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Design and Implementation of a Parallel Algorithm for FPS-MPFA Scheme to Simulate Flow in Anisotropic Porous Media

Dehghan Manshadi, Mostafa | 2015

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 46609 (08)
  4. University: Sharif University of Technology
  5. Department: Mechanical Engineering
  6. Advisor(s): Taghizadeh Manzari, Mehrdad
  7. Abstract:
  8. Continuous approximation of pressure and flux fields is one of main goals of simulating flow in porous media. To compute the pressure field in heterogeneous and anisotropic media using minimum memory and time, it is necessary to use a conservative flux-continuous scheme. Nowadays, one of the most efficient approaches to minimize the solving time of large-scale problems is parallel computing. In this research, a parallel algorithm for flux-continuous multi-point flux approximation (MPFA) scheme with full pressure support (FPS) is designed and implemented on unstructured triangular grids by cell-centered approach. In this work, 2D single phase flows are investigated. The results are presented in two parts. The first part involves verification of the written and used FPS code by solving three sample problems. To investigate the accuracy of the FPS scheme, it’s results are compared with those of the TPS scheme. Comparison shows that the FPS scheme has higher accuracy and convergence rate than the TPS. Besides, the pressure fields obtained by the FPS show less spurious oscillations. In the second part, the results of implementation of parallel FPS algorithms are presented and surveyed. Parallel computations are accomplished at Sharif High Performance Computing Center. The computational domain is decomposed by METIS software. Results show that to obtain the speedup factor greater than one, it is necessary to use overlapped subdomains due to boost communication of subdomains to decrease the number of iterations required to converge to a solution. Also, the optimum overlapping level based on grid size and number of cores is obtained and presented. Results show that as the number of cores increases or size of the grid decreases, greater speedup factor is reachable. By using twenty-four cores, the problem solving time is decreased up to ninety percent. The codes are written and compiled at Linux OS by C++ and g++, respectively. MPI-3 standard (MPICH-3 implementation) is used to implement parallel algorithms. Also,a GMRES solver is used to solve the linear system of equations
  9. Keywords:
  10. Unstructured Grid ; Full Permeability Tensor ; Parallel Processing ; Anisotropic Porous Media ; Full Pressure Continuity ; Multipoint Flux Approximation

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