# Numerical methods

### From CFD-Wiki

(Difference between revisions)

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#### [[Adams Moulton method]] | #### [[Adams Moulton method]] | ||

### [[Implicit second order method]] | ### [[Implicit second order method]] | ||

- | # Linear | + | |

+ | # Linear systems of equations | ||

## [[Introduction and need]] | ## [[Introduction and need]] | ||

## Matrix Related | ## Matrix Related | ||

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#### [[Incomplete LU factorization - ILU]] | #### [[Incomplete LU factorization - ILU]] | ||

#### [[Incomplete Cholesky factorization]] | #### [[Incomplete Cholesky factorization]] | ||

- | ## Direct | + | ## Direct methods |

### [[Gaussian elimination]] | ### [[Gaussian elimination]] | ||

### [[LU decomposition method]] | ### [[LU decomposition method]] | ||

### Direct solution to tridiagonal matrix | ### Direct solution to tridiagonal matrix | ||

#### [[Thomas algorithm]] | #### [[Thomas algorithm]] | ||

- | ## Iterative | + | ## Iterative methods |

### [[Basic concept of iterative solutions]] | ### [[Basic concept of iterative solutions]] | ||

### [[Gauss-Seidel method]] | ### [[Gauss-Seidel method]] |

## Revision as of 20:34, 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
- Introduction and need
- Matrix Related
- Direct methods
- Gaussian elimination
- LU decomposition method
- Direct solution to tridiagonal matrix

- Iterative methods
- Multigrid methods

- 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