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

Area of Science:

• Computational physics
• Chemical engineering
• Materials science

Background:

• Reaction-diffusion processes are crucial in various scientific fields.
• Modeling these processes in particle dispersions presents significant computational challenges.
• Existing methods often require high resolution or complex analytical solutions.

Purpose of the Study:

• To develop an efficient immersed boundary approach for reaction-diffusion modeling in dispersions of reactive spherical particles.
• To represent reactive particles using minimally-resolved "blobs" for reduced computational cost.
• To enable flexible implementation of various physical effects and boundary conditions.

Main Methods:

• An immersed boundary approach representing particles as "blobs" with fewer degrees of freedom.
• On-the-fly computation of regularized discrete Green's functions using grid-based Poisson equation discretization.
• Development of multigrid-based preconditioners for efficient solution of linear systems.

Main Results:

• The blob model provides accurate representations of reaction-diffusion at low to moderate particle packing densities.
• The computational cost is comparable to solving a Poisson equation in the same domain.
• The method demonstrates flexibility in handling different boundary conditions and coupling to other physical phenomena.

Conclusions:

• The immersed boundary blob method offers an efficient and flexible approach for modeling reaction-diffusion in particle dispersions.
• This method overcomes limitations of traditional techniques by avoiding analytical Green's functions.
• It provides a robust framework for studying complex reaction-diffusion systems with potential applications in various scientific disciplines.