Numerical methods
From CFD-Wiki
(Difference between revisions)
Line 25: | Line 25: | ||
# Linear systems of equations | # Linear systems of equations | ||
## [[Introduction and need]] | ## [[Introduction and need]] | ||
- | + | ||
- | + | ||
- | + | ||
- | + | ||
## Direct methods | ## Direct methods | ||
### [[Gaussian elimination]] | ### [[Gaussian elimination]] | ||
Line 34: | Line 31: | ||
### Direct solution to tridiagonal matrix | ### Direct solution to tridiagonal matrix | ||
#### [[Thomas algorithm]] | #### [[Thomas algorithm]] | ||
+ | |||
## Iterative methods | ## Iterative methods | ||
### [[Basic concept of iterative solutions]] | ### [[Basic concept of iterative solutions]] | ||
Line 45: | Line 43: | ||
#### [[Biconjugate gradient method]] | #### [[Biconjugate gradient method]] | ||
#### [[Biconjugate gradient stabilized method]] | #### [[Biconjugate gradient stabilized method]] | ||
+ | |||
+ | ## Matrix factorization and preconditioning | ||
+ | ### [[Incomplete LU factorization - ILU]] | ||
+ | ### [[Incomplete Cholesky factorization]] | ||
+ | |||
## [[Multigrid methods]] | ## [[Multigrid methods]] | ||
### [[Geometric multigrid]] | ### [[Geometric multigrid]] |
Revision as of 20:35, 14 December 2005
Numerical Aspects of CFD
This section covers the numerical soul of CFD.
- Introduction to numerical methods
- Geometrical Calculations
- Discretisation
- Linear systems of equations
- Direct methods
- Gaussian elimination
- LU decomposition method
- Direct solution to tridiagonal matrix
- Direct methods
- Matrix factorization and preconditioning
- Solution of Poisson's equation
- Solution of Navier-Stokes equation
- Velocity-pressure coupling
- Fully coupled methods - FC
- DeCoupled methods - DC
- SIMPLE algorithm
- SIMPLEC algorithm - SIMPLE Consistent
- SIMPLEM algorithm - SIMPLE-Modified
- SIMPLEX algorithm
- SIMPLEST algorithm - SIMPLE ShorTened
- SIMPLER algorithm - SIMPLE - Revised
- PISO algorithm - Pressure Implicit with Split Operator
- PRIME algorithm - PRessure Implicit Momentum Explicit
- MSIMPLEC, MPISO , SIMPLESSEC , SIMPLESSE
- CPC - Compressible Pressure Correction algorithm
- MCBA - Mass Conservation Based Algorithms
- GCBA - Geometric Conservation Based Algorithms
- IPSA - Inter-Phase Slip Algorithm
- CPI - Consistent Physical Interpolation
- MWIM - Momentum Weighted Interpolation Method
- PWIM - Pressure Weighted Interpolation Method
- ACM - Artificial Compressibility Method
- Solution of Euler equation
- Efficiency and stability
- Limiters
- Meshless methods
- Overset grids
- Panel method
- CFD Related algorithms
- Wall distance Calculations