynamics, I have also been contributing in the foundational areas of numerical grid generation.
• Society Memberships
  • Sigma Gamma Tau
  • Sigma Xi
  • Senior Member AIAA
  • American Academy of Mechanics, Member

• Professional Registration
  • None

• Reviewer
  • Air Force Office of Scientific Research
  • Applied Mechanics Reviews
  • AIAA Journal
  • Computer and Fluids
  • Journal of Engineering Mechanics (ASCE)
  • Journal of Fluid Engineering ( ASME)
  • Numerical Heat Transfer
  • Journal of Computational Physics
  • John Wiley & Sons, Inc.
  • National Science Foundation

Awards and Honors

• Medallion Certificate of the Southeastern Section, ASEE, on outstanding contribution in research, 1975
• NASA Certificate of Recognition, November 1981
• Recipient of the Minna-James-Heineman Foundation Fellowship for visiting Professor at the Von Karman Institute for Fluid Dynamics, Belgium, 1984
• Hearin-Hess Distinguished Professor, 1989-1990
• Outstanding Research Paper Award of the College of Engineering, Mississippi State University, 1990
• Hearin-Hess Distinguished Professor, 1992-1993
• Outstanding Research Award, College of Engineering, 1993
• Hearin-Hess Distinguished Professor, 1996-1997

Areas of Teaching and Research Specialization

• Teaching
  • Undergraduate Courses Taught
    • ASE 3333 Gas Dynamics
    • EM 2413 Engineering Mechanics I
    • EM 2433 Engineering Mechanics II
    • EM 3313 Fluid Mechanics
  • Graduate Courses Taught
    • ASE 8313 Advanced Compressible Flows
    • ASE 8343 Laminar Viscous Flows, including boundary layers
    • ASE 8353 Turbulence
    • ASE 8813 Advanced Topics in Fluid Dynamics
    • EM 8113 Theory of Continuous Media
    • EM 8123 Energy Principles
    • EM 8203 Applied Elasticity
    • EM 8813 Applied Tensors

• Research Interests
  • Boundary Layer Theory, Navier-Stokes Solutions, Turbulence Aerodynamics, Non-Newtonian Fluid Dynamics, Application of Numerical Methods in Fluid Dynamics (e.g., Spectral Methods, Grid Generation), Continuum Mechanics.

Grants and Contracts

1. U.S. Army Research Office (co-investigator): March 1967 - December 1971
2. National Aeronautics and Space Administration:
   • NASA NSG-1243: 1976-78
   • NASA NAS8-32912: 1979-80.
3. Air Force Office of Scientific Research:
   • AFOSR 76-2922: 1975-78
   • AFOSR 80-0185: 1979-84
   • AFOSR 85-0143: 1985-88.

Books

1. Numerical Grid Generation: Foundation and Applications, North-Holland, 1985, J.F. Thompson, Z.U.A. Warsi, and C.W. Mastin.
2. Fluid Dynamics: Theoretical and Computational Approaches, CRC Press, Inc., 1993, (4th Printing 1996), Warsi, Z.U.A.
3. Book Chapter, Mathematics of Space And Surface Grid Generation, in Handbook of Grid Generation, CRC Press, ed. J.F. Thompson et al.
4. Book Chapter, Incompressible Laminar Boundary-Layer Flow, in Handbook of Fluid Dynamics, CRC Press, ed. Richard Johnson.

Monographs

1. "A Course of Lectures on the Theoretical Aspects of Laminar Viscous Incompressible Flows," published by the Department of Aerophysics and Aerospace Engineering, Mississippi State University, September 1975.
2. "Tensor and Differential Geometry Applied to Analytic and Numerical Coordinate Generation," January 1981.

