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Courant–Friedrichs–Lewy condition

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(The one-dimensional case)
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<table width="70%"><tr><td>
<table width="70%"><tr><td>
C=c\frac{\Delta t}{\Delta x} \leq 1
C=c\frac{\Delta t}{\Delta x} \leq C_{max}
</td><td width="5%">(2)</td></tr></table>
</td><td width="5%">(2)</td></tr></table>

Revision as of 11:54, 26 August 2012


It is an important stability criterion for hyperbolic equations.

The one-dimensional case

For one-dimensional case, the CFL has the following form:

C=c\frac{\Delta t}{\Delta x} \leq C_{max}

where C is called the Courant number

where the dimensionless number is called the Courant number,

  • u is the velocity (whose dimension is Length/Time)
  • \Delta t is the time step (whose dimension is Time)
  • \Delta x is the length interval (whose dimension is Length).

The value of C_{max} changes with the method used to solve the discretised equation. If an explicit (time-marching) solver is used then typically C_{max} = 1. Implicit (matrix) solvers are usually less sensitive to numerical instability and so larger values of C_{max} may be tolerated.

Courant, R., K. O. Fredrichs, and H. Lewy (1928), "Uber die Differenzengleichungen der Mathematischen Physik", Math. Ann, vol.100, p.32, 1928.

Anderson, Lohn David (1995), "Computational fluid dynamics: the basics with applications", McGraw-Hill, Inc.

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