# Approximation Schemes for convective term - structured grids - Schemes

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- | ''When we shall fill this page, | + | ''When we shall fill this page, we offer to make common identifications and definitions, because in different issues was used different notation. |

- | ''Also we beg everybody to help | + | ''Also we beg everybody to help us with original works. Please see section about what we need. If anyone have literature connected with convective schemes, please drop us a line. Of course You are welcome to participate in Wiki'' |

''We shall be very glad and grateful to hear any critical suggestion (please drop a few lines at Wiki Forum)'' | ''We shall be very glad and grateful to hear any critical suggestion (please drop a few lines at Wiki Forum)'' | ||

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* [[Non-Linear QUICK based Schemes - structured grids #QUICKER - Quadratic Upwind Interpolation Extended and Revised | QUICKER - Quadratic Upwind Interpolation Extended and Revised ]] | * [[Non-Linear QUICK based Schemes - structured grids #QUICKER - Quadratic Upwind Interpolation Extended and Revised | QUICKER - Quadratic Upwind Interpolation Extended and Revised ]] | ||

- | * [[Non-Linear QUICK based Schemes - structured grids #SMART - Sharp and Monotonic Algorithm for Realistic Transport |SMART - Sharp and Monotonic Algorithm for Realistic Transport ]] | + | * [[Non-Linear QUICK based Schemes - structured grids #SMART - Sharp and Monotonic Algorithm for Realistic Transport (Also CCCT - Curvature-Compensated Convective Transport ) |SMART - Sharp and Monotonic Algorithm for Realistic Transport (Also CCCT - Curvature-Compensated Convective Transport ) ]] |

* [[Non-Linear QUICK based Schemes - structured grids #SMARTER - SMART Efficiently Revised |SMARTER - SMART Efficiently Revised ]] | * [[Non-Linear QUICK based Schemes - structured grids #SMARTER - SMART Efficiently Revised |SMARTER - SMART Efficiently Revised ]] | ||

* [[Non-Linear QUICK based Schemes - structured grids #WACEB |WACEB ]] | * [[Non-Linear QUICK based Schemes - structured grids #WACEB |WACEB ]] | ||

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== [[Schemes by Leonard - structured grids ]] == | == [[Schemes by Leonard - structured grids ]] == | ||

- | * [[Schemes by Leonard - structured grids#SHARP | SHARP]] | + | * [[Schemes by Leonard - structured grids#SHARP - Simple High Accuracy Resolution Program | SHARP - Simple High Accuracy Resolution Program]] |

* [[Schemes by Leonard - structured grids#ULTIMATE - Universal Limiter for Transport Interpolation Modelling of the Advective Transport Equation | ULTIMATE - Universal Limiter for Transport Interpolation Modelling of the Advective Transport Equation]] | * [[Schemes by Leonard - structured grids#ULTIMATE - Universal Limiter for Transport Interpolation Modelling of the Advective Transport Equation | ULTIMATE - Universal Limiter for Transport Interpolation Modelling of the Advective Transport Equation]] | ||

* [[Schemes by Leonard - structured grids#ULTIMATE-QUICKEST |ULTIMATE-QUICKEST ]] | * [[Schemes by Leonard - structured grids#ULTIMATE-QUICKEST |ULTIMATE-QUICKEST ]] | ||

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* [[Schemes by Leonard - structured grids#AQUATIC - Adjusted Quadratic Upstream Algorithm for Transient Incompressible Convection |AQUATIC - Adjusted Quadratic Upstream Algorithm for Transient Incompressible Convection ]] | * [[Schemes by Leonard - structured grids#AQUATIC - Adjusted Quadratic Upstream Algorithm for Transient Incompressible Convection |AQUATIC - Adjusted Quadratic Upstream Algorithm for Transient Incompressible Convection ]] | ||

* [[Schemes by Leonard - structured grids#EXQUISITE - Exponential or Quadratic Upstream Interpolation for Solution of the Incompressible Transport Equation |EXQUISITE - Exponential or Quadratic Upstream Interpolation for Solution of the Incompressible Transport Equation ]] | * [[Schemes by Leonard - structured grids#EXQUISITE - Exponential or Quadratic Upstream Interpolation for Solution of the Incompressible Transport Equation |EXQUISITE - Exponential or Quadratic Upstream Interpolation for Solution of the Incompressible Transport Equation ]] | ||