Publications

The following is a listing of journal publications. Some of the notable journals in which my articles have appeared are: American Institute of Aeronautics and Astronautics Journal (AIAA Journal), Journal of Computational Physics, Journal of the Physic al Society of Japan, Physics of Fluids, Quarterly of Applied Mathematics, Quarterly Journal of Mechanics and Applied Mathematics, SIAM Journal of Applied Mathematics, Zietschrift fur Angewandte Mathematik und Physik, (ZAMP), and Zietschrift fur Angewandte Mathematik und Mechanik, (ZAMM).
1. Warsi, Z.U.A., "Boundary Layer Growth on a Sphere," Quarterly Journal of Mechanics and Applied Mathematics, (Oxford), Vol. 16, Part 3, pp. 347-355, 1963.
2. Warsi, Z.U.A., "The Response of Laminar Boundary Layer to a Superposed Fluctuating Flow Past a Body of Revolution," Journal of Physical Society of Japan, Vol. 18, No. 12, pp. 1833-1837, 1963.
3. Warsi, Z.U.A., "Motion in a Three-Dimensional Boundary Layer With a Rapidly Oscillating External Flow," Journal of Physical Society of Japan, Vol. 19, No. 1, pp. 121-124, 1964.
4. Warsi, Z.U.A., "A Note on Three-Dimensional Boundary Layer Growth," Applied Scientific Research, (Netherlands), Vol. 13, Sec. A, pp. 313-320, 1964.
5. Kumar, R. and Warsi, Z.U.A., "Steady Motion of a Viscous Compressible Flow Through Circular and Coaxial Pipes," Bulletin Calcutta Mathematical Society, Vol. 55, No. 3, pp. 131-137, 1964.
6. Choudhury, N.K.D. and Warsi, Z.U.A., "Weighing Functions and Transient Thermal Response of Building," Part I, International Journal of Heat and Mass Transfer, Vol. 7, pp. 1309-1321, 1964.
7. Warsi, Z.U.A. and Choudhury, N.K.D., Ibid, Part II, pp. 1323-1334, 1964.
8. Warsi, Z.U.A., "On Three-Dimensional Periodic Boundary Layers," Ingenieur-rchiv (Göttingen), Vol. 34, No. 5, pp. 313-320, 1965.
9. Warsi, Z.U.A., "Periodic Boundary Layer on a Sphere Performing Torsional Oscillations in a Non-Newtonian Fluid," Anal. Sti. Univ. A1. I. Cuza. Sect. Ia Mat., Vol. XI, pp. 333-345, 1965.
10. Warsi, Z.U.A. and Chand, I., "Wind Tunnel Study of the Effect of Building Orientation and Ceiling Height on Indoor Air Motion," Indian Journal of Technology, Vol. 5, No. 11, 1967.
11. Warsi, Z.U.A. and Chand, I., "Studies of Wakes Created by Building Blocks," Indian Journal of Technology, Vol. 6, No. 1, 1968.
12. Warsi, Z.U.A. and Chand, I, "Distribution of air Velocities in a Room Due to a Ceiling Fan," Indian Journal of Technology, Vol. 5, p. 329, 1967.
13. Warsi, Z.U.A., "Further Theoretical Investigation of the Laminar Boundary Layer over Rotating Blades and Yawed Infinite-Wings," AIAA Journal, Vol. 7, No. 4, pp. 687-693, 1969.
14. Warsi, Z.U.A., "A Comparison of the Solution of Prandtl's and Navier-Stokes Equations in a Superposed Fluctuating Flow," Developments in Theoretical and Applied Mechanics, SECTAM, Vol. 5, pp. 847-863, 1971.
15. Warsi, Z.U.A. and Mertaugh, L.J., "Estimation of Turbulent Energy Dissipation Using Available Transfer Theories," AIAA Journal, Vol. 12, No. 12, pp. 327-339, 1974.
16. Warsi, Z.U.A., "Uniqueness of Mean Turbulent Flows," The Physics of Fluids, Vol. 17, No. 1, pp. 34-36, 1974.
17. Warsi, Z.U.A., "One Parameter Solution of the Spanwise Rotating Blade Boundary Layer Equation," AIAA Journal, Vol. 12, No. 10, pp. 1421-1423, 1974.
18. Warsi, Z.U.A., "A Class of External Flow Exhibiting Self-Similarity in Three Dimensional Boundary Layers," SIAM Journal on Applied Mathematics, Vol. 27, No. 2, pp. 331-340, 1974.
19. Warsi, Z.U.A., "Investigation of the Three-Dimensional Boundary Layer Separation Criteria by a Minimum Principle," International Journal of Engineering Science, Vol. 13, pp. 161-171, 1975.
