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 extended for 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.

中文翻译：

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可压缩气液流动的保正性高阶加权紧致非线性格式

我们提出了一种稳健，高度准确和高效的正负性和保界性扩散界面方法，用于利用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型非线性方案（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之比之间的相对幅值进行温和假设的情况下，我们可以为具有一阶Harten-Lax-van Leer接触的五阶增量模板WCNS（WCNS-IS）构造限制程序（ HLLC）通量，从而可以确保溶液中存在正的局部密度和平方声速，以及有限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，并且还可以轻松地扩展为任何其他保守有限差分或有限体积方案。据报道，用液态水和空气进行的数值测试证明了WCNS-IS的坚固性和高精度，即使在极端条件下，也能保持正负值。