# Numerical simulations for two-dimensional reaction-diffusion problems with formation of multiple dead zones

Source: [Numerical simulations for two-dimensional reaction-diffusion problems with formation of multiple dead zones](<https://www.sota2.com/research/paper/6a210673c10484bac23eff65>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2026-06-04T05:00:05.280Z

Authors: Piotr Skrzypacz, Boris Golman, Jan Valdman

Published: 2026-05-20T01:18:18.000Z

## Abstract

The paper deals with dead-core solutions to an isothermal reaction-diffusion problem with power-law kinetics for a single reaction that takes place in a chemical reactor represented by a bounded domain in two dimensions. The model boundary value problem for the stationary non-linear diffusion-reaction equation is solved numerically using an appropriate time-marching method. The spatial discretization is based on the lumped finite element method for piecewise linear functions. The effects of the reaction order and Thiele modulus on the concentration profiles and the size of dead zones are investigated numerically. The paper demonstrates that the formation of multiple dead zones is possible for particular reactor geometries.

## Recorded benchmark results

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/2606.02587>)

[PDF](<https://arxiv.org/pdf/2606.02587.pdf>)