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Application of Direct Discrete Method for Solving the One-dimensional & Time-independent Correlation Equation

Torabi Mirzaei, Ehsan | 2018

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 51712 (46)
  4. University: Sharif University of Technology
  5. Department: Energy Engineering
  6. Advisor(s): Vosoughi, Naser
  7. Abstract:
  8. Nowadays numerical solution of engineering equations and relationships is one of the most efficient and most important parts of scientific research. Hence, various methods have been developed and expanded for this purpose, and the choice of the best method for solving a problem based on its strengths and weaknesses is essential. Direct discrete method is one of the new numerical methods that has been used for solving magnetic equations for the first time and shown promising results in nuclear researches. In this method, after determining an interpolation function for the unknown quantity, the discrete form of mathematical operators such as integral and gradient is obtained in the grid elements and the equations will be discrete.
    Due to the random nature of nuclear phenomena, the probabilistic investigation and description of these sets is important and in some cases is necessary. Now, if the simulation of spatial-temporal behavior of the moments of the stochastic transport equation is considered, then the first-order moment obtained directly from the random equation governing the collection is nothing more than the classical transport equation of the neutrons. Also, by calculating the second-order moment, the governing equations are obtained for the correlation between the points of the phase space and, if correlation equations can be solved, some of the kinetic and statistical parameters of the system can be achieved.
    In this thesis, the direct discrete method is used to solve the one-dimensional & time-independent correlation equation. Also the use of unstructured triangular meshing and development of a software for solving the discrete equations has been among the purposes of this thesis. For this purpose, the linear interpolation function was used to solve the first moment equation and the results obtained for the two verification questions were consistent with the reference values. A second degree interpolation function is also used for second moment equation and the final answer to the reference values of the verification problem is acceptable
  9. Keywords:
  10. Direct Discrete Method ; Unstructured Network ; Stochastic Transport Equation ; SN Discrete Ordinates Method ; Primary Mesh ; Dual Mesh

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