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Investigation on Improving Direct Discrete Method and its Application in Adjoint Diffusion Equation Numerical Solvers

Ayyoub Zadeh, Mohsen | 2011

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 42154 (46)
  4. University: Sharif University of Technology
  5. Department: Energy Engineering
  6. Advisor(s): Vosoughi, Naser
  7. Abstract:
  8. Numerical analysis method improvement is a topic of interest among all engineering disciplines. Regarding the fact that our ability to predict the behavior of a physical system is often limited by our computational resources, the efficiency of the employed numerical method is an important factor in the degree of approximation used in modeling. One of the recent numerical methods is the Cell Method (CM), which is also known as the Direct Discrete Method (DDM). This method combines some features of a variety of methods, especially finite volume and finite element, and gains some insight from the graph theory used in network analysis. The result is a method in which the set of equations which arise after modeling are of algebraic nature by themselves, which makes further discretization unnecessary. This method uses a double set of mesh structures, namely primal and dual cells. It is known that the dual mesh position has an important effect in the accuracy of the numerical solutions yielded by this method. This topic has been investigated in this thesis and two methods of optimization are presented. One method is based on using the information embedded in the adjoint solution. The other is the identification of the operator which contributes the most to final error, and it’s error minimization by mesh restructuring. It is shown that one could increase the convergence order from 4 to 4.6 by using this method
  9. Keywords:
  10. Cell Method ; Numerical Method ; Adjoint Equations ; Direct Discrete Method ; Diffusion Equation ; Mesh Optimization

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