+ | * [[Schemes by Leonard - structured grids#EULER-QUICK |EULER-QUICK ]] | ||

== [[Other Schemes (unclassified) - structured grids ]] == | == [[Other Schemes (unclassified) - structured grids ]] == | ||

+ | |||

+ | ''Here we placed schemes which were not included into the previous sections (or we can't subdivide its into some class)'' | ||

+ | |||

* [[Other Schemes (unclassified) - structured grids #Chakravarthy-Osher limiter |Chakravarthy-Osher limiter ]] | * [[Other Schemes (unclassified) - structured grids #Chakravarthy-Osher limiter |Chakravarthy-Osher limiter ]] | ||

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* [[Other Schemes (unclassified) - structured grids #COPLA - COmbination of Piecewise Linear Approximation |COPLA - COmbination of Piecewise Linear Approximation ]] | * [[Other Schemes (unclassified) - structured grids #COPLA - COmbination of Piecewise Linear Approximation |COPLA - COmbination of Piecewise Linear Approximation ]] | ||

* [[Other Schemes (unclassified) - structured grids #HLPA - Hybrid Linear / Parabolic Approximation |HLPA - Hybrid Linear / Parabolic Approximation ]] | * [[Other Schemes (unclassified) - structured grids #HLPA - Hybrid Linear / Parabolic Approximation |HLPA - Hybrid Linear / Parabolic Approximation ]] | ||

+ | * [[Other Schemes (unclassified) - structured grids #LODA - Local Oscillation-Damping Algorithm |LODA - Local Oscillation-Damping Algorithm ]] | ||

* [[Other Schemes (unclassified) - structured grids #CLAM - Curved-Line Advection Method |CLAM - Curved-Line Advection Method ]] | * [[Other Schemes (unclassified) - structured grids #CLAM - Curved-Line Advection Method |CLAM - Curved-Line Advection Method ]] | ||

* [[Other Schemes (unclassified) - structured grids #van Leer harmonic |van Leer harmonic ]] | * [[Other Schemes (unclassified) - structured grids #van Leer harmonic |van Leer harmonic ]] | ||

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* [[Other Schemes (unclassified) - structured grids #H-CUS |H-CUS ]] | * [[Other Schemes (unclassified) - structured grids #H-CUS |H-CUS ]] | ||

* [[Other Schemes (unclassified) - structured grids #MLU |MLU ]] | * [[Other Schemes (unclassified) - structured grids #MLU |MLU ]] | ||

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* [[Other Schemes (unclassified) - structured grids #LPPA - Linear and Piecewise / Parabolic Approximasion |LPPA - Linear and Piecewise / Parabolic Approximasion ]] | * [[Other Schemes (unclassified) - structured grids #LPPA - Linear and Piecewise / Parabolic Approximasion |LPPA - Linear and Piecewise / Parabolic Approximasion ]] | ||

* [[Other Schemes (unclassified) - structured grids #GAMMA |GAMMA ]] | * [[Other Schemes (unclassified) - structured grids #GAMMA |GAMMA ]] | ||

* [[Other Schemes (unclassified) - structured grids #CUBISTA - Convergent and Universally Bounded Interpolation Scheme for the Treatment of Advection |CUBISTA - Convergent and Universally Bounded Interpolation Scheme for the Treatment of Advection ]] | * [[Other Schemes (unclassified) - structured grids #CUBISTA - Convergent and Universally Bounded Interpolation Scheme for the Treatment of Advection |CUBISTA - Convergent and Universally Bounded Interpolation Scheme for the Treatment of Advection ]] | ||

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## Latest revision as of 14:48, 4 November 2005

*When we shall fill this page, we offer to make common identifications and definitions, because in different issues was used different notation.*

*Also we beg everybody to help us with original works. Please see section about what we need. If anyone have literature connected with convective schemes, please drop us a line. Of course You are welcome to participate in Wiki*

