Numerical methods
From CFD-Wiki
(Difference between revisions)
(52 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 Poisson's equation]] | # [[Solution of Poisson's equation]] | ||
- | # [[Solution of Navier-Stokes | + | # [[Solution of Navier-Stokes equations]] |
## [[Velocity-pressure coupling]] | ## [[Velocity-pressure coupling]] | ||
+ | ### [[Rhie-Chow interpolation]] | ||
## [[Fully coupled methods - FC]] | ## [[Fully coupled methods - FC]] | ||
## [[DeCoupled methods - DC]] | ## [[DeCoupled methods - DC]] | ||
Line 53: | Line 44: | ||
### [[PRIME algorithm - PRessure Implicit Momentum Explicit]] | ### [[PRIME algorithm - PRessure Implicit Momentum Explicit]] | ||
### [[MSIMPLEC, MPISO , SIMPLESSEC , SIMPLESSE]] | ### [[MSIMPLEC, MPISO , SIMPLESSEC , SIMPLESSE]] | ||
+ | ### [[CPC - Compressible Pressure Correction algorithm]] | ||
### [[MCBA - Mass Conservation Based Algorithms]] | ### [[MCBA - Mass Conservation Based Algorithms]] | ||
### [[GCBA - Geometric Conservation Based Algorithms]] | ### [[GCBA - Geometric Conservation Based Algorithms]] | ||
### [[IPSA - Inter-Phase Slip Algorithm]] | ### [[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 | ||
+ | ### [[Moore's kd-tree algorithm]] | ||
+ | ### [[Transport equation based wall distance calculation]] | ||
+ | # Geometrical Calculations | ||
+ | ## [[Area calculations]] | ||
+ | ## [[Volume calculations]] | ||
+ | # Discretization | ||
+ | ## [[Finite difference]] | ||
+ | ## [[Finite volume]] | ||
+ | ### [[Generic scalar transport equation]] | ||
+ | ### [[Discretization of the diffusion term]] | ||
+ | ### [[Discretization of the convection term]] | ||
+ | ### [[Discretization of the transient term]] | ||
+ | ### [[Source term linearization]] | ||
+ | ### [[Gradient computation]] | ||
+ | ## [[Spectral volume]] | ||
+ | ##[[Discontinuous Galerkin]] | ||
+ | ## [[Finite element]] | ||
+ | ## [[Time discretisation]] | ||
+ | ### [[Euler method]] | ||
+ | ### [[Predictor corrector methods]] | ||
+ | #### [[Runge Kutta methods]] | ||
+ | #### [[Adams Bashforth method]] | ||
+ | #### [[Adams Moulton method]] | ||
+ | ### [[Implicit second order method]] | ||
+ | # Linear systems of equations | ||
+ | ## [[Introduction and need]] | ||
+ | ## [[Direct methods]] | ||
+ | ### [[Gaussian elimination]] | ||
+ | ### [[LU decomposition]] | ||
+ | ### [[Tridiagonal matrix algorithm - TDMA (Thomas algorithm)]] | ||
+ | ## [[Iterative methods]] | ||
+ | ### [[Gauss-Seidel method]] | ||
+ | ### [[Jacobi method]] | ||
+ | ### [[Successive over-relaxation method - SOR]] | ||
+ | ### [[Stone's method]] | ||
+ | ### [[Alternating direction implicit (ADI) method]] | ||
+ | ### [[Conjugate gradient methods]] | ||
+ | #### [[Conjugate gradient method of Golub and van Loan]] | ||
+ | #### [[Biconjugate gradient method]] | ||
+ | #### [[Biconjugate gradient stabilized method]] | ||
+ | ## Matrix factorization and preconditioning | ||
+ | ### [[Incomplete LU factorization - ILU]] | ||
+ | ### [[Incomplete Cholesky factorization]] | ||
+ | ## [[Multigrid methods]] | ||
+ | ### [[Geometric multigrid - FAS]] | ||
+ | ### [[Algebraic multigrid - AMG]] | ||
# [[Efficiency and stability]] | # [[Efficiency and stability]] | ||
## Limiters | ## Limiters | ||
Line 67: | Line 109: | ||
# [[Meshless methods]] | # [[Meshless methods]] | ||
# [[Overset grids]] | # [[Overset grids]] | ||
- | + | # [[Panel method]] | |
- | + | # [[Calculation on non-orthogonal curvelinear structured grids, finite-volume method]] | |
- | + | ||
- | + |
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