A projected dynamical system approach to mineral precipitation-dissolution reactions in geochemistry
Résumé
In this paper, we study kinetically-controlled precipitation-dissolution geochemical reactions. Ordinary differential equations are very often used to model aqueous reactions. However, non smoothness is induced by full dissolution. Moreover, one reaction can include several minerals and one mineral can participate in several reactions. We develop a new model, which is a specific projected dynamical system, with constraints on time derivatives. To prove existence of a solution, we discretize the system with an explicit scheme and prove convergence of the approximate solution. Moreover, we solve the approximate differential system thanks to an alternating projection algorithm. Numerical computations on some examples illustrate this approach.
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