Efficient Numerical Schemes for Nucleation-Aggregation Models: Early Steps
نویسندگان
چکیده
In the formation of large clusters out of small particles, the initializing step is called the nucleation, and consists in the spontaneous reaction of agents which aggregate into small and stable polymers called nuclei. After this early step, the polymers are involved into a bunch of reactions such as polymerization, fragmentation and coalescence. Since there may be several orders of magnitude between the size of a particle and the size of an aggregate, building efficient numerical schemes to capture accurately the kinetics of the reaction is a delicate step of key importance. In this article, we propose a conservative scheme, based on finite volume methods on an adaptive grid, which is able to render out the early steps of the reaction as well as the later chain reactions.
منابع مشابه
Numerical solution of population balance equations for nucleation, growth and aggregation processes
This article focuses on the derivation of numerical schemes for solving population balance models (PBMs) with simultaneous nucleation, growth nd aggregation processes. Two numerical methods are proposed for this purpose. The first method combines a method of characteristics (MOC) or growth process with a finite volume scheme (FVS) for aggregation process. For handling nucleation terms, a cell o...
متن کاملModeling and Simulation of Population Balances for Particulate Processes
This work focuses on the modeling and numerical approximations of population balance equations (PBEs) for the simulation of different phenomena occurring in process engineering. The population balance equation (PBE) is considered to be a statement of continuity. It tracks the change in particle size distribution as particles are born, die, grow or leave a given control volume. In the population...
متن کاملNanovoid nucleation by vacancy aggregation and vacancy-cluster coarsening in high-purity metallic single crystals
A numerical model to estimate critical times required for nanovoid nucleation in high-purity aluminum single crystals subjected to shock loading is presented. We regard a nanovoid to be nucleated when it attains a size sufficient for subsequent growth by dislocation-mediated plasticity. Nucleation is assumed to proceed by means of diffusion-mediated vacancy aggregation and subsequent vacancy cl...
متن کاملPii: S1463-5003(02)00003-3
During the course of developing new numerical algorithms for a terrain-following ocean modeling system (TOMS), different numerical aspects have been evaluated through a comparison between two widely used community ocean models, the Princeton ocean model (POM) and the regional ocean modeling system (ROMS). While both models aim at modeling coastal to basin-scale problems using similar grids, the...
متن کاملEfficient Asymptotic-Preserving (AP) Schemes For Some Multiscale Kinetic Equations
Many kinetic models of the Boltzmann equation have a diiusive scaling that leads to the Navier-Stokes type parabolic equations as the small scaling parameter approaches zero. In practical applications, it is desirable to develop a class of numerical schemes that can work uniformly with respect to this relaxation parameter, from the rareeed kinetic regimes to the hydrodynamic diiusive regimes. A...
متن کامل