20. Warsi, Z.U.A. and Amlicke, B.B., "Improved Algebraic Relation for the Calculation of Reynolds Stresses," AIAA Journal, Vol. 14, No. 12, pp. 1779-1781, 1976.
21. Warsi, Z.U.A., "Optimal Coordinates for Three-Dimensional Incompressible Laminar Boundary Layer," Journal of Applied Mathematics and Physics, (ZAMP), Vol. 28, pp. 467-479, 1977.
22. Warsi, Z.U.A., Devarayalu, K., and Thompson, J.F., "Numerical Solution of the Navier-Stokes Equations for Arbitrary Blunt Bodies in Supersonic Flows," Journal of Numerical Heat Transfer, Vol. 1, pp. 499-516, 1978.
23. Warsi, Z.U.A., "Conservation Form of the Navier-Stokes Equations in General Non-Steady Coordinates," AIAA Journal, Vol. 19, No. 2, pp. 240-241, 1981.
24. Warsi, Z.U.A. and Thompson, J.F., "A Non-Iterative Method for the Generation of Orthogonal Coordinates in Doubly Connected Regions," Mathematics of Computation, Vol. 38, No. 158, pp.510-516, 1982.
25. Thompson, J.F., Warsi, Z.U.A., and Mastin, C.W., "Boundary-Fitted Coordinate Systems for Numerical Solution of Partial Differential Equations - A Review," Journal of Computational Physics, Vol. 47, No. 1, pp. 1-108, 1982.
26. Warsi, Z.U.A., "A Note on the Mathematical Formulation of the Problem of Numerical Coordinate Generation," Quarterly of Applied Mathematics, Vol. 41, pp. 221-236, 1983.
27. Warsi, Z.U.A., "Numerical Grid Generation in Arbitrary Surfaces Through a Second-Order Differential-Geometric Model," Journal of Computational Physics, Vol. 64, pp. 82-96, 1986.
28. Warsi, Z.U.A., "A Synopsis of Elliptic PDE Models for Grid Generation," Applied Mathematical Computations, Vol. 21, pp. 295-311, 1987.
29. Warsi, Z.U.A., "Theoretical Foundation of the Equations for the Generation of Surface Coordinates, AIAA Journal, Vol. 28, pp. 1140-1142, 1990.
30. Warsi, Z.U.A. and Thompson, J.F., "Application of Variational Methods in the Fixed and Adaptive Grid Generation," Computers and Mathematics with Applications, Vol. 19, pp. 31-41, 1990.
31. Warsi, Z.U.A. and Koomullil, G.P., "Numerical Solution of the Faulkner-Skan Equation - A Fresh Look," Ganita, Vol. 41, pp. 49-60, 1990.
32. Warsi, Z.U.A., "Surface Grid Generation and Differential Geometry," SIAM Series, Frontier in Applied Mathematics, Vol. 8, Philadelphia, PA, 1991.
33. Warsi, Z.U.A., "Fluid Dynamics: Theoretical and Computational Approaches," CRC Press, Inc., 1993.
34. Koomullil, G.P. and Warsi, Z.U.A., "Numerical Mapping of Arbitrary Domains Using Spectral Methods, Journal of Computational Physics, Vol. 104, No. 1, pp. 251-262, 1993.
35. Warsi, Z.U.A. and Koomullil, G.P., "Spectral Solutions of the Navier-Stokes Equations in Arbitrary Two-Dimensional Domains," Mathematics and Computers in Simulation (IMACS), Vol. 36, pp. 185-193, 1994.
36. Warsi, Z.U.A., "Unsteady Flow of Power-Law Fluids Through Circular Pipes," Journal of Non-Newtonian Fluid Mechanics, Vol. 55, pp. 197-202, 1994.
37. Warsi, Z.U.A., "Fundamental Theorem of The Surface Theory And Its Extension To Reimannian Manifold of General Relativity," GANITA, Vol. 46, pp. 119-129, 1995.
38. Warsi, Z.U.A., "Operations on the Physical Components of Tensors," Z. Angew. Math. Mech. (ZAMM), Vol. 76, pp. 361-363, 1996.
39. Hamouche, N.C., Warsi, Z.U.A., and McWhorter, John C., "A Spectral Solution For The Bending of Arbitrarily Shaped Plates," Journal of Computers and Structures, Vol. 63, pp. 159-171, 1997.
40. Warsi, Z.U.A., "Vorticity Jump in Surface Coordinates Across A Shock in Nonsteady Flow," AIAA J., Vol. 35, pp.1228-1230, 1997.
41. Warsi, Z.U.A., "Analysis and Numerical Evaluation of The Drift Functions of Darwin and Lighthill for Axisymmetric Flows," Theoretical and Computational Fluid Dynamics, Vol. 10, pp. 439-448, 1998.

