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Applied Numerical Algorithms Group

Greg Miller

Gregory H. Miller
Faculty Scientist
Phone: +1 510 486 5412
Fax: +1 510 486 6900

Research Interests

  • The development of numerical methods for the solution of complex problems in engineering and science, mostly at the continuum scale.
  • Complex rheology: multiscale and continuum methods for incompressible viscoelastic flows.
  • Multiphase flows: compressible and incompressible flows of fluids and elastic-plastic solids in time-dependent domains, interfacial processes.
  • Constitutive modeling: equations of state, thermodynamic modeling, symmetry invariants.
  • Charged systems: plasma physics, boundary charge and bilayer problems.

Journal Articles

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", Molecular Simulation, 2012, doi: 10.1080/08927022.2011.654206

G. H. Miller and D. Trebotich, "An Embedded Boundary Method for the Navier-Stokes Equations on a Time-Dependent Domain", Communications in Applied Mathematics and Computational Science, 7(1):1-31, 2012,

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, 2011,

B. Kallemov, G. H. Miller, S. Mitran and D. Trebotich, "Multiscale Rheology: New Results for the Kinetic Scale", NSTI-Nanotech 2011, Vol. 2, pp. 575-578 (2011), 2011,

B. Kallemov, G. H. Miller and D. Trebotich, "A Higher-Order Accurate Fluid-Particle Algorithm for Polymer Flows", Molecular Simulation, 37(8):738-745 (2011), 2011,

B. Kallemov, G. H. Miller and D. Trebotich, "A Duhamel Approach for the Langevin Equations with Holonomic Constraints", Molecular Simulation, 35(6):440-447, 2009,

A. Nonaka, D. Trebotich, G. H. Miller, D. T. Graves, and P. Colella, "A Higher-Order Upwind Method for Viscoelastic Flow", Comm. App. Math. and Comp. Sci., 4(1):57-83, 2009,

D. T. Graves, D Trebotich, G. H. Miller, P. Colella, "An Efficient Solver for the Equations of Resistive MHD with Spatially-Varying Resistivity", Journal of Computational Physics Vol 227 (2008) pp.4797-4804., 2008,

D. Trebotich, G. H. Miller and M. D. Bybee, "A Penalty Method to Model Particle Interactions in DNA-laden Flows", J. Nanosci. Nanotechnol., 8(7):3749-3756, 2008,

G. H. Miller and D. Trebotich, "Toward a Mesoscale Model for the Dynamics of Polymer Solutions", J. Comput. Theoret. Nanosci. 4(4):797-801, 2007,

D. Trebotich, G. H. Miller and M. D. Bybee, "A Hard Constraint Algorithm to Model Particle Interactions in DNA-laden Flows", Nanoscale and Microscale Thermophysical Engineering 11(1):121-128, 2007,

Trebotich, D., Colella, P., Miller, G.H., "A Stable and Convergent Scheme for Viscoelastic Flow in Contraction Channels", J. Comput. Phys. Vol.205 (2005), pp. 315-342, 2005,

Trebotich, D., Miller, G.H., Colella, P., Graves, D.T., Martin, D.F., Schwartz, P.O., "A Tightly Coupled Particle-Fluid Model for DNA-Laden Flows in Complex Microscale Geometries", Computational Fluid and Solid Mechanics 2005, pp. 1018-1022, Elsevier (K. J. Bathe editor), 2005,

Miller, G.H., "Minimal Rotationally Invariant Bases for Hyperelasticity", SIAM J. Appl. Math Vol.64, No. 6 (2004), pp. 2050-2075, 2004,

Miller, G.H., "An Iterative Riemann Solver for Systems of Hyperbolic Conservation Laws, with Application to Hyperelastic Solid Mechanics", J. Comp. Physics Vol.193 (2003), pp. 198-225, 2003,

Miller, G.H., Colella, P., "A Conservative Three-Dimensional Eulerian Method for Coupled Solid-Fluid Shock Capturing", J. Comput. Phys. Vol.183 (2002), pp. 26, 2002,

Miller, G.H., Colella, P., "A Higher-Order Godunov Method for Elastic-Plastic Flow in Solids", J. Comput. Phys. Vol.167 (2001), pp. 131, 2001,

Conference Papers

B. Kallemov, G. H. Miller and D. Trebotich, "Numerical Simulation of Polymer Flow in Microfluidic Devices", 009 Proceedings of the Fourth SIAM Conference on Mathematics for Industry (MI09) pp. 93-98, 2010,

G.H. Weber, V. Beckner, H. Childs, T. Ligocki, M. Miller, B. van Straalen, E.W. Bethel, "Visualization of Scalar Adaptive Mesh Refinement Data", Numerical Modeling of Space Plasma Flows: Astronum-2007 (Astronomical Society of the Pacific Conference Series), April 2008, 385:309-320, LBNL 220E,

D. Trebotich and G. H. Miller, "Simulation of Flow and Transport at the Micro (Pore) Scale", Proceedings of the 2nd International Conference on Porous Media and its Applications in Science and Engineering, ICPM2 June 17-21, Kauai, Hawaii, USA, 2007,

Trebotich, D., Colella, P., Miller, G.H., Nonaka, A., Marshall, T., Gulati, S., Liepmann, D., "A Numerical Algorithm for Complex Biological Flow in Irregular Microdevice Geometries", Technical Proceedings of the 2004 Nanotechnology Conference and Trade Show Vol.2 (2004), pp. 470-473, 2004,