∇

Properties

  • Second order
  • Transient
  • Bounded
  • When using uniform time steps the scheme equates to:
\[\ddt{\phi} = \frac{\phi - \oldold{\phi}}{2 \Delta t}\]

Usage

The scheme is specified using:

ddtSchemes
{
    default         CrankNicolson <coeff>
    ddt(phi)        CrankNicolson <coeff>;
}

The coefficient provides a blending between Euler and Crank-Nicolson schemes:

  • 0: Euler
  • 1: Crank-Nicolson
  • A value of 0.9 is a good compromise between accuracy and robustness

Further information

Source code

Reference

  • Crank and Nicolson [11]