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

• 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:
  • Daniel Appelo, University of New Mexico.
  • Jeff Banks, Lawrence Livermore National Laboratory.
  • Rich Braun, University of Delaware.
  • Kyle Chand, Lawrence Livermore National Laboratory.
  • Ash Kapila, Rensselaer Polytechnic Institute.
  • Kara Maki, Rochester Institute of Technology.
  • Don Schwendeman, Rensselaer Polytechnic Institute.
  • Bjorn Sjogreen, Lawrence Livermore National Laboratory.

• Recent publications (full list with links):
  • Longfei Li, William D. Henshaw, Jeffrey W. Banks, Donald W. Schwendeman, and Geoffrey A. Main.
    A stable partitioned FSI algorithm for incompressible flow and deforming beams.
    (arXiv:1507.06041), 2016.
    AStablePartitionedFSIAlgorithmForIncompressibleFlowAndDeformingBeams_Li_Henshaw_Banks_Schwendeman_Main_2016.pdf.
    
  • Jeffrey W. Banks, William D. Henshaw, and Donald W. Schwendeman.
    An added-mass partitioned algorithm for fluid-structure interactions of compressible fluids and nonlinear solids.
    J. Comput. Phys., 305:1037-1064, 2016.
    AddedMassPartitionedFSIofCompressibleFluidsAndNonlinearSolids_Banks_Henshaw_Kapila_Schwendeman_2016.pdf.
    
  • Ashwana K. Kapila, Donald W. Schwendeman, J. Gambino, and William D. Henshaw.
    A numerical study of the dynamics of detonation initiated by cavity collapse.
    Shock Waves, 25(6):545-572, 2015.
    NumericalStudyOfTheDynamicsOfDetonationInitiatedByCavityCollapse_Kapila_Schwendeman_Gambino_Henshaw_2015.pdf.
    
  • Jeffrey W. Banks and William D. Henshaw and Donald W. Schwendeman.
    An analysis of a new stable partitioned algorithm for FSI problems. Part I: Incompressible flow and elastic solidsUpwind schemes for the wave equation in second-order form.
    J. Comput. Phys., 269:108-137, 2014.
    AMPInsBulkBanksHenshawSchwendeman2014.pdf.

  • Jeffrey W. Banks and William D. Henshaw and Donald W. Schwendeman.
    An analysis of a new stable partitioned algorithm for FSI problems. Part II: Incompressible flow and structural shells.
    J. Comput. Phys., 268:399-416, 2014.
    AMPInsShellBanksHenshawSchwendeman2014.pdf.

  • 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.

• Spring semester, 2020
  • MATH 6840 Numerical Solution of PDEs

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