Model Solution Library
From CSDMS
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.