Efficient and robust relaxation procedures for multi-component mixtures including phase transition

• Published in: Journal of computational physics 2017-06, Vol.338, p.217-239
• Main Authors: Han, Ee, Hantke, Maren, Müller, Siegfried
• Format: Article
• Language: English
• Subjects: CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Computational physics; COMPUTERIZED SIMULATION; CONVERGENCE; Distributed processing; EFFICIENCY; FLOW MODELS; Grid adaptation; ITERATIVE METHODS; MASS TRANSFER; Mathematical models; MIXTURES; Multi-component fluids; Non-equilibrium model; Numerical methods; ONE-DIMENSIONAL CALCULATIONS; PHASE TRANSFORMATIONS; Phase transition; Phase transitions; RELAXATION; Relaxation procedures; Robustness (mathematics); SOURCE TERMS; THERMAL EQUILIBRIUM; THERMODYNAMICS; TWO-PHASE FLOW
• ISSN: 0021-9991; 1090-2716
• DOI: 10.1016/j.jcp.2017.02.066

We consider a thermodynamic consistent multi-component model in multi-dimensions that is a generalization of the classical two-phase flow model of Baer and Nunziato. The exchange of mass, momentum and energy between the phases is described by additional source terms. Typically these terms are handled by relaxation procedures. Available relaxation procedures suffer from efficiency and robustness resulting in very costly computations that in general only allow for one-dimensional computations. Therefore we focus on the development of new efficient and robust numerical methods for relaxation processes. We derive exact procedures to determine mechanical and thermal equilibrium states. Further we introduce a novel iterative method to treat the mass transfer for a three component mixture. All new procedures can be extended to an arbitrary number of inert ideal gases. We prove existence, uniqueness and physical admissibility of the resulting states and convergence of our new procedures. Efficiency and robustness of the procedures are verified by means of numerical computations in one and two space dimensions. •We develop novel relaxation procedures for a generalized, thermodynamically consistent Baer–Nunziato type model.•Exact procedures for mechanical and thermal relaxation procedures avoid artificial parameters.•Existence, uniqueness and physical admissibility of the equilibrium states are proven for special mixtures.•A novel iterative method for mass transfer is introduced for a three component mixture providing a unique and admissible equilibrium state.