Numerical methods

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Revision as of 20:34, 14 December 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. Discretisation
   1. Finite difference
   2. Finite volume
      1. Generic scalar transport equation
      2. Discretization of the diffusion term
      3. Discretization of the convection term
      4. Discretization of the transient term
      5. Source term linearization
      6. Gradient computation
   3. Finite element
   4. Time discretisation
      1. Euler method
      2. Predictor corrector methods
         1. Runge Kutta methods
         2. Adams Bashforth method
         3. Adams Moulton method
      3. Implicit second order method

1. Linear systems of equations
   1. Introduction and need
   2. Matrix Related
      1. Matrix factorisation
         1. Incomplete LU factorization - ILU
         2. Incomplete Cholesky factorization
   3. Direct methods
      1. Gaussian elimination
      2. LU decomposition method
      3. Direct solution to tridiagonal matrix
         1. Thomas algorithm
   4. Iterative methods
      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
         3. Biconjugate gradient stabilized method
   5. Multigrid methods
      1. Geometric multigrid
      2. Additive corrective multigrid
2. Solution of Poisson's equation
3. Solution of Navier-Stokes equation
   1. Velocity-pressure coupling
      1. Rhie-Chow interpolation
   2. Fully coupled methods - FC
   3. DeCoupled methods - DC
      1. SIMPLE algorithm
      2. SIMPLEC algorithm - SIMPLE Consistent
      3. SIMPLEM algorithm - SIMPLE-Modified
      4. SIMPLEX algorithm
      5. SIMPLEST algorithm - SIMPLE ShorTened
      6. SIMPLER algorithm - SIMPLE - Revised
      7. PISO algorithm - Pressure Implicit with Split Operator
      8. PRIME algorithm - PRessure Implicit Momentum Explicit
      9. MSIMPLEC, MPISO , SIMPLESSEC , SIMPLESSE
      10. CPC - Compressible Pressure Correction algorithm
      11. MCBA - Mass Conservation Based Algorithms
      12. GCBA - Geometric Conservation Based Algorithms
      13. IPSA - Inter-Phase Slip Algorithm
      14. CPI - Consistent Physical Interpolation
      15. MWIM - Momentum Weighted Interpolation Method
      16. PWIM - Pressure Weighted Interpolation Method
      17. ACM - Artificial Compressibility Method
4. Solution of Euler equation
5. Efficiency and stability
   1. Limiters
      1. Flux limiters
      2. Gradient limiters
6. Meshless methods
7. Overset grids
8. Panel method
9. CFD Related algorithms
   1. Wall distance Calculations
      1. Moore's kd-tree algorithm
      2. Transport equation based wall distance calculation