A piecewise parabolic method for barotropic and nonbarotropic two‐fluid flows

Abstract

PurposeThe aim of the study is to present a piecewise parabolic method (PPM) for numerical simulation of barotropic and nonbarotropic two‐fluid flows in more than one space dimension.Design/methodology/approachIn 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 third‐order PPM is extended to the two‐fluid case and used to solve the model system.FindingsThe 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 limitations/implicationsWith the mixture model system, there may be energy gain or loss for the nonbarotropic component on the material interfaces.Practical implicationsThe method can be applied to a wide range of practical problems.Originality/valueThe method is simple. It not only has the advantage of Lagrangian‐type schemes but also keeps the robustness of Eulerian schemes.