A mathematical model of sulphite chemical aggression of limestones with high permeability. Part I. Modeling and qualitative analysis

Abstract

We introduce a degenerate nonlinear parabolic-elliptic system, which describes the chemical aggression of limestones under the attack of SO 2 , in high permeability regime. By means of a dimensional scaling, the qualitative behavior of the solutions in the fast reaction limit is investigated. Explicit asymptotic conditions for the front formation are derived.

A mathematical model of sulphite chemical aggression of limestones with high permeability. Part II: Numerical approximation

“…Figures 3 and 4 show how the parameter δ affects the system. Recall the asymptotics given in Alì et al (2006), which predict that in the fast reaction limit there can be no formation of propagation front for With the parameter values used in our simulations this implies δ<−11. We see that the numerical solution still shows a propagation front for values of δ under this limitation.…”

“…According to their physical meaning, see (Alì et al 2006), the parameters and µ are positive, and the conductivity κ(c) is a non-decreasing function of c. Also, we assume that ρ s is a decreasing, and c an increasing function of x, with…”

“…We still use the scaled model (3), and fix the parameters as in Table 1. In addition we choose the parameter ω 2 , representing the boundary condition for g, to match the fast reaction profile function derived in Alì et al (2006), that is,…”

“…Test 1 then corresponds to the assumptions made in the deduction of the fast reaction limit functions in Alì et al (2006). Figure 1 shows the numerical solutions for this case, along with their corresponding fast reaction profile.…”

“…For this problem we have also to specify initial and boundary conditions, according to the problem under examination. This model was introduced in the first part of this paper (Alì et al(2006)), to which we refer the reader for the derivation of the model, including the physical meaning of the equations as well as of the parameters δ, , and µ, and for some qualitative results, which show the behavior of self-similar waves. More precisely a propagating front exists does or does not, according to the value of the parameter δ, for solutions in the positive half-line.…”