A minimally-resolved immersed boundary model for reaction-diffusion problems.

Amneet Pal Singh Bhalla, Boyce E. Griffith, Neelesh A. Patankar, Aleksandar Donev

Research output: Contribution to journalArticle

Abstract

We develop an immersed boundary approach to modeling reaction-diffusion processes in dispersions of reactive spherical particles, from the diffusion-limited to the reaction-limited setting. We represent each reactive particle with a minimally-resolved "blob" using many fewer degrees of freedom per particle than standard discretization approaches. More complicated or more highly resolved particle shapes can be built out of a collection of reactive blobs. We demonstrate numerically that the blob model can provide an accurate representation at low to moderate packing densities of the reactive particles, at a cost not much larger than solving a Poisson equation in the same domain. Unlike multipole expansion methods, our method does not require analytically computed Green's functions, but rather, computes regularized discrete Green's functions on the fly by using a standard grid-based discretization of the Poisson equation. This allows for great flexibility in implementing different boundary conditions, coupling to fluid flow or thermal transport, and the inclusion of other effects such as temporal evolution and even nonlinearities. We develop multigrid-based preconditioners for solving the linear systems that arise when using implicit temporal discretizations or studying steady states. In the diffusion-limited case the resulting linear system is a saddle-point problem, the efficient solution of which remains a challenge for suspensions of many particles. We validate our method by comparing to published results on reaction-diffusion in ordered and disordered suspensions of reactive spheres.

Original languageEnglish (US)
Article number214112
Pages (from-to)214112
Number of pages1
JournalJournal of Chemical Physics
Volume139
Issue number21
DOIs
StatePublished - Dec 7 2013

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Poisson equation
Green's function
Linear systems
Suspensions
linear systems
Green's functions
discrete functions
Dispersions
Flow of fluids
packing density
Boundary conditions
saddle points
multipoles
fluid flow
flexibility
degrees of freedom
nonlinearity
grids
inclusions
boundary conditions

ASJC Scopus subject areas

  • Physics and Astronomy(all)
  • Physical and Theoretical Chemistry

Cite this

A minimally-resolved immersed boundary model for reaction-diffusion problems. / Pal Singh Bhalla, Amneet; Griffith, Boyce E.; Patankar, Neelesh A.; Donev, Aleksandar.

In: Journal of Chemical Physics, Vol. 139, No. 21, 214112, 07.12.2013, p. 214112.

Research output: Contribution to journalArticle

Pal Singh Bhalla, Amneet ; Griffith, Boyce E. ; Patankar, Neelesh A. ; Donev, Aleksandar. / A minimally-resolved immersed boundary model for reaction-diffusion problems. In: Journal of Chemical Physics. 2013 ; Vol. 139, No. 21. pp. 214112.
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