Patents

• None

Reviews On My Book

1. Applied Mechanics Review, Vol. 46, No. 5, 1993, Review No. 5R36, on Fluid Dynamics: Theoretical and Computational Approaches.

Presentations

1. Warsi, Z.U.A. and Choudhury, N.K.D., "On Vibration of a Thin Semi-Finite-Plate," International Acoustic Congress, Brussels, Vol. 2, 1966.
2. Warsi, Z.U.A., "A Numerical Method of Solving the Three-Dimensional Boundary Layer Equations with Application to Rotating Flat Blade," AIAA 69-227, 1969.
3. Warsi, Z.U.A., "Analysis of Three-Dimensional Turbulent Boundary Layers on Rotating Blades," Proceedings, Themes Symposium on Vehicular Dynamics, Rock Island Arsenal/University of Iowa, pp. 443-470, November 1971.
4. Warsi, Z.U.A. and Kiran, N.S., "The Response of Laminar Boundary Layer on a Yawed Flat Plat in an Adverse Pressure Gradient to Small Perturbations," Indian Society of Theoretical and Applied Mechanics, December 1972.
5. Thompson, J.F. and Warsi, Z.U.A., "Numerical Solutions for Laminar and Turbulent Viscous Flow Over Single and Multi-Element Airfoils Using Body-Fitted Coordinate System," NASA CP-200, Vol. 4, pp. 1397-1408, 19762.
6. Warsi, Z.U.A., " Numerical Generation of Two-Dimensional Orthogonal Curvilinear Coordinates in an Euclidean Space," Proceedings of a workshop held at NASA Langley Research Center, Hampton, VA, NASA Conference Publication 2166, October 6-7, 1980.
7. Warsi, Z.U.A., "Basic Differential Models for Coordinate Generation," Numerical Grid Generation, Elsevier Scientific Publishing Co., pp. 41-77, 1982.
8. Warsi, Z.U.A. and Ziebarth, J., "Numerical Generation of Three-Dimensional Coordinates Between Bodies of Arbitrary Shapes," Numerical Grid Generation, Elsevier Scientific Publishing Co., pp. 717-728, 1982.
9. Thompson, J.F. and Warsi, Z.U.A., "Three-Dimensional Grid Generation from Elliptic Systems," AIAA-83-1905.
10. Warsi, Z.U.A., "Generation of Three-Dimensional Grids Through Elliptic Differential Equations," presented at the 4th Computational Fluid Dynamics Conference, Von Karman Institute for Fluid Dynamics, Belgium, March 1984.
11. Warsi, Z.U.A., "The Importance of Dynamically-Adaptive Grids in the Numerical Solution of Partial Differential Equations," presented at the 4th Computational Fluid Dynamics Conference, Von Karman Institute for Fluid Dynamics, Belgium, March 1984.
12. Warsi, Z.U.A., "Generation of Surface Coordinates by Elliptic Partial Differential Equations," Presented at NASA Conference of Computational Geometry and Computer-Aided Design, June 1985.
13. Warsi, Z.U.A., "Numerical Grid Generation Through Second Order Differential-Geometric Models, 11th IMACS World Conference, Oslo, August 1985. (Published in Numerical Mathematics and Applications, Eds. R. Vichnevetsky and J. Vignes, Elsevier, pp. 199-203, 1986.
14. Warsi, Z.U.A., "Surface Mesh Generation Using Elliptic Equations," Numerical Grid Generation in Computational Fluid Dynamics, Landshut, West Germany, July 1986. (published in Numerical Grid Generation in Computational Fluid Dynamics, Eds. J. Hauser and C. Taylor, Pineridge, Press, U.K., pp. 95-110, 1986.
15. Warsi, Z.U.A., "Surface Grid Generation Through Elliptic PDE's," Numerical Grid Generation in Computational Fluid Mechanics, '88, Eds. S. Sengupta et al., Pineridge Press, pp. 207-216, 1988.
16. Thompson, J.F. and Warsi, Z.U.A., "Surface Grid Generation for Composite Block Grids," Ibid, p. 167, 1988.
17. Warsi, Z.U.A. and Koomullil, G.P., "Application of Spectral Techniques in Surface Grid Generation," 3rd International Conference Numerical Grid Generation in Computational Fluid Dynamics, June 1991.
18. Warsi, Z.U.A. and Koomullil, G.P., "Spectral Solution Methodology For Navier-Stokes Equations," Presented at the Society of Engineering Science, New Orleans, LA, October 29, 1995.

Invited Lectures

1. "Computational Models in Grid Generation for Problems in Fluid Flow," Von Karman Institute of Fluid Dynamics, Belgium, 1984.
2. "Mesh Generation," CFD Group, Air Force Wright Aeronautical Laboratories, Wright-Patterson Air Force Base, Ohio, 1986.
3. "Surface Grid Generation and Differential Geometry," SIAM Meeting, Minneapolis, Minnesota, 1988.
4. "Differential and Variational Models in Surface Grid Generation," SIAM - AMS Meeting, Albuquerque, New Mexico, April 19-21, 1990.
5. "Numerical Mapping of Arbitrary Domains Using Spectral Methods," ICASE, NASA Langley, Hampton, Virginia, January 4, 1991.
6. "A Course of Lectures in Grid Generation and Turbulence Modeling," at the Mathematical Modeling Center, Central Water and Power Research Station, Pune, India, 15 May - 3 June 1995. (Under the auspices of the United Nations, Project No. IND/90/038.
7. "Analysis and Numerical Evaluation of the Drift Function of Darwin and Lighthill for Axisymmetric Flows," paper Presented In Honor of Sir James Lighthill, Florida State University, November, 1996.

