Lagrangian Particle Methods for Biological Systems - Porous Media: Applications in Biological Systems and Biotechnology - page 286

biomass growth and spreading to be studied—a phenomena that is out of reach
of all but impractically large MD simulations. On larger scales, where thermo-
dynamic fluctuations are not important and biogeochemical processes can be
accurately described by deterministic partial differential equations (NS and
advection-diffusion-reaction equations), SPH is an ecient tool. Due to the
presence of moving interfaces, the PDEs describing biofilm growth and min-
eral precipitation are highly nonlinear and present a significant challenge to
traditional grid-based methods. Owing to their Lagrangian nature, SPH mod-
els handle moving boundaries without any complications. Also, SPH, MD, and
DPD allow complex interactions between biomass, fluid, and substratum to
be simulated using simple pair-wise interactions that significantly simplify the
biofilm and mineral precipitation models (in some cases, there are advantages
to using more complex interactions that depend on the local particle density).
Despite the superior accuracy of pore-scale models, their high compu-
tational cost does not allow them to completely replace pore network and
Darcy-scale models in a large computational domain. We presented a hybrid
(multiphysics) numerical model that employs a SPH approach as the numeri-
cal engine for a scenario in which mineral precipitation is highly localized and
coarse-scale continuum models fail to accurately describe the reactive trans-
port in only a small part of a computational domain. The main advantages of
the hybrid model are as follows: (1) Effective parameters in the hybrid model
characterize the continuum properties of the porous media and/or proper-
ties of the solutions. They can be measured by standard laboratory or field
experiments, and they are tabulated for a wide class of soils and chemical
compounds. Parameterization of the hybrid model does not require any addi-
tional parameters beyond those used in the Darcy-scale or pore-scale models
and hence can be easily achieved; (2) The continuum representation and effec-
tive parameters are used only in the part of the computational domain where
no significant precipitation occurs. As a result, the effective parameters used in
the continuum model do not change during a simulation, and this significantly
increases the fidelity of the hybrid model predictions.
7.7 References
Abraham, F. F., Brodbeck, D., Rudge, W. E., and Xu, X. P. (1997). A
molecular dynamics investigation of rapid fracture mechanics. Journal of
the Mechanics and Physics of Solids , 45 (9):1595-1619.
Albuquerque, P., Alemani, D., Chopard, B., and Leone, P. (2006). A hybrid
lattice Boltzmann finite difference scheme for the diffusion equation. Inter-
national Journal of Multiscale Computational Engineering , 4 :209-219.