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A Piecewise Parabolic Method For Barotropic Two-Fluid Flows

Author

Listed:
  • J. G. ZHENG

    (Department of Mechanical Engineering, National University of Singapore, Singapore 119260, Singapore)

  • T. S. LEE

    (Department of Mechanical Engineering, National University of Singapore, Singapore 119260, Singapore)

  • D. J. MA

    (Department of Modern Mechanics, University of Science and Technology of China, Hefei, Anhui 230027, China)

Abstract

In this paper, a third-order Piecewise Parabolic Method for barotropic two-fluid flows with Tait equation of state is presented. In transition layers between two different fluids, a mixture model system based on the assumption of equilibrium pressure is introduced. It conserves the mass of each fluid, the total momentum and energy of the mixture and is supplemented with an advection equation for the volume fraction of one of the two fluids. To close the model and recover the pressure, a nonbarotropic equation of state describing the thermodynamic properties of the mixture is used. However, in pure barotropic fluid regions, the isentropic version of Euler equations is employed. In addition, the third-order Piecewise Parabolic Method is employed to solve the model equations. The governing equations are first evolved in the Lagrangian coordinate system and then the computed results are mapped onto the fixed Eulerian grid in the following remapping step. As compared with other methods, a remarkable feature of our approach is that the scheme is third-order accurate in smooth regions of the solution and is able to give a steeper representation of discontinuities. Numerical results demonstrate satisfactory performances of this approach.

Suggested Citation

  • J. G. Zheng & T. S. Lee & D. J. Ma, 2007. "A Piecewise Parabolic Method For Barotropic Two-Fluid Flows," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 18(03), pages 375-390.
    • Handle: RePEc:wsi:ijmpcx:v:18:y:2007:i:03:n:s0129183107010516
    DOI: 10.1142/S0129183107010516
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