Model Solution Library

  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.

Navier-Stokes Equation

Lamb vortex

Burgers' vortex

Rankine vortex (not a solution, though)

Taylor-Couette flow (and 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

2D Potential 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

Channel and Pipe Flow Solutions

Poisseuille Flow

Driven Cavity Solutions

Numeric solution

Analytic solution

Boundary Layer Equation

Blasius

Falkners-Skan solution

Stokes First Problem

Stokes Second Problem

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)

Landscape Evolution Equations

Steady-state, slope vs. area solution

Terry Smith longitudinal profile solutions

Peckham steady-state "ideal landform equation" solutions

Infiltration Theory

Broadsbent-Hammersley Solution

Heat Equation

Gaussian, radially-symmetric similarity solution

Burgers' Equation

many, via Cole-Hopf transformation to Heat Equation