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MATH 4820

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Mathematical Sciences
William D. Henshaw

Margaret A. Darrin Distinguished Professor in Applied Mathematics
Ph.D. California Institute of Technology
Computational and Applied Mathematics

William D. Henshaw
Research

  • Interests:

    • Numerical algorithms for solving partial differential equations,
    • High-order accurate methods,
    • Approximations for adaptive and overlapping grids,
    • Incompressible and compressible fluid flows, fluid-structure interactions, solid mechanics and electromagnetics.
    • Overture framework http://www.OvertureFramework.org

  • Collaborators:

  • Recent publications (full list with links):

    • Jeffrey W. Banks, William D. Henshaw, and Donald W. Schwendeman.
      A stable partitioned FSI algorithm for incompressible flow and elastic solids.
      Research Report LLNL-JRNL-642572, Lawrence Livermore National Laboratory, 2013.
      arXiv:1308.5913.

    • Jeffrey W. Banks, William D. Henshaw, and Donald W. Schwendeman.
      A stable partitioned FSI algorithm for incompressible flow and structural shells.
      Research Report LLNL-JRNL-642503, Lawrence Livermore National Laboratory, 2013.
      arXiv:1308.5722.

    • Jeffrey W. Banks, William D. Henshaw, and Björn Sjögreen.
      A stable FSI algorithm for light rigid bodies in compressible flow.
      J. Comput. Phys., 231(17):5854-5889, 2013.
      BanksHenshawSjogreenFSIforLightRigidBodies2012.pdf.

    • Jeffrey W. Banks and William D. Henshaw.
      Upwind schemes for the wave equation in second-order form.
      J. Comput. Phys., 231(17):5854-5889, 2012.
      BanksHenshawSOSUP2012.pdf.

    • Andrea Lani, Björn Sjögreen, H. C. Yee, and William D. Henshaw.
      Variable high-order multiblock overlapping grid methods for mixed steady and unsteady multiscale viscous flows, part II: hypersonic nonequilibrium flows.
      Commun. Comput. Phys., 13(2):583-602, 2012.

    • D.W. Schwendeman, A.K. Kapila and W.D. Henshaw, A Hybrid Two-Phase Mixture Model of Detonation Diffraction with Compliant Confinement, Comptes Rendus Mathematique, 340 (2012), 804-817.

    • D. Appelo, J.W. Banks, W.D. Henshaw and D.W. Schwendeman, Numerical methods for solid mechanics on overlapping grids: linear elasticity, J. Comput. Physics, 231 (2012), 6012-6050.

    • D.W. Schwendeman, A.K. Kapila and W.D. Henshaw, A comparative study of two macro-scale models of condensed-phase explosives, IMA J. Applied Math., 77 (2012), 2-17.

    • M. Ozlem, D.W. Schwendeman, A.K. Kapila and W.D. Henshaw, A numerical study of shock-induced cavity collapse, Shock Waves, 22 (2012), 89-117.

    • J.W. Banks, W.D. Henshaw and D.W. Schwendeman, Deforming composite grids for solving fluid structure problems, J. Comput. Physics, 231 (2012), pp. 3518-3547.

    • D.W. Schwendeman, A.K. Kapila and W.D. Henshaw, A Study of Detonation Diffraction and Failure for a Model of Compressible Two-Phase Reactive Flow, Combust. Theory and Modeling, 14 (2010), pp. 331-366.

    • William D. Henshaw.
      Encyclopedia of Aerospace Engineering, chapter Adaptive Mesh and Overlapping Grid Methods, pages 623-630.
      Wiley, 2010.

    • K. L. Maki, R. L. Braun, W. D. Henshaw, and P. E. King-Smith.
      Tear film dynamics on an eye-shaped domain I: Pressure boundary conditions.
      Mathematical Medicine and Biology, electronic, 2010.

    • K. L. Maki, R. L. Braun, P. Ucciferro, W. D. Henshaw, and P. E. King-Smith.
      Tear film dynamics on an eye-shaped domain II: Flux boundary conditions.
      Journal of Fluid Mechanics, 647:361-390, 2010.

    • M. A. Singer, W. D. Henshaw, and S. L. Wang.
      Computational modeling of blood flow in the Trapease inferior Vena Cava filter.
      Journal of Vascular and Interventional Radiology, 20:S136-S137, 2009.

    • Jeffrey W. Banks, William D. Henshaw, and John N. Shadid.
      An evaluation of the FCT method for high-speed flows on structured overlapping grids.
      J. Comput. Phys., 228:5349-5369, 2009.
      BanksHenshawShadidOversetFCT2009.pdf.

    • William D. Henshaw and Kyle K. Chand.
      A composite grid solver for conjugate heat transfer in fluid-structure systems.
      J. Comput. Phys., 228:3708-3741, 2009.
      henshawChandCHT2009.pdf.

    • W.D. Henshaw and D.W. Schwendeman, Parallel computation of three-dimensional flows using overlapping grids with adaptive mesh refinement, J. Comput. Physics, 227 (2008), pp. 7469-7502.

    • J.W. Banks, D.W. Schwendeman, A.K. Kapila and W.D. Henshaw, A study of detonation propagation and diffraction with compliant confinement, Combust. Theory and Modeling, 12 (2008), pp. 769-808.


Course Information

  • Spring semester, 2014
    • MATH 4820 An Introduction to Numerical Methods for Differential Equations


Contact Information

William Henshaw
Department of Mathematical Sciences, AE 304
Rensselaer Polytechnic Institute
110 8th Street
Troy, New York 12180

Phone: (518) 276-2994
Fax: (518) 276-4824
Email: henshw@rpi.edu

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