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.

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 (Goertler and Tollmien are special cases.)

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

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 moving-boundary solutions (via Legendre transform)

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) 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

Many, via Cole-Hopf transformation to Heat Equation