A new projection method for a generic two-fluid model is presented in this work. To be specific, it is shown that the projection method for solving single-phase variable density incompressible flows or compressible flows can be extended to the case of viscous compressible two-fluid flows. The idea relies on the property that the single pressure $p$ can be uniquely determined by the products of volume fractions and densities $\phi_k \rho_k$ of the two fluids, respectively. Moreover, a suitable assignment of the intermediate step variables is necessary to maintain the stability. The energy stability for the proposed numerical scheme is proved and the first order convergence in time is justified by three numerical tests.

翻译：本文提出了一种适用于通用双流体模型的新型投影方法。具体而言，研究表明，求解单相变密度不可压缩流或可压缩流的投影方法可以推广至粘性可压缩双流体流动情形。该方法的核心思想在于：单一压力$p$可由两种流体各自的体积分数与密度乘积$\phi_k \rho_k$唯一确定。此外，为保证稳定性，需对中间步变量进行适当赋值。本文证明了所提数值格式的能量稳定性，并通过三个数值算例验证了时间方向的一阶收敛性。