Model Solution Library

=   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.
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: 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
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: Inclined plane solution
: Dam Break Characteristic Solution
: Similarity solutions
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: Halfar (1983) radially-symmetric (Glen Law) similarity solution
: Bueler et al. (****) similarity solution
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* See: 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
: Darcy flow solutions
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: 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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: Poisseuille Flow (See: Poiseuille flow.)
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: Lid-driven or buoyancy-driven, etc. ?
: Numeric solution
: Analytic solution
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* See: Boundary layer.
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: Blasius (See: Blasius boundary layer.)
: Falkners-Skan solution (See: Blasius boundary layer.)
: Stokes First Problem
: Stokes Second Problem
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* See: Stoke's Law.
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* See: Waves.
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: Airy waves
: Capillary waves
: Cnoidal waves
: Kelvin waves
: Roll waves
: Rossby waves
: Stokes wave
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: G. Seminara analytic solutions ??
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* See: 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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: Peckham (2008) prograding solutions (obtained using Laplace transforms, including traveling-wave solutions)
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: 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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* See: Infiltration (hydrology).
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: Solutions in: Smith, R.E. (2002) Infiltration Theory for Hydrologic Applications, AGU monograph.
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* See: Wave equation.
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: d'Alembert solution (See: d'Alembert formula.)
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* See: Heat equation.
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: Gaussian, radially-symmetric similarity solution
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* See: Laplace equation.
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: Many, via separation of variables method.
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* See: Poisson equation.
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: Many, from Poisson representation formula
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* See: Minimal surface equation.
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: 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.
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* See: Burgers' Equation.)
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: Many, via the Cole-Hopf transformation to Heat Equation
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* See: Soliton.
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