Abstract
A coupled system of nonlinear parabolic PDEs arising in modeling of surface reactions with piecewise continuous kinetic data is studied. The nonclassic conjugation conditions are used at the surface of the discontinuity of the kinetic data. The finite-volume technique and the backward Euler method are used to approximate the given mathematical model. The monotonicity, conservativity, positivity of the approximations are investigated by applying these finite-volume schemes for simplified subproblems, which inherit main new nonstandard features of the full mathematical model. Some results of numerical experiments are discussed.
Highlights
Coupled systems of PDEs with piecewise continuous kinetic data typically arise in modeling of reactions proceeding over supported catalysts
Kinetic models of reactions proceeding over supported catalysts are of great complexity due to the spillover phenomenon, which is caused (i) by diffusion of molecules of reactants adsorbed on the surface of the inactive for reaction support towards the catalyst-support interface and their jump across the interface onto the active surface and (ii) by diffusion of adsorbate of reactants and intermediate reaction products towards the interface and their jump across the interface onto the support
Mathematical models describing the spillover phenomenon in some reactions taking into account the surface diffusion based on the diffusion model [7] and their numerical simulations are considered in [14, 15] and works mentioned there
Summary
Coupled systems of PDEs with piecewise continuous (discontinuous) kinetic data typically arise in modeling of reactions proceeding over supported (composite) catalysts. The numerical scheme is based on the approximation of nonlinear differential equations by using the finite-volume method [10]. An extensive review of results for numerical schemes for solving nonlinear complex reaction-diffusion-advection problems is given in [1,6,10,12]. They mimic the most important properties of the full nonlinear differential. These simplified benchmark subproblems are used to test monotonicity of the discrete solution due to the main part of the nonlinear source terms and the stability and conservativity of approximation of nonstandard conjugate conditions. A summary of main results in Section 5 concludes the paper
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