In this paper, we present a unified nonequilibrium model of continuum mechanics for compressible multiphase flows. The model, which is formulated within the framework of Symmetric Hyperbolic Thermodynamically Compatible (SHTC) equations, can describe the arbitrary number of phases that can be heat-conducting inviscid and viscous fluids, as well as elastoplastic solids. The phases are allowed to have different velocities, pressures, temperatures, and shear stresses, while the material interfaces are treated as diffuse interfaces with the volume fraction playing the role of the interface field. To relate our model to other multiphase approaches, we reformulate the SHTC governing equations in terms of the phase state parameters and put them in the form of Baer-Nunziato-type models. It is the Baer-Nunziato form of the SHTC equations which is then solved numerically using a robust second-order path-conservative MUSCL-Hancock finite volume method on Cartesian meshes. Due to the fact that the obtained governing equations are very challenging, we restrict our numerical examples to a simplified version of the model, focusing on the isentropic limit for three-phase mixtures. To address the stiffness properties of the relaxation source terms present in the model, the implemented scheme incorporates a semi-analytical time integration method specifically designed for the non-linear stiff source terms governing the strain relaxation. The validation process involves a wide range of benchmarks and several applications for compressible multiphase problems. Notably, results are presented for multiphase flows in all the relaxation limit cases of the model, including inviscid and viscous Newtonian fluids, as well as non-linear hyperelastic and elastoplastic solids.

翻译：本文提出了一种适用于可压缩多相流的统一非平衡连续介质力学模型。该模型基于对称双曲热力学兼容（SHTC）方程框架构建，可描述任意数量的相，包括可导热无粘流体、黏性流体及弹塑性固体。各相允许具有不同的速度、压力、温度和剪切应力，而材料界面则采用扩散界面处理，其中体积分数扮演界面场角色。为将本模型与其他多相方法关联，我们以相状态参数重新表述了SHTC控制方程，并将其转化为Baer-Nunziato型模型形式。随后采用稳健的二阶路径守恒MUSCL-Hancock有限体积法在笛卡尔网格上对SHTC方程的Baer-Nunziato形式进行数值求解。鉴于所得控制方程极具挑战性，本文将数值算例限制在简化模型版本，聚焦于三相混合物的等熵极限情形。为处理模型中松弛源项的刚度特性，所实施的方案引入了专为控制应变演化的非线性刚性源项设计的半解析时间积分方法。验证过程涵盖可压缩多相问题的广泛基准测试及多项应用。值得注意的是，本文展示了模型在所有松弛极限情形下的多相流结果，包括无粘流体、黏性牛顿流体以及非线性超弹性与弹塑性固体。