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

+ | == [[Approximation Schemes for convective term - structured grids - Common#Basic Discretisation schemes | Basic Discretisation schemes]] == | ||

+ | * [[Approximation Schemes for convective term - structured grids - Common#Central Differencing Scheme (CDS) | Central Differencing Scheme (CDS) ]] | ||

+ | * [[Approximation Schemes for convective term - structured grids - Common#Upwind Differencing Scheme (UDS) also (First-order upwind - FOU) | Upwind Differencing Scheme (UDS) also (First-order upwind - FOU) ]] | ||

+ | * [[Approximation Schemes for convective term - structured grids - Common#Hybrid Differencing Scheme (HDS also HYBRID) |Hybrid Differencing Scheme (HDS also HYBRID) ]] | ||

+ | * [[Approximation Schemes for convective term - structured grids - Common#Power-Law Scheme (also Exponencial scheme or PLDS )| Power-Law Scheme (also Exponencial scheme or PLDS ) ]] | ||

== [[Linear Schemes - structured grids ]] == | == [[Linear Schemes - structured grids ]] == | ||

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+ | * [[Linear Schemes - structured grids #SOU - Second Order Upwind (also LUDS or UDS-2) | SOU - Second Order Upwind (also LUDS or UDS-2) ]] | ||

+ | * [[Linear Schemes - structured grids #Skew - Upwind |Skew - Upwind ]] | ||

+ | * [[Linear Schemes - structured grids #QUICK - Quadratic Upwind Interpolation for Convective Kinematics (also UDS-3 or QUDS) |QUICK - Quadratic Upwind Interpolation for Convective Kinematics (also UDS-3 or QUDS) ]] | ||

+ | * [[Linear Schemes - structured grids #LUS - Linear Upwind Scheme| LUS - Linear Upwind Scheme ]] | ||

+ | * [[Linear Schemes - structured grids #Fromm - Fromm's Upwind Scheme |Fromm - Fromm's Upwind Scheme ]] | ||

+ | * [[Linear Schemes - structured grids #CUDS - Cubic Upwind Difference Scheme (also CUS or UDS-4) |CUDS - Cubic Upwind Difference Scheme (also CUS or UDS-4) ]] | ||

+ | * [[Linear Schemes - structured grids #CUI - Cubic Upwind Interpolation |CUI - Cubic Upwind Interpolation ]] | ||

== [[Non-Linear QUICK based Schemes - structured grids ]] == | == [[Non-Linear QUICK based Schemes - structured grids ]] == | ||

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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 #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 #WACEB |WACEB ]] | ||

+ | * [[Non-Linear QUICK based Schemes - structured grids #VONOS - Variable-Order Non-Oscillatory Scheme |VONOS - Variable-Order Non-Oscillatory Scheme ]] | ||

+ | * [[Non-Linear QUICK based Schemes - structured grids #CHARM - Cubic / Parabolic High-Accuracy Resolution Method |CHARM - Cubic / Parabolic High-Accuracy Resolution Method ]] | ||

+ | * [[Non-Linear QUICK based Schemes - structured grids #UMIST - Upstream Monotonic Interpolation for Scalar Transport |UMIST - Upstream Monotonic Interpolation for Scalar Transport ]] | ||

- | == [[Fromm based Schemes - structured grids ]] == | + | == [[ Fromm based Schemes - structured grids ]] == |

- | * Fromm scheme | + | |

- | * MUSCL - Monotonic Upwind Scheme for Conservation Laws | + | * [[Fromm based Schemes - structured grids#Fromm scheme| Fromm scheme]] |

- | * van Leer limiter | + | * [[Fromm based Schemes - structured grids#MUSCL - Monotonic Upwind Scheme for Conservation Laws |MUSCL - Monotonic Upwind Scheme for Conservation Laws ]] |

- | * van Albada | + | * [[Fromm based Schemes - structured grids#van Leer limiter |van Leer limiter ]] |

- | * OSPRE | + | * [[Fromm based Schemes - structured grids#van Albada | van Albada ]] |

+ | * [[Fromm based Schemes - structured grids#OSPRE |OSPRE ]] | ||

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

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

- | * 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]] |

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

- | * ULTRA-SHARP : Universal Limiter for Thight Resolution and Accuracy in combination with the Simple High-Accuracy Resolution Program (also ULTRA-QUICK) | + | * [[Schemes by Leonard - structured grids#ULTRA-SHARP : Universal Limiter for Thight Resolution and Accuracy in combination with the Simple High-Accuracy Resolution Program (also ULTRA-QUICK) |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 | + | * [[Schemes by Leonard - structured grids#UTOPIA - Uniformly Third Order Polynomial Interpolation Algorithm |UTOPIA - Uniformly Third Order Polynomial Interpolation Algorithm ]] |

