Kernel-based Lagrangian method for imperfectly-mixed chemical reactions, A

Current Lagrangian (particle-tracking) algorithms used to simulate diffusion-reaction equations must employ a certain number of particles to properly emulate the system dynamics---particularly for imperfectly-mixed systems. The number of particles is tied to the statistics of the initial concentration fields of the system at hand. Systems with shorter-range correlation and/or smaller concentration variance require more particles, potentially limiting the computational feasibility of the method. For the well-known problem of bimolecular reaction, we show that using kernel-based, rather than Dirac delta, particles can significantly reduce the required number of particles. We derive the fixed half-width of a Gaussian kernel for a given reduced number of particles that analytically eliminates the error between kernel and Dirac solutions at any specified time. We also show how to solve for the fixed kernel size by minimizing the squared differences between solutions over any given time interval. Numerical results show that the half-width of the kernel should be kept below about 12% of the domain size, and that the analytic equations used to derive kernel size suffer significantly from the neglect of higher-order moments. The simulations with a kernel half-width given by least squares minimization perform better than those made to match at one specific time. A heuristic time-variable kernel size, based on the previous results, performs on par with the least squares fixed kernel size.

Name thesis:degree_name

Master of Science (M.S.)

Level thesis:degree_level

Masters

Discipline thesis:degree_discipline

Applied Mathematics and Statistics

Grantor dc:publisher

Colorado School of Mines. Arthur Lakes Library

Year dc:date.issued

2018

Author dc:creator

• Schmidt, Michael J.

Advisors dc:contributor.advisor

• Pankavich, Stephen
• Benson, David A.

Committee members dc:contributor.committeemember

• Tenorio, Luis
• Leiderman, Karin

• imperfect mixing
• diffusion-reaction equation
• particle methods

Statement dc:rights

• Copyright of the original work is retained by the author.

Language dc:language.iso

eng, English

Identifier

T 8531

OAI identifier oai:identifier

oai:repository.mines.edu:11124/172365