My research concerns the development of numerical algorithms for problems in continuum mechanics.  One recurring theme is multiphase flow, where the boundary between coexisting phases is fully resolved.

  1. G.H. Miller and D. Trebotich, A front tracking embedded boundary method for two-fluid incompressible Navier-Stokes problems with surface tension.  2014.  In prep.

  2. W.-C. Tsai and G.H. Miller, Numerical simulations of viscoelastic flow in complex geometries using a multi-mode Giesekus model, J. Non-Newtonian Fluid Mech., 210:29-40, 2014.

  3. M. Vahab and G.H. Miller, A front-tracking shock-capturing method for two fluids.  Comm. App. Math. Comput. Sci., 2013.  submitted.

  4. G.H. Miller and E.G. Puckett, a Neumann-Neumann preconditioned iterative substructuring approach for computing solutions to Poisson’s equation with prescribed jumps on an embedded boundary.  J. Comput. Phys., 235:683-700, 2013.

  5. B. Kallemov, G.H. Miller, S. Mitran, and D. Trebotich, Calculation of viscoelastic bead-rod flow mediated by a homogenized kinetic scale with holonomic constraints, Mol. Simulat., 38:786-792, 2012.

  6. G.H. Miller and D. Trebotich.  An embedded boundary method for the Navier-Stokes equations on a time-dependent domain.  Comm. App. Math. Comput. Sci., 7(1):1-31, 2012.

  7. B. Wang, G. Miller, and P. Colella.  An adaptive high-order phase-space remapping for the two-dimensional Vlasov-Poisson equations.  SIAM J. Sci. Comput., 34:B909-B924, 2012.

  8. B. Kallemov and G. H. Miller, A second-order strong method for the Langevin equations with holonomic constraints.  SIAM J. Sci. Comput., 33(2):653-676, 2011.

  9. B. Kallemov, G. H. Miller, and D. Trebotich, A higher-order accurate fluid-particle algorithm for polymer flows.  Mol. Simulat., 37(8):738-745, 2011.

  10. B. Wang, G.H. Miller, and P. Colella, A particle-in-cell method with adaptive phase-space remapping for kinetic plasmas.  SIAM J. Sci. Comput., 33(6):3509-3537, 2011.

  11. B. Kallemov, G.H. Miller, and D. Trebotich, Numerical simulation of polymer flow in microfluidic devices.  In Proc. 4th SIAM Conference on Mathematics for Industry, p. 93-98, 2010.

  12. S.A. Conley, I. Faloona, G.H. Miller, D.H. Lenshow, B. Blomquist, and A. Bandy.  Closing the dimethyl sulfide budget in the tropical marine boundary layer during the Pacific Atmospheric Sulfur Experiment.  Atmos. Chem. Phys., 9:8745-8756, 2009.

  13. B. Kallemov, G.H. Miller, and D. Trebotich, A Duhamel approach for the Langevin equations with holonomic constraints.  Mol. Simulat., 35(6):440-447, 2009.

  14. A. Nonaka, D. Trebotich, G.H. Miller, D.T. Graves, and P. Colella, A higher-order upwind method for viscoelastic flow.  Comm. App. Math. Comput. Sci., 4:57-83, 2009.

  15. D.T. Graves, D. Trebotich, G.H. Miller, and P. Colella.  An efficient solver for the equations of resistive MHD with spatially-varying resistivity.  J. Comput. Phys., 227:4797-4804, 2008.

  16. B. Kallemov, G.H. Miller, and D. Trebotich.  A higher-order approach to fluid-particle coupling in microscale polymer flows.  In Nanotechnology 2008:  Microsystems, Photonics, Sensors, Fluidics, Modeling, and Simulation, v3, Boston, MA, June 1-5, 2008.

  17. G.H. Miller.  An iterative boundary potential method for the infinite-domain Poisson problem with interior Dirichlet boundaries.  J. Comput. Phys., 227:7917-7928, 2008.

  18. G.H. Miller and D. Trebotich.  Toward a mesoscale model for the dynamics of polymer solutions.  J. Comput. Theor. Nanosci., 4:797-801, 2007.

  19. D. Trebotich, G.H. Miller, and M.D. Bybee.  A penalty method to model particle interactions in DNA-laden flows.  J. Nanosci. Nanotech., 8:1-8, 2007.

  20. D. Trebotich, P. Colella, and G.H. Miller, A stable and convergent scheme for viscoelastic flow in contraction channels.  J. Comput. Phys., 205:315-342, 2005.

  21. D. Trebotich and G.H. Miller, Modeling and simulation of DNA flow in a microfluidic-based pathogen detection system.  In Proc. 3rd Annual International IEEE EMBS Special Topic Conference on Microtechnologies in Medicine and Biology, Kahuku, Oahu, Hawaii. 12-15 May 2004, p. 353-355, 2005.

  22. D. Trebotich, G.H. Miller, P. Colella, D.T. Graves, D.F. Martin, and P.O. Schwartz.  A tightly-coupled particle-fluid method for DNA-laden flows in complex microscale geometries.  In Computational Fluid and Solid Mechanics 2005, p. 1018-1022, 2005.

  23. J.E. Bowen , M.W. Wactor, G.H. Miller, and M. Capelli-Schellpfeffer.  Catch the Wave: Modeling of the Pressure Wave Associated with Arc Fault.  IEEE Industry Applications Magazine, 10:59-67, 2004.

  24. G.H. Miller.  Minimal rotationally-invariant bases for hyperelasticity.  SIAM J. Appl. Math., 64:2050-2075, 2004.

  25. D. Trebotich, P. Colella, G.H. Miller, A. Nonaka, T. Marshall, S. Gulati, and D. Liepmann.  A numerical algorithm for complex biological flow in irregular microdevice geometries.  In Technical Proceedings of the 2004 Nanotechnology Conference and Trade Show, v2, p. 470-473, 2004.

  26. G.H. Miller.  An iterative Riemann solver for systems of hyperbolic conservation laws, with application to hyperelastic solid mechanics.  J. Comput. Phys., 193:198-225 2003.

  27. D. Trebotich, P. Colella, G. Miller, and D. Liepmann.  A numerical model of viscoelastic flow in microchannels.  In Technical Proceedings of the 2003 Nanotechnology Conference and Trade Show, v. 2, p. 520-523, 2003.

  28. G.H. Miller and P. Colella, A conservative three-dimensional Eulerian method for coupled fluid-solid shock capturing.  J. Comput. Phys., 183:26-82, 2002.

  29. J.G. Blank, G.H. Miller, M.H. Ahrens, and R.E. Winans.  Experimental shock chemistry of aqueous amino acid solutions and the cometary delivery of prebiotic compounds.  Origins of Life Evol. B., 31:15-51, 2001.

  30. G.H. Miller and P. Colella, A high-order Eulerian Godunov method for elastic-plastic flow in solids.  J. Comput. Phys., 167:131-176, 2001.

Since 2000:

Mehdi Vahab and Wan-Chi Tsai, 2014.

The velocity field for an air bubble rising in water.