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Mathematical Sciences
Amos Eaton Building
Department of Mathematical Sciences Faculty:

Kristin Bennett
Mohamed Boudjelkha
Margaret Cheney
Donald Drew
Joseph Ecker
Joseph E. Flaherty
Isom Herron
Mark Holmes
David Isaacson
Ashwani Kapila
Maya Kiehl
Gregor Kovacic
Peter Kramer
Gina Kucinski
Rongjie Lai
Fengyan Li
Chjan Lim
Yuri Lvov
Harry McLaughlin
Joyce McLaughlin
John Mitchell
Clifford Nolan
Bruce Piper
Victor Roytburd
David Schmidt
Donald Schwendeman
William Siegmann
Michael Zuker

Mathematical Sciences Faculty
Donald Schwendeman

Professor of Mathematical Sciences


Ph.D., California Institute of Technology

Research Areas:

Numerical methods for partial differential equations.
Gas dynamics and wave propagation.
Multiscale and multiphase reactive flow.
Adaptive mesh refinement and parallel algorithms.
Mathematical modeling and computations in industrial applications.

Selected Publications:

J.W. Banks, D.W. Schwendeman, A.K. Kapila and W.D. Henshaw, A high-resolution Godunov method for compressible multi-material flow on overlapping grids, J. Comput. Physics, submitted.

A.K. Kapila, D.W. Schwendeman, J.B. Bdzil and W.D. Henshaw, A study of detonation diffraction in the ignition-and-growth model, Combust. Theory and Modeling, submitted.

W.D. Henshaw and D.W. Schwendeman, Moving overlapping grids with adaptive mesh refinement for high-speed reactive and nonreactive flow, J. Comput. Physics, accepted.

D.W. Schwendeman, C.W. Wahle and A.K. Kapila, The Riemann problem and a high resolution Godunov method for a model of compressible two-phase flow, J. Comput. Physics, 212 (2006), pp. 490-526.

L.J. Borucki, T. Witelski, C. Please, P.R. Kramer and D.W. Schwendeman, A theory of pad conditioning for chemical-mechanical polishing, J. Engineering Mathematics, 50 (2004), pp. 1-24.

A.K. Kapila and D.W. Schwendeman, Detonation initiation: modelling, computation and mechanisms, Proceedings of the International Symposium on Advances in Computational Heat Transfer, Bergen, Norway, April 19-24, 2004.

W.D. Henshaw and D.W. Schwendeman, An adaptive numerical method for high-speed reactive flow on overlapping grids, J. Comput. Physics, 191 (2003), pp. 420-447.

A.K. Kapila, D.W. Schwendeman, J.J. Quirk and T. Hawa, Mechanisms of detonation formation due to a temperature gradient, Combustion Theory and Modeling, 6 (2002), pp. 553-594.

D.G. Thakurta, D.W. Schwendeman, R.J. Gutmann, S. Shankar, L. Jiang and W.N. Gill, Three-dimesional wafer-scale copper chemical-mechanical planarization model, Thin Solid Films, 414 (2002), pp. 78-90.

D.W. Schwendeman, On converging shock waves of spherical and polyhedral form, J. Fluid Mech., 454 (2002), pp. 365-386.

A.D. Fitt, P.D. Howell, J.R. King, C.P. Please and D.W. Schwendeman, Multiphase flow in a roll press nip, Euro. J. Appl. Math., 13 (2002), pp. 225-259.

D.W. Schwendeman and A.K. Kapila, Effect of thermal nonhomogeneity on the occurrence of thermal explosion or detonation in an annular cookoff, Proceedings of the Twelfth Symposium (International) on Detonation, San Diego, CA, 2002.

D.G. Thakurta, C.L. Borst, D.W. Schwendeman, R.J. Gutmann and W.N. Gill, Three-dimensional chemical-mechanical planarization slurry flow model based on lubrication theory, J. Electrochemical Society, 148 (2001), pp. G207-G214.

H.G. Hornung and D.W. Schwendeman, Oblique shock reflection from an axis of symmetry: Shock dynamics and relation to the Guderley singularity, J. Fluid Mech., 438 (2001), pp. 231-245.

D.G. Thakurta, C.L. Borst, D.W. Schwendeman, R.J. Gutmann, and W.N. Gill, Pad porosity, compressibility and slurry delivery effects in chemical-mechanical planarization: modeling and experiments, Thin Solid Films, 366 (2000), pp. 181-190.

