4.3. MODELING FLUID FLOW USING LATTICE GASES AND THE LATTICE BOLTZMANN MODEL
regulated by a temperature sensing and the next step in identifying the morphogenetic pathway should be focused on diffusive limitation. In the case
of the geographic differences in morphology, greater random asymmetry in
the branching process for one population relative to the other suggests an
instability in the sequence of events that leads to branch formation or the
physical integrity of the structure. A suitable hypothesis to follow up this
result might be that the number of secondary connections which crosslink
the filaments of this pseudoparenchymatous structure might be genetically
fixed and different in the two populations. Although it would have been possible to determine if this were the case without using any kind of growth
model, looking only at the microscopic internal structures from individuals
of both populations, it is much easier to invest the effort once a hypothetical
mechanism has been identified. In this case, comparison of actual growth
dynamics to a simplistic model allowed us to distinguish between different
hypothetical modes of morphogenesis.
4.3 Modeling Fluid Flow Using Lattice Gases
and the Lattice Boltzmann Model
As discussed in Sect. 2.1.1 hydrodynamics has a strong impact on the growth
process of marine sessile organisms. Traditionally hydrodynamics is modeled using the macroscopical equations, shown in (2.1) and (2.2), describing
the conservation of mass and momentum. Solutions to these equations are
usually approximated by using numerical solvers (see for example Roache
1976). When developing models of the impact of hydrodynamics on the
growth process of marine sessile organisms we are faced with a number of
problems, which cannot easily be solved using numerical approximations of
the macroscopic equations. Some of the problems we want to address are
varying the Reynolds number (Re, see (2.3)) and the Peeler number (Pe, see
(2-4)) independently, and studying the influence of turbulence and the contribution of diffusion processes in the dispersion of nutrients. Marine sessile
organisms usually have complex-shaped, fractal -like growth forms, which
impose a number of problems in the specification of boundary conditions
in numerical solvers. Similar problems are encountered in studies on flow
and diffusion processes in porous media (Heijs and Lowe 1995). Furthermore, as discussed in Sect. 2.1.1, hydrodynamics influences the distribution
of food particles, so it is required to include simulated food particles in
the hydrodynamic model. In addit ion the hydrodynamic impact consists
of the influence of hydrodynamic forces, erosion effects, and deposition
processes. Another complication is that the simulat ion of hydrodynamic
processes around complex-shaped, three-dimensional objects requires an
enormous computational effort, which can be done only with solving techniques which are suitable for large-scale computing on parallel computers. In
the next section an alternative method, stemming from the study of porous
media, is presented in which the problems mentioned above can be solved
to a certain extent. This alternative method is a particle-based technique in
which the fluid and suspended material are described by microscopic rules
and it seems to be in general very suitable for studying diffusion and flow
processes in biology.
99
regulated by a temperature sensing and the next step in identifying the morphogenetic pathway should be focused on diffusive limitation. In the case
of the geographic differences in morphology, greater random asymmetry in
the branching process for one population relative to the other suggests an
instability in the sequence of events that leads to branch formation or the
physical integrity of the structure. A suitable hypothesis to follow up this
result might be that the number of secondary connections which crosslink
the filaments of this pseudoparenchymatous structure might be genetically
fixed and different in the two populations. Although it would have been possible to determine if this were the case without using any kind of growth
model, looking only at the microscopic internal structures from individuals
of both populations, it is much easier to invest the effort once a hypothetical
mechanism has been identified. In this case, comparison of actual growth
dynamics to a simplistic model allowed us to distinguish between different
hypothetical modes of morphogenesis.
4.3 Modeling Fluid Flow Using Lattice Gases
and the Lattice Boltzmann Model
As discussed in Sect. 2.1.1 hydrodynamics has a strong impact on the growth
process of marine sessile organisms. Traditionally hydrodynamics is modeled using the macroscopical equations, shown in (2.1) and (2.2), describing
the conservation of mass and momentum. Solutions to these equations are
usually approximated by using numerical solvers (see for example Roache
1976). When developing models of the impact of hydrodynamics on the
growth process of marine sessile organisms we are faced with a number of
problems, which cannot easily be solved using numerical approximations of
the macroscopic equations. Some of the problems we want to address are
varying the Reynolds number (Re, see (2.3)) and the Peeler number (Pe, see
(2-4)) independently, and studying the influence of turbulence and the contribution of diffusion processes in the dispersion of nutrients. Marine sessile
organisms usually have complex-shaped, fractal -like growth forms, which
impose a number of problems in the specification of boundary conditions
in numerical solvers. Similar problems are encountered in studies on flow
and diffusion processes in porous media (Heijs and Lowe 1995). Furthermore, as discussed in Sect. 2.1.1, hydrodynamics influences the distribution
of food particles, so it is required to include simulated food particles in
the hydrodynamic model. In addit ion the hydrodynamic impact consists
of the influence of hydrodynamic forces, erosion effects, and deposition
processes. Another complication is that the simulat ion of hydrodynamic
processes around complex-shaped, three-dimensional objects requires an
enormous computational effort, which can be done only with solving techniques which are suitable for large-scale computing on parallel computers. In
the next section an alternative method, stemming from the study of porous
media, is presented in which the problems mentioned above can be solved
to a certain extent. This alternative method is a particle-based technique in
which the fluid and suspended material are described by microscopic rules
and it seems to be in general very suitable for studying diffusion and flow
processes in biology.
99