*We shall be very glad and grateful to hear any critical suggestion (please drop a few lines at Wiki Forum)*

*It is just a skeleton, but we hope that it will be developed into the good thing*

## Contents |

## Basic Discretisation schemes

- Central Differencing Scheme (CDS)
- Upwind Differencing Scheme (UDS) also (First-order upwind - FOU)
- Hybrid Differencing Scheme (HDS also HYBRID)
- Power-Law Scheme (also Exponencial scheme or PLDS )

## Linear Schemes - structured grids

- SOU - Second Order Upwind (also LUDS or UDS-2)
- Skew - Upwind
- QUICK - Quadratic Upwind Interpolation for Convective Kinematics (also UDS-3 or QUDS)
- LUS - Linear Upwind Scheme
- Fromm - Fromm's Upwind Scheme
- CUDS - Cubic Upwind Difference Scheme (also CUS or UDS-4)
- CUI - Cubic Upwind Interpolation

## Non-Linear QUICK based Schemes - structured grids

- QUICKER - Quadratic Upwind Interpolation Extended and Revised
- SMART - Sharp and Monotonic Algorithm for Realistic Transport (Also CCCT - Curvature-Compensated Convective Transport )
- SMARTER - SMART Efficiently Revised
- WACEB
- VONOS - Variable-Order Non-Oscillatory Scheme
- CHARM - Cubic / Parabolic High-Accuracy Resolution Method
- UMIST - Upstream Monotonic Interpolation for Scalar Transport

## Fromm based Schemes - structured grids

- Fromm scheme
- MUSCL - Monotonic Upwind Scheme for Conservation Laws
- van Leer limiter
- van Albada
- OSPRE

## Schemes by Leonard - structured grids

- SHARP - Simple High Accuracy Resolution Program
- ULTIMATE - Universal Limiter for Transport Interpolation Modelling of the Advective Transport Equation
- ULTIMATE-QUICKEST
- ULTRA-SHARP : Universal Limiter for Thight Resolution and Accuracy in combination with the Simple High-Accuracy Resolution Program (also ULTRA-QUICK)
- UTOPIA - Uniformly Third Order Polynomial Interpolation Algorithm
- NIRVANA - Non-oscilatory Integrally Reconstructed Volume-Avaraged Numerical Advection scheme
- ENIGMATIC - Extended Numerical Integration for Genuinely Multidimensional Advective Transport Insuring Conservation
- MACHO : Multidimensional Advective - Conservative Hybrid Operator
- COSMIC : Conservative Operator Splitting for Multidimensions with Internal Constancy
- QUICKEST - Quadratic Upstream Interpolation for Convective Kinematics with Estimated Streaming Terms
- AQUATIC - Adjusted Quadratic Upstream Algorithm for Transient Incompressible Convection
- EXQUISITE - Exponential or Quadratic Upstream Interpolation for Solution of the Incompressible Transport Equation
- EULER-QUICK

## Other Schemes (unclassified) - structured grids

*Here we placed schemes which were not included into the previous sections (or we can't subdivide its into some class)*

- Chakravarthy-Osher limiter
- Sweby Φ - limiter
- Superbee limiter
- R-k limiter
- MINMOD - MINimum MODulus
- SOUCUP - Second-Order Upwind Central differnce-first order UPwind
- ISNAS - Interpolation Scheme which is Nonoscillatory for Advected Scalars
- COPLA - COmbination of Piecewise Linear Approximation
- HLPA - Hybrid Linear / Parabolic Approximation
- LODA - Local Oscillation-Damping Algorithm
- CLAM - Curved-Line Advection Method
- van Leer harmonic
- BSOU
- MSOU - Monotonic Second Order Upwind Differencing Scheme
- Koren
- H-CUS
- MLU
- LPPA - Linear and Piecewise / Parabolic Approximasion
- GAMMA
- CUBISTA - Convergent and Universally Bounded Interpolation Scheme for the Treatment of Advection

## reference shablon

**SMITH (3000)**, "XXX", XXX.

* Return to Numerical Methods *

* Return to Approximation Schemes for convective term - structured grids *