S. Sundararajan, D.G. Thakurta, D.W. Schwendeman, S.P. Murarka, and W.N. Gill, Two-dimensional wafer-scale chemical-mechanical planarization models based on lubrication theory and mass transport, J. Electro. Society, 146 (1999), pp. 761-766.

D.W. Schwendeman, A higher order Godunov method for the hyperbolic equations modeling shock dynamics, Proc. Royal Society Lond., A455 (1999), pp. 1215-1233.

B.L. Bihari and D.W. Schwendeman, Multiresolution schemes for the reactive Euler equations, J. Comput. Physics, 154 (1999), pp. 197-230.

S.A. Triantafillou, D.W. Schwendeman, and J.D. Cole, Optimization of conical wings in hypersonic flow, J. Theoret. and Comput. Aerodynamics, 12 (1998), pp. 219-232.

D.W. Schwendeman, A front dynamics approach to curvature-dependent flow, SIAM J. Applied Math, 56 (1996), pp. 1523-1538.

D.W. Schwendeman, M.C.A. Kropinski and J.D. Cole, An analytical and numerical study of optimal critical airfoils, J. Applied Math and Mech. (ZAMM), 76 (1996), pp. 365-368.

M.C.A. Kropinski, D.W. Schwendeman, and J.D. Cole, Hodograph design of lifting airfoils with high critical Mach numbers, J. Theoret. and Comput. Aerodynamics, 7 (1995), pp. 173-188.

C.P. Please, D.W. Schwendeman, and P.S. Hagan, Ohmic heating of foods during aseptic processing, IMA J. of Mathematics Applied to Business and Industry, 5 (1995), pp. 283-301.

D.W. Schwendeman, Accuracy of shock wave propagation using geometrical shock dynamics, Proc. 20th International Symp. on Shock Waves, Pasadena, California, July 23-28, 1995.

P.S. Hagan, C.P. Please, and D.W. Schwendeman, Light-off behavior of catalytic converters, SIAM J. Appl. Math., 54 (1994), pp. 72-92.

D.W. Schwendeman, A new numerical method for shock wave propagation based on geometrical shock dynamics, Proc. Royal Society, A441 (1993), pp. 331-341.

D.W. Schwendeman, M.C.A. Kropinski, and J.D. Cole, On the construction and calculation of optimal nonlifting critical airfoils, J. Appl. Math. and Phys. (ZAMP), 44 (1993), pp. 556-571.

R. Akbar, D.W. Schwendeman, J.E. Shephard, R.L. Williams, and G.O. Thomas, Wave shaping channels for gaseous detonations, Proc. 19th International Symp. on Shock Waves, Marseille, France, July 26-30, 1993.

C.C. Lim, J.M. Pimbley, C. Schmeiser, and D.W. Schwendeman, Rotating waves for semiconductor inverter rings, SIAM J. Appl. Math., 52 (1992), pp. 671-690.

J.D. Cole, M.C.A. Kropinski and D.W. Schwendeman, A study of critical airfoils, Proc. International Symp. on C.F.D., Davis, CA, 1991.

D.W. Schwendeman, Numerical shock propagation using a full potential equation, Proc. International Symp. on C.F.D., Davis, CA, 1991.

D.W. Schwendeman, Nonlinear diffusion of impurities in semiconductors, J. Appl. Math. and Phys. (ZAMP), 41 (1990), pp. 607-627.

J.D. Cole and D.W. Schwendeman, Hodograph design of shock-free transonic bodies, Proc. 3rd International Conf. on Hyperbolic Problems, Uppsala, Sweden 1990.

D.W. Schwendeman, A numerical scheme for shock propagation in three dimensions, Proc. Royal Society, A416 (1988), pp. 179-198.

D.W. Schwendeman, Numerical shock propagation in non-uniform media, J. Fluid Mech., 188 (1988), pp. 383-410.

D.W. Schwendeman and G.B. Whitham, On converging shock waves, Proc. Royal Society, A413 (1987), pp. 297-311.

W.D. Henshaw, N.F. Smyth and D.W. Schwendeman, Numerical shock propagation using geometrical shock dynamics, J. Fluid Mech., 171 (1986), pp. 519-545.

Contact Information:

Donald Schwendeman
(518) 276-2647

More Info:


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