Mathematical and Numerical Study of a Dusty Knudsen Gas Mixture

• Published in: Acta applicandae mathematicae Vol. 168; no. 1; pp. 17 - 31
• Main Authors: Charles, Frédérique, Salvarani, Francesco
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Netherlands 01-08-2020; Springer Nature B.V; Springer Verlag
• Subjects: Analysis of PDEs; Applications of Mathematics; Calculus of Variations and Optimal Control; Optimization; Computational Mathematics and Numerical Analysis; Dust; Energy transfer; Gas mixtures; Mathematical analysis; Mathematics; Mathematics and Statistics; Partial Differential Equations; Probability Theory and Stochastic Processes; Knudsen gas; Particle method; Moving domain
• ISSN: 0167-8019; 1572-9036
• DOI: 10.1007/s10440-019-00277-x

We consider a mixture composed of a gas and dust particles in a very rarefied setting. Whereas the dust particles are individually described, the surrounding gas is treated as a Knudsen gas, in such a way that interactions occur only between gas particles and dust by means of diffuse reflection phenomena. After introducing the model, we prove the existence and the uniqueness of the solution and provide a numerical strategy for the study of the equations. At the numerical level, we focus our attention on the phenomenon of energy transfer between the gas and the moving dust particles.