Multicomponent flow modeling

Abstract

We first present multicomponent flow models derived from the kinetic theory of gases. We then investigate the symmetric hyperbolic-parabolic structure of the resulting system of partial differential equations and discuss the Cauchy problem for smooth solutions. We also address the existence of deflagration waves also termed anchored waves. We further indicate related models which have a similar hyperbolic-parabolic structure, notably the Saint-Venant system with a temperature equation as well as the equations governing chemical equilibrium flows. We next investigate multicomponent ionized and magnetized flow models with anisotropic transport fluxes which have a different mathematical structure. We finally discuss numerical algorithms specifically devoted to complex chemistry flows, in particular the evaluation of multicomponent transport properties, as well as the impact of multicomponent transport.

Parareal operator splitting techniques for multi-scale reaction waves: Numerical analysis and strategies

“…Numerical simulations of multi-scale phenomena are commonly requested for modelling purposes in many applications such as combustion [10,31,40,49,50], chemical vapor deposition [32], or air pollution modelling [39,48,61]. The important development of the numerical strategies in these and in other fields such as nonlinear chemical dynamics for excitable media [6,20,21] or biomedical engineering [12,22,34] is mainly due to the constant increase of the computer power (see for instance [23] for a recent review of methods applied to turbulent combustion).…”

Stability of the Derivative of a Canonical Product

“…In [15,Section 7.7.1], the matrix with elements −a ij c j is analyzed and it is shown that it is symmetric, positive semi-definite, irreducible, and a singular M-matrix as well as that a generalized inverse can be defined. Our approach is to apply the Perron-Frobenius theory to A, following [4].…”

“…For more general expressions of d i , we refer to [15,Chapter 7]. The chemical potential under isothermal, isobaric conditions is defined by µ i = ∂G/∂c i , where G is the Gibbs free energy.…”

“…Then the total molar concentration N +1 i=1 c i is constant and we set this constant equal to one. More general situations are investigated, e.g., in [15]. The dynamics of the mixture is given by the mass balance equations in Ω, i = 1, .…”

“…Under some general assumptions on the nonlinearities, Giovangigli proved that there exists a unique global solution to the whole-space Maxwell-Stefan system if the initial datum is sufficiently close to the equilibrium state [15,Theorem 9.4.1]. Bothe [4] showed the existence of a unique local solution for general initial data.…”