Lagrangian Particle Methods for Biological Systems - Porous Media: Applications in Biological Systems and Biotechnology - page 251

7

Lagrangian Particle Methods for Biological
Systems

Alexandre M. Tartakovsky
Pacific Northwest National Laboratory, Computational Mathematics Group,
Richland, WA

Zhijie Xu
Idaho National Laboratory, Energy Resource Recovery & Management,
Idaho Falls, ID

Paul Meakin
Idaho National Laboratory, Center for Advanced Modeling and Simulation,
Idaho Falls, ID
Physics of Geological Processes, University of Oslo, Oslo, Norway
Multiphase Flow Assurance Innovation Center, Institute for Energy
Technology, Kjeller, Norway

CONTENTS
7.1

Introduction ................................................................. 252

7.2 DPD Models for Biological Applications ................................... 254

7.3 SPHs Models for Biofilm Growth ........................................... 265

7.3.1 Model 1 ............................................................. 267

7.3.2 Model 2 ............................................................. 268

7.3.3 Implementation of the SPH Model ................................. 269

7.3.4 Numerical Results ................................................... 269

7.4 An SPH Model for Mineral Precipitation .................................. 271

7.5 Hybrid Models for Diffusion-Reaction Systems............................. 274

7.5.1 Hybrid Formulation for Reaction-Diffusion Systems

in Porous Media..................................................... 275

7.5.2 Pore-Scale Description and Its SPH Formulation .................. 276

7.5.3 SPH Representation of the Pore-Scale RDEs ....................... 277

7.5.4 Darcy-Scale (Continuum) Description .............................. 278

7.5.5 SPH Representation of Averaged Darcy-Scale RDEs............... 279

7.5.6 Hybrid Formulation ................................................. 280

Acknowledgments
This research was supported by the Oce of Science of the U.S. Department of Energy
under Scientific Discovery through Advanced Computing. Pacific Northwest National
Laboratory is operated for the U.S. Department of Energy by Battelle under contract DE-
AC06-76RL01830, and the Idaho National Laboratory is operated for the U.S. Department
of Energy by the Battelle Energy Alliance under contract DE-AC07-05ID14517.

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