We present a robust, highly accurate, and efficient positivity- and boundedness-preserving diffuse interface method for the simulations of compressible gas-liquid two-phase flows with the five-equation model by Allaire et al. using high-order finite difference weighted compact nonlinear scheme (WCNS) in the explicit form. The equation of states of gas and liquid are given by the ideal gas and stiffened gas laws respectively. Under a mild assumption on the relative magnitude between the ratios of specific heats of the gas and liquid, we can construct limiting procedures for the fifth order incremental-stencil WCNS (WCNS-IS) with the first order Harten–Lax–van Leer contact (HLLC) flux such that positive partial densities and squared speed of sound can be ensured in the solutions, together with bounded volume fractions and mass fractions. The limiting procedures are discretely conservative for all conservative equations in the five-equation model and can also be easily applied to any other conservative finite difference or finite volume scheme. Numerical tests with liquid water and air are reported to demonstrate the robustness and high accuracy of the WCNS-IS with the positivity- and boundedness-preserving limiters even under extreme conditions.

我们提出了一种稳健、高精度、高效的正性和有界性扩散界面方法，用于使用 Allaire 等人的五方程模型模拟可压缩气液两相流。使用显式形式的高阶有限差分加权紧凑非线性方案（WCNS）。气体和液体的状态方程分别由理想气体定律和硬化气体定律给出。在对气体和液体的比热比之间的相对大小进行温和假设的情况下，我们可以构建具有一阶 Harten-Lax-van Leer 接触的五阶增量模板 WCNS（WCNS-IS）的限制程序（ HLLC) 通量，以便在溶液中确保正的部分密度和声速的平方，以及有界的体积分数和质量分数。限制程序对于五方程模型中的所有保守方程都是离散保守的，也可以很容易地应用于任何其他保守的有限差分或有限体积方案。据报道，使用液态水和空气进行的数值测试证明了 WCNS-IS 的稳健性和高精度，即使在极端条件下也具有正和有界保持限制器。