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Numerical methods

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## [[Introduction and need]]
## [[Introduction and need]]
## [[Direct numerical solutions]]
## [[Direct numerical solutions]]
 +
### [[Gauss elimination]]
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### [[LU decomposition method]]
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### [[LU factorisation]]
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#### [[LU factorisation for sparse matrices]]
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### [[Direct solution to tridiagonal matrix]]
## [[Iterative solutions]]
## [[Iterative solutions]]
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### [[Basic concept of iterative solutions]]
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### [[Gauss-Seidel method]]
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### [[Jacobi method]]
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### [[successive over-relaxation method]]
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### [[Stone's method]]
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### [[Alternating direction implicit (ADI) method]]
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### [[Congugate gradient methods]]
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#### [[Conjugate gradient method of Golub and van Loan]]
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#### [[Biconjugate gradient method]]
# [[Efficiency and stability]]
# [[Efficiency and stability]]

Revision as of 02:14, 14 September 2005

Numerical Aspects of CFD

This section covers the numerical soul of CFD.

  1. Introduction to numerical methods
  2. Geometrical Calculations
    1. Area calculations
    2. Volume calculations
  3. Gradient calculations
  4. Discretisation
    1. Finite differences
    2. Finite volume
      1. Discretisation of convective term
      2. Discretisation of diffusive term
    3. Finite element
    4. Time discretisation
  5. Linear equation systems
    1. Introduction and need
    2. Direct numerical solutions
      1. Gauss elimination
      2. LU decomposition method
      3. LU factorisation
        1. LU factorisation for sparse matrices
      4. Direct solution to tridiagonal matrix
    3. Iterative solutions
      1. Basic concept of iterative solutions
      2. Gauss-Seidel method
      3. Jacobi method
      4. successive over-relaxation method
      5. Stone's method
      6. Alternating direction implicit (ADI) method
      7. Congugate gradient methods
        1. Conjugate gradient method of Golub and van Loan
        2. Biconjugate gradient method
  6. Efficiency and stability
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