Model Solution Library: Difference between revisions
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= '''CSDMS Model Solution Library''' = | = '''CSDMS Model Solution Library''' = | ||
:This is a collection of analytic or closed-form solutions to a variety of different mathematical models in the realm of surface process dynamics. | : This is a collection of analytic or closed-form solutions to a variety of different mathematical models that are used in the realm of surface process dynamics. It is provided for the purpose of model validation by the CSDMS Cyber-informatics and Numerics Working Group. In the near future, this will include links to pages or papers where the solutions are given and described. | ||
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== {{ Bar Heading| text=Navier-Stokes Equation}} == | |||
: Batchelor vortex (See: [http://en.wikipedia.org/wiki/Batchelor_vortex Batchelor vortex], approximate solution.) | |||
: Burgers vortex (See: [http://en.wikipedia.org/wiki/Burgers_vortex Burgers vortex].) | |||
: Couette flow (See: [http://en.wikipedia.org/wiki/Couette_flow Couette flow].) | |||
: Hill spherical vortex (See: [http://en.wikipedia.org/wiki/Vortex_ring Vortex ring].) | |||
: Lamb-Chaplygin Dipole vortex | |||
: Lamb-Oseen vortex (See: [http://en.wikipedia.org/wiki/Lamb_vortex Lamb vortex].) | |||
: Rankine vortex (See: [http://en.wikipedia.org/wiki/Rankine_vortex Rankine vortex]. This is a model, not an actual solution.) | |||
: Taylor-Couette flow (See: [http://en.wikipedia.org/wiki/Taylor–Couette_flow Taylor-Couette flow].) | |||
: Taylor-Dean flow | |||
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== {{ Bar Heading| text=Shallow Water Equations}} == | |||
: Inclined plane solution | : Inclined plane solution | ||
: Dam Break Characteristic Solution | : Dam Break Characteristic Solution | ||
: Similarity solutions | : Similarity solutions | ||
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== {{ Bar Heading| text=Glacier Flow Equations}} == | |||
: Halfar (1983) radially-symmetric (Glen Law) similarity solution | |||
: Bueler et al. (****) similarity solution | |||
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== {{ Bar Heading| text=Potential Flow, 2D}} == | |||
* See: [http://en.wikipedia.org/wiki/Potential_flow Potential flow] for an overview. | |||
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: Point source or sink | |||
: Free vortex (inviscid flow) | |||
: | : Flow around a semi-infinite plate (power-law conformal map: n=1/2) | ||
: | : Flow around a right-angle corner (power-law conformal map: n=2/3) | ||
: | : Uniform flow (power-law conformal map: n = 1) | ||
: Power-law conformal map: n=3/2 | |||
: Flow through a right-angle corner or at a stagnation point (power-law conformal map: n=2) | |||
: Flow into a 60-degree corner (power-law conformal map: n=3) | |||
: Doublet solution (source-sink pair; power-law conformal map: n=-1) | |||
: Quadrupole solution (power-law conformal map: n=-2) | |||
: Joukowski airfoil solution | : Joukowski airfoil solution | ||
: Darcy flow solutions | : Darcy flow solutions | ||
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== {{ Bar Heading| text=Jet, Wake and Mixing Layer Solutions}} == | |||
: Albertson 2D turbulent jet approximation | |||
: Goertler 2D turbulent jet solution | |||
: Peckham 2D turbulent jet solution (Peckham, 2008; Goertler and Tollmien are special cases.) | |||
: Tollmien 2D turbulent jet solution | |||
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== {{ Bar Heading| text=Channel and Pipe Flow Solutions}} == | |||
: Poisseuille Flow (See: [http://en.wikipedia.org/wiki/Poiseuille_flow Poiseuille flow].) | |||
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== {{ Bar Heading| text=Driven Cavity Solutions}} == | |||
: Lid-driven or buoyancy-driven, etc. ? | |||
: Numeric solution | : Numeric solution | ||
: Analytic solution | : Analytic solution | ||
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: Blasius | |||
: Falkners-Skan solution | == {{ Bar Heading| text=Boundary Layer Equation}} == | ||
* See: [http://en.wikipedia.org/wiki/Boundary_layer Boundary layer]. | |||
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: Blasius (See: [http://en.wikipedia.org/wiki/Blasius_boundary_layer Blasius boundary layer].) | |||
: Falkners-Skan solution (See: [http://en.wikipedia.org/wiki/Blasius_boundary_layer Blasius boundary layer].) | |||
: Stokes First Problem | : Stokes First Problem | ||
: Stokes Second Problem | : Stokes Second Problem | ||
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== {{ Bar Heading| text=Stokes Settling Solutions}} == | |||
* See: [http://en.wikipedia.org/wiki/Stokes%27_law Stoke's Law]. | |||
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== {{ Bar Heading| text=Water Wave Solutions and Models}} == | |||
