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)

• Shallow Water Equations

Inclined plane solution

Dam Break Characteristic Solution

Similarity solutions

• Glacier Flow

Nye (200X) radially-symmetric (Glen Law) similarity solution

• Potential Flow Solutions

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

• Channel and Pipe Solutions

Poisseuille Flow

• Taylor-Couette Flow Solution

• Driven Cavity Solution

Numeric solution

Analytic solution

• Boundary Layer Equation Solutions

Blasius

Falkners-Skan solution

Stokes First Problem

Stokes Second Problem

• Stokes Settling Solutions

• Ekman Spiral Solution

• Minimal Surface Equation Solutions

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)

• Landform Evolution Equation Solutions

Steady-state, slope vs. area solution

Terry Smith longitudinal profile solutions

Peckham steady-state "ideal landform equation" solutions

• Infiltration Theory Solutions

Broadsbent-Hammersley Solution