172
5 Complex Reactive Applications: A Forward Look to Open Science
one may not even want to derive the complete detailed information on initial and/or
final states. For example, in the case in which one wants to know the more likely
transient or transition state the efficiency of a reaction at a given temperature T , the
dimensionality of the problem can be simplified by compacting the description of
one or more clusters of atoms not directly involved in the process into a single body.
Obviously, when more accuracy is needed, mixed quantum (QM) and molecular
dynamics (MD) methods can be used.
5.2.4 Toward Multiscale Treatments
As already mentioned, elementary processes are often to be considered as building blocks of more complex (multiscale) procedures in which numerical estimates
obtained from a (reasonably accurate and realistic) description of a scientific and/or
technological formulation of the problem are accompanied by additional treatments.
These additional treatments are often concerned with the reduction of the molecular
granularity thanks to the clustering of more atoms in a single body. This requires
an organization of the related computational procedures in workflows structured
both horizontally (for computations occurring at the same level of granularity) and
vertically (for computations occurring at different levels of granularity).
In chapter one we have already considered, in this respect, the disentangling of
computational complexity in combustion processes and the disentangling of complexity arising from higher scale kinetic treatments coupling several elementary
processes. Here, although this is not a goal of the present book, in order to give a
detailed account of multiscale methods, we refer to another technological application in which the detailed microscopic (atomistic) level considered for the elementary
processes of small molecules is mitigated by the application of higher scale statistical
treatments. This is the case, for the example we consider here, of studies of the properties of several gaseous systems for which use is made of direct simulation Monte
Carlo (DSMC) techniques [120]. DSMC leverages on probabilistic (Monte Carlo)
simulations to solve the Boltzmann equation for finite Knudsen number (Kn) fluid
flows. The method is of widespread use in the modeling of rarefied gas flows in which
the mean free path of a body is of the same order (or greater) than a representative
physical length scale often expressed in terms of Kn that is given by a dimensionless
number defined as the ratio between the molecular mean free path length λ and a
physical length (L) like the radius of the bodies forming the fluid. For example, for
a Boltzmann gas, the mean free path is given by
Kn =
k B T
√
2πd 2 pL
(5.25)
with k B being the Boltzmann constant, T the thermodynamic temperature, d the
particle hard sphere diameter, p the total pressure. For particle dynamics in the
atmosphere, when assuming standard temperature and pressure (i.e., 25
◦ C and 1 atm)
5 Complex Reactive Applications: A Forward Look to Open Science
one may not even want to derive the complete detailed information on initial and/or
final states. For example, in the case in which one wants to know the more likely
transient or transition state the efficiency of a reaction at a given temperature T , the
dimensionality of the problem can be simplified by compacting the description of
one or more clusters of atoms not directly involved in the process into a single body.
Obviously, when more accuracy is needed, mixed quantum (QM) and molecular
dynamics (MD) methods can be used.
5.2.4 Toward Multiscale Treatments
As already mentioned, elementary processes are often to be considered as building blocks of more complex (multiscale) procedures in which numerical estimates
obtained from a (reasonably accurate and realistic) description of a scientific and/or
technological formulation of the problem are accompanied by additional treatments.
These additional treatments are often concerned with the reduction of the molecular
granularity thanks to the clustering of more atoms in a single body. This requires
an organization of the related computational procedures in workflows structured
both horizontally (for computations occurring at the same level of granularity) and
vertically (for computations occurring at different levels of granularity).
In chapter one we have already considered, in this respect, the disentangling of
computational complexity in combustion processes and the disentangling of complexity arising from higher scale kinetic treatments coupling several elementary
processes. Here, although this is not a goal of the present book, in order to give a
detailed account of multiscale methods, we refer to another technological application in which the detailed microscopic (atomistic) level considered for the elementary
processes of small molecules is mitigated by the application of higher scale statistical
treatments. This is the case, for the example we consider here, of studies of the properties of several gaseous systems for which use is made of direct simulation Monte
Carlo (DSMC) techniques [120]. DSMC leverages on probabilistic (Monte Carlo)
simulations to solve the Boltzmann equation for finite Knudsen number (Kn) fluid
flows. The method is of widespread use in the modeling of rarefied gas flows in which
the mean free path of a body is of the same order (or greater) than a representative
physical length scale often expressed in terms of Kn that is given by a dimensionless
number defined as the ratio between the molecular mean free path length λ and a
physical length (L) like the radius of the bodies forming the fluid. For example, for
a Boltzmann gas, the mean free path is given by
Kn =
k B T
√
2πd 2 pL
(5.25)
with k B being the Boltzmann constant, T the thermodynamic temperature, d the
particle hard sphere diameter, p the total pressure. For particle dynamics in the
atmosphere, when assuming standard temperature and pressure (i.e., 25
◦ C and 1 atm)