Abstract
We study a model for compressible multiphase flows involving N non miscible barotopic phases where N is arbitrary. This model boils down to the barotropic Baer-Nunziato model when N = 2. We prove the weak hyperbolicity property, the non-strict convexity of the natural mathematical entropy, and the existence of a symmetric form.
Highlights
The modeling and numerical simulation of multiphase flows is a relevant approach for a detailed investigation of some patterns occurring in many industrial sectors.In [4,8,9,14], some modeling efforts have been provided for the design of compressible multiphase flow models allowing unique jump conditions and for which the initial-value problem is well posed
As in the Baer-Nunziato model, the partial differential equations (PDEs) are composed of a hyperbolic first order convective part consisting in N Euler-like systems coupled through non-conservative terms and zero-th source terms accounting for pressure, velocity and temperature relaxation phenomena between the phases
In [5, 11], two crucial properties have been proven for a class of two phase flow models containing the BaerNunziato model, namely, the convexity of the natural entropy associated with the system, and the existence of a symmetric form
Summary
The modeling and numerical simulation of multiphase flows is a relevant approach for a detailed investigation of some patterns occurring in many industrial sectors. The N -phase flow models developed therein consist in an extension to N ≥ 3 phases of the well-known Baer-Nunziato two phase flow model [1]. As in the Baer-Nunziato model, the PDEs are composed of a hyperbolic first order convective part consisting in N Euler-like systems coupled through non-conservative terms and zero-th source terms accounting for pressure, velocity and temperature relaxation phenomena between the phases. In [5, 11], two crucial properties have been proven for a class of two phase flow models containing the BaerNunziato model, namely, the convexity of the natural entropy associated with the system, and the existence of a symmetric form. We prove the convexity of the entropy and the existence of a symmetric form for a barotropic multiphase flow model with N - where N is arbitrarily large - phases. We restrict the study to the case where the interfacial velocity coincides with one of the phasic material velocities
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