# Numerical methods

### From CFD-Wiki

(Difference between revisions)

(8 intermediate revisions not shown) | |||

Line 2: | Line 2: | ||

This section covers the numerical soul of CFD. | This section covers the numerical soul of CFD. | ||

# [[Introduction to numerical methods]] | # [[Introduction to numerical methods]] | ||

+ | # [[Basic aspects of discretization]] | ||

+ | ## [[Classification of govering equations]] | ||

+ | ### [[Integral form of govering equations]] | ||

+ | ### [[Differential form of govering equations]] | ||

+ | ### [[Forms of the govering equations suited for CFD]] | ||

+ | ### [[Generic scalar transport equation]] | ||

+ | ## [[Mathematical behaivior of Partial Differential Equations]] | ||

+ | ### [[Classification of physical behaviour]] | ||

+ | #### [[Equilibrium problems]] | ||

+ | #### [[Marching problems]] | ||

+ | ### [[Mathematical Classification of flows]] | ||

+ | #### [[Hyperbolic flows]] | ||

+ | #### [[Parabolic flows]] | ||

+ | #### [[Elliptic flows]] | ||

+ | #### [[Mixed flow types]] | ||

+ | ### [[Stability Analysis]] | ||

+ | #### [[Fourier stability analysis]] | ||

+ | #### [[von Neuman stability analysis]] | ||

+ | #### [[Courant–Friedrichs–Lewy condition]] | ||

+ | ## [[Properties of Numerical Solution Methods]] | ||

+ | ### [[Consistency]] | ||

+ | ### [[Stability]] | ||

+ | ### [[Conservation]] | ||

+ | ### [[Boundedness]] | ||

+ | ### [[Realizability]] | ||

+ | ### [[Accuracy]] | ||

# [[Solution of Euler equation]] | # [[Solution of Euler equation]] | ||

# [[Solution of Poisson's equation]] | # [[Solution of Poisson's equation]] | ||

Line 46: | Line 72: | ||

### [[Gradient computation]] | ### [[Gradient computation]] | ||

## [[Spectral volume]] | ## [[Spectral volume]] | ||

+ | ##[[Discontinuous Galerkin]] | ||

## [[Finite element]] | ## [[Finite element]] | ||

## [[Time discretisation]] | ## [[Time discretisation]] | ||

Line 74: | Line 101: | ||

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

## [[Multigrid methods]] | ## [[Multigrid methods]] | ||

- | ### [[Geometric multigrid]] | + | ### [[Geometric multigrid - FAS]] |

### [[Algebraic multigrid - AMG]] | ### [[Algebraic multigrid - AMG]] | ||

# [[Efficiency and stability]] | # [[Efficiency and stability]] |

## Latest revision as of 12:42, 26 August 2012

## Numerical Aspects of CFD

This section covers the numerical soul of CFD.

- Introduction to numerical methods
- Basic aspects of discretization
- Solution of Euler equation
- Solution of Poisson's equation
- Solution of Navier-Stokes equations
- 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
- CIP - Cubic Interpolating Polynomial Method

- Discrete Operator Splitting

- Solution of Boltzmann Equation
- CFD Related algorithms
- Wall distance Calculations

- Geometrical Calculations
- Discretization
- Linear systems of equations
- Introduction and need
- Direct methods
- Iterative methods
- Matrix factorization and preconditioning
- Multigrid methods

- Efficiency and stability
- Limiters

- Meshless methods
- Overset grids
- Panel method
- Calculation on non-orthogonal curvelinear structured grids, finite-volume method