- | * NIRVANA - Non-oscilatory Integrally Reconstructed Volume-Avaraged Numerical Advection scheme | + | * [[Schemes by Leonard - structured grids#NIRVANA - Non-oscilatory Integrally Reconstructed Volume-Avaraged Numerical Advection scheme |NIRVANA - Non-oscilatory Integrally Reconstructed Volume-Avaraged Numerical Advection scheme ]] |

- | * ENIGMATIC - Extended Numerical Integration for Genuinely Multidimensional Advective Transport Insuring Conservation | + | * [[Schemes by Leonard - structured grids#ENIGMATIC - Extended Numerical Integration for Genuinely Multidimensional Advective Transport Insuring Conservation |ENIGMATIC - Extended Numerical Integration for Genuinely Multidimensional Advective Transport Insuring Conservation ]] |

- | * MACHO : Multidimensional Advective - Conservative Hybrid Operator | + | * [[Schemes by Leonard - structured grids#MACHO : Multidimensional Advective - Conservative Hybrid Operator |MACHO : Multidimensional Advective - Conservative Hybrid Operator ]] |

- | * COSMIC : Conservative Operator Splitting for Multidimensions with Internal Constancy | + | * [[Schemes by Leonard - structured grids#COSMIC : Conservative Operator Splitting for Multidimensions with Internal Constancy |COSMIC : Conservative Operator Splitting for Multidimensions with Internal Constancy ]] |

- | * QUICKEST - Quadratic Upstream Interpolation for Convective Kinematics with Estimated Streaming Terms | + | * [[Schemes by Leonard - structured grids#QUICKEST - Quadratic Upstream Interpolation for Convective Kinematics with Estimated Streaming Terms |QUICKEST - Quadratic Upstream Interpolation for Convective Kinematics with Estimated Streaming Terms ]] |

- | * 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 ]] |

- | * 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 ]] == | ||

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

- | * Sweby Φ - limiter | + | |

- | * Superbee limiter | + | |

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

- | * MINMOD - MINimum MODulus | + | * [[Other Schemes (unclassified) - structured grids #Sweby Φ - limiter |Sweby Φ - limiter ]] |

- | * SOUCUP - Second-Order Upwind Central differnce-first order UPwind | + | * [[Other Schemes (unclassified) - structured grids #Superbee limiter |Superbee limiter ]] |

- | * ISNAS - Interpolation Scheme which is Nonoscillatory for Advected Scalars | + | * [[Other Schemes (unclassified) - structured grids #R-k limiter |R-k limiter ]] |

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

- | * HLPA - Hybrid Linear / Parabolic Approximation | + | * [[Other Schemes (unclassified) - structured grids #SOUCUP - Second-Order Upwind Central differnce-first order UPwind |SOUCUP - Second-Order Upwind Central differnce-first order UPwind ]] |

- | * CLAM - Curved-Line Advection Method | + | * [[Other Schemes (unclassified) - structured grids #ISNAS - Interpolation Scheme which is Nonoscillatory for Advected Scalars |ISNAS - Interpolation Scheme which is Nonoscillatory for Advected Scalars ]] |

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

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

- | * MSOU - Monotonic Second Order Upwind Differencing Scheme | + | * [[Other Schemes (unclassified) - structured grids #LODA - Local Oscillation-Damping Algorithm |LODA - Local Oscillation-Damping Algorithm ]] |

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

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

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

- | * | + | * [[Other Schemes (unclassified) - structured grids #MSOU - Monotonic Second Order Upwind Differencing Scheme |MSOU - Monotonic Second Order Upwind Differencing Scheme ]] |

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

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

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

+ | * [[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 #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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{{reference-paper | author=SMITH | year= 3000 | title= XXX | {{reference-paper | author=SMITH | year= 3000 | title= XXX | ||

| rest= XXX }} | | rest= XXX }} | ||

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+ | ---- | ||

+ | <i> Return to [[Numerical methods | Numerical Methods]] </i> | ||

+ | |||

+ | <i> Return to [[Approximation Schemes for convective term - structured grids]] </i> |

## 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 *