# A Monte Carlo method for the simulation of coagulation and nucleation based on weighted particles and the concepts of stochastic resolution and merging

## Abstract

Monte Carlo simulations based on weighted simulation particles can solve a variety of population balance problems and allow thus to formulate a solution-framework for many chemical engineering processes. This study presents a novel concept for the calculation of coagulation rates of weighted Monte Carlo particles by introducing a family of transformations to non-weighted Monte Carlo particles. The tuning of the accuracy (named ‘stochastic resolution’ in this paper) of those transformations allows the construction of a constant-number coagulation scheme. Furthermore, a parallel algorithm for the inclusion of newly formed Monte Carlo particles due to nucleation is presented in the scope of a constant-number scheme: the low-weight merging. This technique is found to create significantly less statistical simulation noise than the conventional technique (named ‘random removal’ in this paper). Both concepts are combined into a single GPU-based simulation method which is validated by comparison with the discrete-sectional simulation technique. Two test models describing a constant-rate nucleation coupled to a simultaneous coagulation in 1) the free-molecular regime or 2) the continuum regime are simulated for this purpose.

- Authors:

- Publication Date:

- OSTI Identifier:
- 22622302

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Computational Physics; Journal Volume: 340; Other Information: Copyright (c) 2017 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ACCURACY; ALGORITHMS; BALANCES; COMPARATIVE EVALUATIONS; COMPUTERIZED SIMULATION; INCLUSIONS; MATHEMATICAL SOLUTIONS; MONTE CARLO METHOD; NOISE; NUCLEATION; PARTICLES; RANDOMNESS; RESOLUTION; STOCHASTIC PROCESSES; TRANSFORMATIONS; WEIGHT

### Citation Formats

```
Kotalczyk, G., E-mail: Gregor.Kotalczyk@uni-due.de, and Kruis, F.E.
```*A Monte Carlo method for the simulation of coagulation and nucleation based on weighted particles and the concepts of stochastic resolution and merging*. United States: N. p., 2017.
Web. doi:10.1016/J.JCP.2017.03.041.

```
Kotalczyk, G., E-mail: Gregor.Kotalczyk@uni-due.de, & Kruis, F.E.
```*A Monte Carlo method for the simulation of coagulation and nucleation based on weighted particles and the concepts of stochastic resolution and merging*. United States. doi:10.1016/J.JCP.2017.03.041.

```
Kotalczyk, G., E-mail: Gregor.Kotalczyk@uni-due.de, and Kruis, F.E. Sat .
"A Monte Carlo method for the simulation of coagulation and nucleation based on weighted particles and the concepts of stochastic resolution and merging". United States.
doi:10.1016/J.JCP.2017.03.041.
```

```
@article{osti_22622302,
```

title = {A Monte Carlo method for the simulation of coagulation and nucleation based on weighted particles and the concepts of stochastic resolution and merging},

author = {Kotalczyk, G., E-mail: Gregor.Kotalczyk@uni-due.de and Kruis, F.E.},

abstractNote = {Monte Carlo simulations based on weighted simulation particles can solve a variety of population balance problems and allow thus to formulate a solution-framework for many chemical engineering processes. This study presents a novel concept for the calculation of coagulation rates of weighted Monte Carlo particles by introducing a family of transformations to non-weighted Monte Carlo particles. The tuning of the accuracy (named ‘stochastic resolution’ in this paper) of those transformations allows the construction of a constant-number coagulation scheme. Furthermore, a parallel algorithm for the inclusion of newly formed Monte Carlo particles due to nucleation is presented in the scope of a constant-number scheme: the low-weight merging. This technique is found to create significantly less statistical simulation noise than the conventional technique (named ‘random removal’ in this paper). Both concepts are combined into a single GPU-based simulation method which is validated by comparison with the discrete-sectional simulation technique. Two test models describing a constant-rate nucleation coupled to a simultaneous coagulation in 1) the free-molecular regime or 2) the continuum regime are simulated for this purpose.},

doi = {10.1016/J.JCP.2017.03.041},

journal = {Journal of Computational Physics},

number = ,

volume = 340,

place = {United States},

year = {Sat Jul 01 00:00:00 EDT 2017},

month = {Sat Jul 01 00:00:00 EDT 2017}

}