A piecewise parabolic method for barotropic and nonbarotropic twofluid flows

• Published in: International journal of numerical methods for heat & fluid flow Vol. 18; no. 6; pp. 708 - 729
• Main Authors: Zheng, J.G., Lee, T.S., Winoto, S.H.
• Format: Journal Article
• Language: English
• Published: Emerald Group Publishing Limited 08-08-2008
• Subjects: Compressible flow; Liquid flow; Mixtures; Simulation
• ISSN: 0961-5539
• DOI: 10.1108/09615530810885533

Purpose The aim of the study is to present a piecewise parabolic method PPM for numerical simulation of barotropic and nonbarotropic twofluid flows in more than one space dimension. Designmethodologyapproach In transition layers of two components, a fluid mixture model system is introduced. Besides, conserving the mass, momentum and energy for the mixture, the model is supplemented with an advection equation for the volume fraction of one of the two fluid components to recover the pressure and track interfaces. The Tait and stiffened gas equations of state are used to describe thermodynamic properties of the barotropic and nonbarotropic components, respectively. To close the model system, a mixture equation of state is derived. The classical thirdorder PPM is extended to the twofluid case and used to solve the model system. Findings The feasibility of this method has been demonstrated by good results of sample applications. Each of the material interfaces is resolved with two grid cells and there is no any pressure oscillation on the interfaces. Research limitationsimplications With the mixture model system, there may be energy gain or loss for the nonbarotropic component on the material interfaces. Practical implications The method can be applied to a wide range of practical problems. Originalityvalue The method is simple. It not only has the advantage of Lagrangiantype schemes but also keeps the robustness of Eulerian schemes.