In this paper, a thermodynamically consistent solution of the interfacial Riemann problem for the first-order hyperbolic continuum model of Godunov, Peshkov and Romenski (GPR model) is presented. In the presence of phase transition, interfacial physics are governed by molecular interaction on a microscopic scale, beyond the scope of the macroscopic continuum model in the bulk phases. The developed two-phase Riemann solvers tackle this multi-scale problem, by incorporating a local thermodynamic model to predict the interfacial entropy production. Using phenomenological relations of non-equilibrium thermodynamics, interfacial mass and heat fluxes are derived from the entropy production and provide closure at the phase boundary. We employ the proposed Riemann solvers in an efficient sharp interface level-set Ghost-Fluid framework to provide coupling conditions at phase interfaces under phase transition. As a single-phase benchmark, a Rayleigh-B\'enard convection is studied to compare the hyperbolic thermal relaxation formulation of the GPR model against the hyperbolic-parabolic Euler-Fourier system. The novel interfacial Riemann solvers are validated against molecular dynamics simulations of evaporating shock tubes with the Lennard-Jones shifted and truncated potential. On a macroscopic scale, evaporating shock tubes are computed for the material n-Dodecane and compared against Euler-Fourier results. Finally, the efficiency and robustness of the scheme is demonstrated with shock-droplet interaction simulations that involve both phase transfer and surface tension, while featuring severe interface deformations.

翻译：本文针对Godunov、Peshkov与Romenski提出的双曲型连续介质模型（GPR模型），提出了一阶连续体相界面黎曼问题的热力学相容解。在相变存在的情况下，界面物理过程由微观尺度的分子相互作用主导，超出了体相宏观连续介质模型的适用范围。所发展的两相黎曼解法器通过引入局部热力学模型预测界面熵产，解决了这一多尺度问题。利用非平衡热力学的唯象关系，从熵产推导出界面质量通量与热通量，从而在相边界处提供闭合条件。我们采用所提出的黎曼解法器，在高效的尖界面水平集幽灵流体框架下，为相变过程中的相界面提供耦合条件。作为单相基准测试，研究了Rayleigh-Bénard对流问题，将GPR模型的双曲型热弛豫公式与双曲抛物型Euler-Fourier系统进行对比。新型界面黎曼解法器通过与采用Lennard-Jones截断移位势的蒸发激波管分子动力学模拟结果进行验证。在宏观尺度上，针对正十二烷材料计算了蒸发激波管，并与Euler-Fourier结果进行了比较。最后，通过涉及相变与表面张力、且伴随严重界面变形的激波-液滴相互作用模拟，展示了该方案的高效性与鲁棒性。