Model Solution Library
From CSDMS
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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. 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 where the solutions are given and described.
- Batchelor vortex
- Burgers vortex
- Hill spherical vortex
- Lamb vortex
- Lamb-Chaplygin Dipole vortex
- Lamb-Oseen vortex
- Rankine vortex (not a solution, though)
- Taylor-Couette flow (and Taylor-Dean flow ??)
- Vortex ring solution (???)
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
- 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 solution
- Goertler 2D turbulent jet solution
- Peckham 2D turbulent jet solution
- Tollmien 2D turbulent jet solution
Channel and Pipe Flow Solutions
- Poisseuille Flow
Driven Cavity Solutions
- Lid-driven or buoyancy-driven, etc. ?
- Numeric solution
- Analytic solution
Boundary Layer Equation
- Blasius
- Falkners-Skan solution
- Stokes First Problem
- Stokes Second Problem
Stokes Settling Solutions
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"
Infiltration Theory
- Broadsbent-Hammersley Solution
Wave Equation
- d'Alembert solution
Heat Equation
- Gaussian, radially-symmetric similarity solution
Laplace Equation
- Many, via separation of variables method.
Poisson Equation
- Many, from Poisson representation formula
Minimal Surface Equation
- Inclined plane solution
- Helicoid solution (Meusnier, 1776)
- Catenoid solution (Meusnier, 1776)
- Scherk's first surface solution (Scherk, 1834)
- Scherk's second surface solution (Scherk, 1834)
- Costa surface solution (Costa, 1984)
Burgers' Equation
- many, via Cole-Hopf transformation to Heat Equation