TY - JOUR

T1 - Entropy stable modeling of non-isothermal multi-component diffuse-interface two-phase flows with realistic equations of state

AU - Kou, Jisheng

AU - Sun, Shuyu

N1 - KAUST Repository Item: Exported on 2021-02-23
Acknowledged KAUST grant number(s): BAS/1/1351-01, URF/1/2993-01, REP/1/2879-01
Acknowledgements: The work is supported in part by funding from King Abdullah University of Science and Technology (KAUST) through the grants BAS/1/1351-01, URF/1/2993-01, and REP/1/2879-01.

PY - 2018/7/5

Y1 - 2018/7/5

N2 - In this paper, we consider mathematical modeling and numerical simulation of non-isothermal compressible multi-component diffuse-interface two-phase flows with realistic equations of state. A general model with the general reference velocity is derived rigorously through thermodynamical laws and Onsager’s reciprocal principle, and it is capable of characterizing compressibility and partial miscibility between multiple fluids. We prove a novel relation between the pressure, temperature and chemical potentials, which results in a new formulation of the momentum conservation equation indicating that the gradients of chemical potentials and temperature become the primary driving force of the fluid motion except for the external forces. A key challenge in numerical simulation is to develop entropy stable numerical schemes preserving the laws of thermodynamics. Based on the convex–concave splitting of Helmholtz free energy density with respect to molar densities and temperature, we propose an entropy stable numerical method, which solves the total energy balance equation directly, and thus, naturally satisfies the first law of thermodynamics. Unconditional entropy stability (the second law of thermodynamics) of the proposed method is proved by estimating the variations of Helmholtz free energy and kinetic energy with time steps. Numerical results validate the proposed method.

AB - In this paper, we consider mathematical modeling and numerical simulation of non-isothermal compressible multi-component diffuse-interface two-phase flows with realistic equations of state. A general model with the general reference velocity is derived rigorously through thermodynamical laws and Onsager’s reciprocal principle, and it is capable of characterizing compressibility and partial miscibility between multiple fluids. We prove a novel relation between the pressure, temperature and chemical potentials, which results in a new formulation of the momentum conservation equation indicating that the gradients of chemical potentials and temperature become the primary driving force of the fluid motion except for the external forces. A key challenge in numerical simulation is to develop entropy stable numerical schemes preserving the laws of thermodynamics. Based on the convex–concave splitting of Helmholtz free energy density with respect to molar densities and temperature, we propose an entropy stable numerical method, which solves the total energy balance equation directly, and thus, naturally satisfies the first law of thermodynamics. Unconditional entropy stability (the second law of thermodynamics) of the proposed method is proved by estimating the variations of Helmholtz free energy and kinetic energy with time steps. Numerical results validate the proposed method.

UR - http://hdl.handle.net/10754/627322

UR - https://www.sciencedirect.com/science/article/pii/S0045782518302998

UR - http://www.scopus.com/inward/record.url?scp=85050142681&partnerID=8YFLogxK

U2 - 10.1016/j.cma.2018.06.002

DO - 10.1016/j.cma.2018.06.002

M3 - Article

AN - SCOPUS:85050142681

VL - 341

SP - 221

EP - 248

JO - Computer Methods in Applied Mechanics and Engineering

JF - Computer Methods in Applied Mechanics and Engineering

SN - 0045-7825

ER -