We deal with the reduced four-equation model for dynamics of the heterogeneous compressible binary mixtures with the stiffened gas equations of state. We study its further reduced form, with the excluded volume concentrations and a quadratic equation for the common pressure of the components, that can be called quasi-homogeneous form. We prove new properties of this equation, derive a simple formula for the squared speed of sound, give an alternative proof for a formula that relates it to the squared Wood speed of sound, and a short derivation of the pressure balance equation. For the first time, we introduce regularizations of the heterogeneous model (in the quasi-homogeneous form). In the 1D case, we construct the corresponding explicit two-level in time and symmetric three-point in space finite-difference schemes without limiters and present various numerical results for flows with shock waves.

翻译：我们研究以刚性气体状态方程为特征的异质可压缩二元混合物动力学的简化四方程模型。我们进一步研究其简化形式（可称为准均匀形式），该形式包含排除体积浓度和关于各组分共同压力的二次方程。我们证明了该方程的新性质，推导出声速平方的简洁公式，给出了将其与伍德声速平方关联的公式的替代证明，以及压力平衡方程的简短推导。首次引入了异质模型（以准均匀形式）的正则化方法。在一维情形下，我们构造了相应的无限制显式时间双层和空间对称三点有限差分格式，并展示了包含激波流动的各种数值结果。