* See: [http://en.wikipedia.org/wiki/Waves Waves]. | |||
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: Airy waves | |||
: Capillary waves | |||
: Cnoidal waves | |||
: Kelvin waves | |||
: Roll waves | |||
: Rossby waves | |||
: Stokes wave | |||
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== {{ Bar Heading| text=Ekman Spiral Solution}} == | |||
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== {{ Bar Heading| text=River Meandering Model}} == | |||
: G. Seminara analytic solutions ?? | |||
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== {{ Bar Heading| text=Landscape Evolution Equations}} == | |||
* See: [http://en.wikipedia.org/wiki/Landscape_evolution_model Landscape evolution model]. | |||
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: Steady-state, slope vs. area solution | |||
: Terry Smith longitudinal profile solutions | |||
: Peckham steady-state, uniform-rainrate solutions to "ideal landform equation" | |||
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== {{ Bar Heading| text=Stratigraphic Evolution Equations}} == | |||
: Peckham (2008) prograding solutions (obtained using Laplace transforms, including traveling-wave solutions) | |||
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== {{ Bar Heading| text=Coastline Evolution Equations}} == | |||
: Larson, M., H. Hanson, and N. C. Kraus (1987), Analytical solutions of the one‐line model of shoreline change, Tech. Rep. CERC‐87‐15, U.S. Army Waterw. Exp. Stn., Vicksburg, Miss. | |||
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== {{ Bar Heading| text=Infiltration Theory}} == | |||
* See: [http://en.wikipedia.org/wiki/Infiltration_(hydrology) Infiltration (hydrology)]. | |||
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: Solutions in: Smith, R.E. (2002) Infiltration Theory for Hydrologic Applications, AGU monograph. | |||
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== {{ Bar Heading| text=Wave Equation}} == | |||
* See: [http://en.wikipedia.org/wiki/Wave_equation Wave equation]. | |||
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: d'Alembert solution (See: [http://en.wikipedia.org/wiki/D%27Alembert%27s_formula d'Alembert formula].) | |||
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== {{ Bar Heading| text=Heat Equation}} == | |||
* See: [http://en.wikipedia.org/wiki/Heat_equation Heat equation]. | |||
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: Gaussian, radially-symmetric similarity solution | |||
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== {{ Bar Heading| text=Laplace Equation}} == | |||
* See: [http://en.wikipedia.org/wiki/Laplace_equation Laplace equation]. | |||
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: Many, via separation of variables method. | |||
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== {{ Bar Heading| text=Poisson Equation}} == | |||
* See: [http://en.wikipedia.org/wiki/Poisson_equation Poisson equation]. | |||
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: Many, from Poisson representation formula | |||
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: | == {{ Bar Heading| text=Minimal Surface Equation}} == | ||
* See: [http://en.wikipedia.org/wiki/Minimal_surface_equation Minimal surface equation]. | |||
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: Inclined plane solution | |||
: Helicoid solution (Meusnier, 1776) See: [http://en.wikipedia.org/wiki/Helicoid Helicoid]. | |||
: | : Catenoid solution (Meusnier, 1776) See: [http://mathworld.wolfram.com/Catenoid.html Catenoid solution] and [http://en.wikipedia.org/wiki/Catenoid Catenoid]. | ||
: Scherk's first surface solution (Scherk, 1834) See: [http://en.wikipedia.org/wiki/Scherk_surface Scherk surface]. | |||
: Scherk's second surface solution (Scherk, 1834) | |||
: Costa surface solution (Costa, 1984) See: [http://en.wikipedia.org/wiki/Costa_surface Costa surface]. | |||
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== {{ Bar Heading| text=Burgers' Equation}} == | |||
* See: [http://en.wikipedia.org/wiki/Burgers_equation Burgers' Equation].) | |||
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: Many, via the Cole-Hopf transformation to Heat Equation | |||
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== {{ Bar Heading| text=Soliton Solutions}} == | |||
* | * See: [http://en.wikipedia.org/wiki/Soliton Soliton]. | ||
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Latest revision as of 09:06, 23 May 2014
CSDMS Model Solution Library
- This is a collection of analytic or closed-form solutions to a variety of different mathematical models that are used in the realm of surface process dynamics. It is provided for the purpose of model validation by the CSDMS Cyber-informatics and Numerics Working Group. In the near future, this will include links to pages or papers where the solutions are given and described.
