2026, Vol.29, No.2, pp.162-169

This paper presents a three-dimensional numerical study of diffusion in a multicomponent ideal gas mixture with a diffusion coefficient dependent on the entropy of mixing. The limitations of the classical Maxwell-Stefan approach for modelling diffusion in multicomponent gas mixtures are discussed, including its numerical complexity and dependence on binary diffusion coefficients. As an alternative, an entropy-based diffusion model is considered and formulated for an n-component ideal gas mixture, with particular attention given to a ternary mixture as the minimal multicomponent system exhibiting cross-diffusion effects. The governing equations are transformed into a weak form suitable for finite element implementation, and a fully implicit time-stepping scheme combined with Newton's method is used to solve the resulting nonlinear algebraic system. \ Logarithmic regularization is introduced to ensure numerical stability and positivity of component concentrations. The proposed approach is implemented in a three-dimensional finite element method framework using a tetrahedral mesh. Numerical simulations of diffusive gas mixing in a cylindrical domain are performed for the isothermal case. The results demonstrate the applicability of the proposed model to simulate multicomponent gas diffusion without the need to prescribe the binary diffusion coefficients required in the Maxwell--Stefan formulation. The developed methodology provides a promising basis for modelling diffusion and cross effects in multicomponent gas mixtures, including cases with prescribed non-uniform temperature fields.

Key words: computer modeling, mathematical modeling, gas diffusion, fem, numerical methods

DOI: https://doi.org/10.5281/zenodo.21105439

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