Crank-Nicolson time scheme

Table of Contents

• Properties
• Usage
• Further information

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

• Foam::fv::CrankNicolsonDdtScheme

Reference

• Crank and Nicolson [11]

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