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 a 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 numerical results for various flows with shock waves.

翻译：本文研究具有刚性气体状态方程的异质可压缩二元混合物动力学的简化四方程模型。我们进一步研究了其简化形式（可称为准均匀形式），该形式引入了排除体积浓度和组元公共压力的二次方程。我们证明了该方程的新性质，导出了声速平方的简单公式，给出了该公式与伍德声速平方关联的另类证明，以及压力平衡方程的简短推导。我们首次引入了异质模型（准均匀形式）的正则化方法。在一维情形下，我们构造了相应的显式时间双层、空间对称三点无限制器有限差分格式，并给出了含激波多种流动的数值结果。