2014/12/29 by Grégoire Allaire, Allaire, Grégoire, Harsha Hutridurga +1 · 1 citation
Computer Science · Engineering · #Advanced Mathematical Modeling in Engineering #Composite Material Mechanics #Advanced Numerical Methods in Computational Mathematics
paper · pdf · doi:10.48550/arxiv.1412.8301
We consider the homogenization of a model of reactive flows through periodic\nporous media involving a single solute which can be absorbed and desorbed on\nthe pore boundaries. This is a system of two convection-diffusion equations,\none in the bulk and one on the pore boundaries, coupled by an exchange reaction\nterm. The novelty of our work is to consider a nonlinear reaction term, a\nso-called Langmuir isotherm, in an asymptotic regime of strong convection. We\ntherefore generalize previous works on a similar linear model [G. Allaire et\nal, Chemical Engineering Science, 65 (2010), pp.2292-2300], [G. Allaire et al,\nSIAM J. Math. Anal., 42 (2010), pp.125-144], [Allaire et al, IMA J Appl Math.,\n77 (2012), pp.788-815]. Under a technical assumption of equal drift velocities\nin the bulk and on the pore boundaries, we obtain a nonlinear monotone\ndiffusion equation as the homogenized model. Our main technical tool is the\nmethod of two-scale convergence with drift [Marusic-Paloka et al, Journal of\nLondon Math. Soc., 72 (2005), pp.391-409]. We provide some numerical test cases\nin two space dimensions to support our theoretical analysis.\n