Numerical Analysis by Godunov-Type Scheme for Kazhikhov-Smagulov Pollution Model

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Résumé

The pollution model based on the Kazhikhov-Smagulov equations, a set of equations in fluid mechanics and environmental modeling, is thoroughly investigated numerically in this paper. We investigate the intricate behavior of pollution in a single spatial dimension using a Godunov-type method, which is renowned for its ability to capture discontinuities and shocks effectively. Our 1D simulations illustrate frequently overlooked facets of mixture phenomena, highlighting the model’s complex and varied dynamics. Numerical experiments illustrate the relevance of the proposed numerical procedure.

Mots-clés

Godunov-type scheme; Kazhikhov-Smagulov equations; Riemann problem; Riemann solver; stability.