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Simulation of 2D and Two-Phase Flows in Porous Media Using MLPG Method

Fathi, Abdolhamid | 2020

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 53222 (06)
  4. University: Sharif University of Technology
  5. Department: Chemical and Petroleum Engineering
  6. Advisor(s): Pishvaie, Mahmoud Reza; Bazargan, Mohammad
  7. Abstract:
  8. Conventional methods of solving partial differential equations such as finite difference method, finite volume method, and finite element method require mesh generation in the problem domain. When these methods are applied to solve problems involving shock propagation, crack propagation or deformable domain, or in the case of mesh refinement, multiple mesh regenerations are needed which is laborious and time consuming. In recent years, meshless methods have been developed to avoid difficulties of mesh-based methods. Meshless Local Petrov-Galerkin (MLPG) method is a truly meshless method that does not rely on mesh neither in function approximation nor in the integration of the weak form. In this study, MLPG method is used to simulate the unsteady state diffusion problem, Buckley-Leverett problem, and two-phase flow in two-dimensional reservoirs with compressible rock and fluids. To improve accuracy in Buckley-Leverett problem, two node-refinement techniques are applied. Also, a novel scheme for stabilizing convection-dominated problems is proposed. It is concluded that MLPG method, as an effective, flexible and parallelizable method can replace mesh-based methods
  9. Keywords:
  10. Meshless Local Petrov-Galerkin (MLPG)Method ; Two Phase Flow ; Two-Dimensional Flows ; Burger Equation ; Moving Least Squares Approximation ; Upwinding Scheme ; Point Interpolation Method (PIM)

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