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Numerical Solution of Three Phase Buckley-Leverett Problem in One-Dimension

Ramzanpour, Mohammad Reza | 2015

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 47071 (08)
  4. University: Sharif University of Technology
  5. Department: Mechanical Engineering
  6. Advisor(s): Taghizadeh Manzari, Mehrdad
  7. Abstract:
  8. The solution to the hyperbolic conservation laws may involve discontinuities or shocks even if initial condition is smooth. Devising low cost methods which can identify shocks accurately, has always been a challenge. This project focuses on applying high resolution schemes to the solution of two and three phase Buckley-Leverett equation and hyperbolic conservation laws in general.Buckley-Leverett equation is a transport equation which is used to describe two and three phase flows in porous media. Weighted Essentially Non-Oscillatory (WENO) schemes with reconstruction on fluxes in finite difference formulation are used to solve one dimensional systems of equations including Euler equation as well as three phase Buckley-Leveret equations. Avoiding characteristic decomposition is the main advantage of this method. The first step of WENO method with flux reconstruction is flux splitting. One of the most popular flux splitting methods is the Lax-Friedrich method which uses the maximum eigenvalue of the system of equations. But the experience shows that this method may cause some overshoots in the solution. By means of a dominant wave speed definition, a new flux splitting method is introduced and the results obtained by this method are compared with those of the classic Lax-Friedrich flux splitting method. The numerical results show an improved accuracy
  9. Keywords:
  10. Buckley-Leverett Equation ; Three Phase Flow ; Dominant Wave ; Hyperbolic Conservation Laws ; Weighted Essentially Non-Oscillatory Schemes

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