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.

Navier-Stokes Equation

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

See: Landscape evolution model.

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.