NumDF

NumDF is a finite element based method for constructing the probability density of a field (e.g. temperature as a function of space) specified as function, either analytically or by direct numerical simulation. By making explicit use of the functional form of the expression or simulation field provided, NumDF is a powerful way to better exploit the information provided by a pseudo-spectral method, finite-element or high-order spectral method. Initially motivated by the need to calculate the probability density of the buoyancy field in order to estimate the available potential energy (ape) of a body of fluid (Lorenz, E.N. 1955), we envisage NumDF as a useful tool to provide an accurate an robust estimation of this quantity.

NumDF is written in python and makes extensive use of the finite element method solver Firedrake.

NumDF documentation

Contents:

• Installing NumDF
• Methodology
  • Part 1 - Constructing the CDF
  • Part 2 - Constructing the PDF
  • Part 3 - Constructing the inverse CDF
  • Part 4 - Composing density objects
• Tutorials & Examples
  • Example 1 - Analytic functions
  • Example 2 - Numerical functions
  • Example 3 - Available potential energy
  • Example 4 - Numerical convergence
• Class documentation
  • Ptp
  • Density

Links

• Code repository: https://github.com/mannixp/D.stratify-pdfe

• Documentation:

Developers

• Paul Mannix

• David Ham

• John Craske