- Batchelor vortex (See: Batchelor vortex, approximate solution.)
- Burgers vortex (See: Burgers vortex.)
- Couette flow (See: Couette flow.)
- Hill spherical vortex (See: Vortex ring.)
- Lamb-Chaplygin Dipole vortex
- Lamb-Oseen vortex (See: Lamb vortex.)
- Rankine vortex (See: Rankine vortex. This is a model, not an actual solution.)
- Taylor-Couette flow (See: Taylor-Couette flow.)
- Taylor-Dean flow
Shallow Water Equations
- Inclined plane solution
- Dam Break Characteristic Solution
- Similarity solutions
Glacier Flow Equations
- Halfar (1983) radially-symmetric (Glen Law) similarity solution
- Bueler et al. (****) similarity solution
Potential Flow, 2D
- See: Potential flow for an overview.
- Point source or sink
- Free vortex (inviscid flow)
- Flow around a semi-infinite plate (power-law conformal map: n=1/2)
- Flow around a right-angle corner (power-law conformal map: n=2/3)
- Uniform flow (power-law conformal map: n = 1)
- Power-law conformal map: n=3/2
- Flow through a right-angle corner or at a stagnation point (power-law conformal map: n=2)
- Flow into a 60-degree corner (power-law conformal map: n=3)
- Doublet solution (source-sink pair; power-law conformal map: n=-1)
- Quadrupole solution (power-law conformal map: n=-2)
- Joukowski airfoil solution
- Darcy flow solutions
Jet, Wake and Mixing Layer Solutions
- Albertson 2D turbulent jet approximation
- Goertler 2D turbulent jet solution
- Peckham 2D turbulent jet solution (Peckham, 2008; Goertler and Tollmien are special cases.)
- Tollmien 2D turbulent jet solution
Channel and Pipe Flow Solutions
- Poisseuille Flow (See: Poiseuille flow.)
Driven Cavity Solutions
- Lid-driven or buoyancy-driven, etc. ?
- Numeric solution
- Analytic solution
Boundary Layer Equation
- See: Boundary layer.
- Blasius (See: Blasius boundary layer.)
- Falkners-Skan solution (See: Blasius boundary layer.)
- Stokes First Problem
- Stokes Second Problem
Stokes Settling Solutions
- See: Stoke's Law.
Water Wave Solutions and Models
- See: Waves.
- Airy waves
- Capillary waves
- Cnoidal waves
- Kelvin waves
- Roll waves
- Rossby waves
- Stokes wave
Ekman Spiral Solution
River Meandering Model
- G. Seminara analytic solutions ??
Landscape Evolution Equations
- Steady-state, slope vs. area solution
- Terry Smith longitudinal profile solutions
- Peckham steady-state, uniform-rainrate solutions to "ideal landform equation"
Stratigraphic Evolution Equations
- Peckham (2008) prograding solutions (obtained using Laplace transforms, including traveling-wave solutions)
Coastline Evolution Equations
- Larson, M., H. Hanson, and N. C. Kraus (1987), Analytical solutions of the one‐line model of shoreline change, Tech. Rep. CERC‐87‐15, U.S. Army Waterw. Exp. Stn., Vicksburg, Miss.
Infiltration Theory
- See: Infiltration (hydrology).
- Solutions in: Smith, R.E. (2002) Infiltration Theory for Hydrologic Applications, AGU monograph.
Wave Equation
- See: Wave equation.
- d'Alembert solution (See: d'Alembert formula.)
Heat Equation
- See: Heat equation.
- Gaussian, radially-symmetric similarity solution
Laplace Equation
- See: Laplace equation.
- Many, via separation of variables method.
Poisson Equation
- See: Poisson equation.
- Many, from Poisson representation formula
Minimal Surface Equation
- See: Minimal surface equation.
- Inclined plane solution
- Helicoid solution (Meusnier, 1776) See: Helicoid.
- Catenoid solution (Meusnier, 1776) See: Catenoid solution and Catenoid.
- Scherk's first surface solution (Scherk, 1834) See: Scherk surface.
- Scherk's second surface solution (Scherk, 1834)
- Costa surface solution (Costa, 1984) See: Costa surface.
Burgers' Equation
- See: Burgers' Equation.)
- Many, via the Cole-Hopf transformation to Heat Equation
Soliton Solutions
- See: Soliton.