Regularized Equations for Dynamics of the Heterogeneous Binary Mixtures of the Noble-Abel Stiffened-Gases and Their Application

Doklady Mathematics. 2023. Vol. 108. No. 3. P. 443–449.

Zlotnik A., Lomonosov T.

We consider the so-called four-equation model for dynamics of the heterogeneous compressible binary mixtures with the Noble-Abel stiffened-gas equations of state. We exploit its quasi-homogeneous form that arises after excluding the volume concentrations from the sought functions and is based on a quadratic equation for the common pressure of the components. We present new properties of this equation and a simple formula for the squared speed of sound, suggest an alternative derivation for a formula relating it to the squared Wood speed of sound and state the pressure balance equation. For the first time, we give a quasi-gasdynamic-type regularization of the heterogeneous model (in the quasi-homogeneous form), construct explicit two-level in time and symmetric three point in space finite-difference scheme without limiters to implement it in the 1D case and present numerical results.

Keywords: gas dynamics, heterogeneous binary gas mixture, four-equation model, quasi-gasdynamic regularization, Noble-Abel stiffened-gas, explicit in time and symmetric in space scheme