A positivity-preserving high-order weighted compact nonlinear scheme for compressible gas-liquid flows

• Published in: Journal of computational physics 2021-11, Vol.444, p.110569, Article 110569
• Main Authors: Wong, Man Long, Angel, Jordan B., Barad, Michael F., Kiris, Cetin C.
• Format: Article
• Language: English
• Subjects: Boundedness-preserving; Compressibility; Computational physics; Constraining; Diffuse interface method; Finite difference method; Finite volume method; Gas laws; Ideal gas; Liquid flow; Multi-phase; Positivity-preserving; Robustness (mathematics); Shock-capturing; Two phase flow; Water; Weighted essentially non-oscillatory (WENO)
• ISSN: 0021-9991; 1090-2716
• DOI: 10.1016/j.jcp.2021.110569

•Novel positivity-preserving limiters for high-order methods are developed for compressible gas-liquid flows.•The interpolation and flux limiters ensure bounded volume fractions and positive densities and squared sound speed.•The positivity-preserving properties of the HLLC flux for the five-equation model by Allaire et al. are shown.•The flux limiting on any high-order flux is discretely conservative for all conservative equations of the flow model.•The fifth order incremental-stencil WCNS with the limiters is shown to be robust with intense problems. 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.