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Implementation and Validation of TVD Schemes for Modelling of Multiphase Flow

  • Author / Creator
    Zhang, Qianyu
  • This work focuses on the implementation and validation of the implicit Total Variation Diminishing (TVD) schemes for modelling of two-dimensional multiphase flow. The TVD schemes are designed to mitigate the numerical diffusion at the interface where discontinuities of fluid properties exist while preserving the boundedness of the solutions. The volume of fluid approach was taken. The one-dimensional code was implemented in FORTRAN 77 and MATLAB, and the two-dimensional code was implemented in FORTRAN 77. The in-house developed code can be expanded into three-dimensions using similar algorithms and structures. The programs can be served as computational tools in the future studies of multiphase flow.
    To validate the code, a one-dimensional passive scalar convection-diffusion problem, the lids-driven cavity (LDC) problem and the cylinder convection problem were investigated. The code results were compared with the solutions from a commercial computational fluid dynamics software ANSYS Fluent and the analytical solutions. In the one-dimensional case, with a grid size of 0.125 m, the TVD code produced an average relative error in the order of 10−1, while Fluent produced an average relative error in the order of 100 with its most accurate discretization scheme. The maximum error between the code prediction and the Fluent prediction for the LDC problem was 7% using the second-order upwind scheme at a grid size of 0.01 m. The relative error for the first and third-order schemes was close to 1%.
    In the cylinder advection studies, the TVD schemes were effective in the cylinder volume conservation. Among the four TVD schemes tested, the SUPERBEE flux limiter function produced the most accurate results while consuming the longest time; whereas the Lin-Lin flux limiter function was the best in terms of the usage of computational resources. With a 0.02 m mesh size, the SUPERBEE method gave an error of 7% in cylinder volume after 80 seconds of elapsed time.

  • Subjects / Keywords
  • Graduation date
    Fall 2019
  • Type of Item
    Thesis
  • Degree
    Master of Science
  • DOI
    https://doi.org/10.7939/r3-373h-tf95
  • License
    Permission is hereby granted to the University of Alberta Libraries to reproduce single copies of this thesis and to lend or sell such copies for private, scholarly or scientific research purposes only. Where the thesis is converted to, or otherwise made available in digital form, the University of Alberta will advise potential users of the thesis of these terms. The author reserves all other publication and other rights in association with the copyright in the thesis and, except as herein before provided, neither the thesis nor any substantial portion thereof may be printed or otherwise reproduced in any material form whatsoever without the author's prior written permission.