Reports (Published as MSSU-EIRS)

1. Warsi, Z.U.A. and Thompson, J.F., "Machine Solutions of Partial Differential Equations in the Numerically Generated Coordinate Systems," MSSU-EIRS-ASE-77-1, August 1976.
2. Warsi, Z.U.A. and Amlicke, B.B., "Structure of the Near-Wall Region in a Turbulent Flow," MSSU-EIRS-SE-77-3, September 1976.
3. Warsi, Z.U.A., Devarayalu, K., and Thompson, J.F., "Numerical Solution of the Navier-Stokes Equations for Blunt Nosed Bodies in Supersonic Flows," MSSU-EIRS-ASE-78-1, NASA CR-157083, May 1978.
4. Warsi, Z.U.A., Amlicke, B.B., and Thompson, J.F., "Numerical Solution of the Two-Dimensional Incompressible Average Navier-Stokes Equations for Finite Arbitrary Shaped Isolated Bodies," MSSU-EIRS-ASE-79-1, November 1979.
5. Warsi, Z.U.A., Weed, R.A., and Thompson, J.F., "Numerical Generation of Two-Dimensional Orthogonal Curvilinear Coordinates in an Euclidean Space," MSSU-EIRS-ASE-80-3, June 1980.
6. Warsi, Z.U.A. and Weed, R.A., "On the Solution of the Unsteady Navier-Stokes Equations for Hypersonic Flow About Axially-Symmetric Blunt Bodies," MSSU-EIRS-ASE-6, September 1980.
7. Warsi, Z.U.A., "A Method for the Generation of General Three-Dimensional Coordinates Between Bodies of Arbitrary Shapes," MSSU-EIRS-80-7, October 1980.
8. Warsi, Z.U.A., "Tensor and Differential Geometry Applied to Analytic and Numerical Coordinate Generation," MSSU-EIRS-81-1, January 1981.
9. Warsi, Z.U.A., "Numerical Generation of Orthogonal and Non-Orthogonal Coordinates in Two-Dimensional Simply-and Doubly-Connected Regions," Von Karman Institute, Technical Note 151, May 1984.
10. Koomullil, G.P. and Warsi, Z.U.A., "Numerical Mapping of Arbitrary Domains Using Spectral Methods," MSSU-EIRS-ASE-92-2, January 1992.
11. Hamouche, N., Warsi, Z.U.A., and McWhorter, J.C., "Numerical Solution of the Biharmonic Plate Equation for Arbitrary Shaped Plates Utilizing Spectral Methods," MSSU-EIRS-ASE-94-1, 1993.
12. Beddhu, M. and Warsi, Z.U.A., "A Fractional Time-Stepping Method for Solving the Compressible Navier-Stokes Equations," MSSU-EIRS-ASE-94-2, 1994.

University Service

• Member of various college and departmental committees

Students Advised

• Michael R. Smith, Ph.D. 1970
• Gerald A. Jones, M.S. 1971
• N.S. Kiran, Ph.D. 1972
• James A. Collins, M.S. 1972
• Thomas J. Plant, M.S. 1973
• Lawrence J. Mertaugh, Jr., Ph.D. 1975
• Bruce Amlicke, M.S. 1976
• Krishna Devarayalu, Ph.D. 1978
• Bruce Amlicke, Ph.D. 1978
• W.-Nrung Tiarn, M.S. 1983
• Johnny P. Ziebarth, Ph.D. 1983
• J.-Hwa Lee, M.S. 1985
• W.-Nrung Tiarn, Ph.D. 1988
• George P. Koomullil, Ph.D. 1991
• Murali Beddhu, Ph.D. 1992
• Ho-Jae Son, M.S. 1993
• Nakhle C. Hamouche, Ph.D. 1993
• Clifton A. Stokes, M.S. 1994
• Ahmad Khanayesh, Ph.D. 1994 (Minor Professor)
• Ho-Jae Son, Ph.D. 1996
• Toh Hoong Thiam, M.S. 1997

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