What is courant number ?.what is the significance of courant number?Is it related to time step?

Courant number C = dt/(dx/U)

ie the ratio of time step to cell residence time. dt = time step, dx = grid cell size, and U = fluid velocity.

It is common to make the time step dt proportional to the Courant number C via the foregoing expression. Explicit solution methods are numerically stable only when C <=1. Implicit solution methods allow much larger Courant numbers than explicit methods, but they are not unconditionally stable and using too large a C value can lead to loss of numerical accuracy.

Thank u mike.

What is Courant number?. How/Where is it applied?

Courant number is a parameter used in the stability analysis of finite difference equations (algebraic eqns used to approximate the partial differential eqns that model the flow).

It is the ratio of the time step / spatial resolution the whole multiplied by a constant (Eg: the velocity of sound,C, in case of wave eqn).

Courant no = -C (dt / dx)

For certain explicit approximations, Couran no tells us is the finite difference approximation is stable or not.

The courant no needs to be less than or equal to 1.0 for a stable approximation.

Try looking at the explanation given in CFD by John D Anderson.

Bye! Aneet

sir,

I just want to know about courant no in use of unsteady advection problem.