## JMI2010B-7 Multiscale sulfate attack on sewer pipes: Numerical study of a fast micro-macro mass transfer limit (pp.171-181)

Author(s)： Vladimir Chalupecky, Tasnim Fatima and Adrian Muntean

J. Math-for-Ind. **2B** (2010) 171-181.

- File： JMI2010B-7.pdf (383KB)

Abstract

We present two multiscale reaction-diffusion (RD) systems modeling sulfate attack in concrete structures (here: sewer pipes). The systems are posed on two different spatially separated scales. The only difference between them is the choice of the *micro-macro transmission condition*. We explore numerically the way in which the macroscopic Biot number $Bi^M$ connects the two reaction-diffusion scenarios. We indicate connections between the solution of the "regularized" system (with moderate size of $Bi^M$) and the solution to the "matched" system (with blowing up size of $Bi^M$), where Henry's law plays the role of the micro-macro transmission condition.

Keyword(s). Multiscale RD system, micro-macro transmission conditions, sulfate corrosion, acid attack, modeling of concrete, finite difference scheme, convergence rates