# Communications in Mathematical Sciences

## Volume 19 (2021)

### Homogenization of a discrete network model for chemical vapor infiltration process

Pages: 1809 – 1826

DOI: https://dx.doi.org/10.4310/CMS.2021.v19.n7.a3

#### Authors

Chun Xiao (School of Mathematical Sciences, Soochow University, Suzhou, China; and School of Mathematics and Statistics, Lingnan Normal University, Zhanjiang, China)

Shixin Xu (Department of Mathematics, Duke Kunshan University, Kunshan, China)

Xingye Yue (School of Mathematical Sciences, Soochow University, Suzhou, China)

Changjuan Zhang (South China Research Center for Applied Mathematics and Interdisciplinary Studies, South China Normal University, Guangzhou, China)

Changrong Zhang (High Speed Aerodynamics Institute, China Aerodynamics Development and Research Center, Mianyang, China)

#### Abstract

Chemical vapor infiltration (CVI) is an important engineering process for manufacturing composite materials. Reaction-diffusion of the reactant gas and the structure change are two mutual influence processes. Some works have been done on the multi-scale modeling and simulation for the CVI process. The homogenization theory has not been rigorously established for the coupled nonlinear system on the concentration of the reactant gas and porosity of the media yet. In this work, we establish a discrete multi-scale node-bond network model for CVI process which contains a spatially discrete reaction-diffusion equation coupled with a spatially discrete porosity evolution equation. The tortuosity factor for the bonds in the node-bond structure is considered. The corresponding continuous homogenized system for the discrete model is given and the error estimation between the solutions of the homogenized system and the discrete one is derived.

#### Keywords

CVI process, node-bond network, homogenization, difference operator

#### 2010 Mathematics Subject Classification

35B27, 35K40, 35K55, 35K57

C. Xiao is grateful for the financial support of the China Scholarship Council (CSC) during his visit to York University in Toronto, where part of this work was done.

S.X. Xu is supported by the NSFC under Grant 12071190.

X.Y. Yue is supported by the NSFC under Grants 11971342 and 11271281.