Sir,

what is the physical significance of CFL criteria?

Does the CFL criterian takes care of the number of grid points on which the solution at a single grid point depends at a particular "time-level". IF yes then HOW?

Does the CFL criterian means that "as you proceed in time-domain .. . the number of grid points on which a solution at a particular grid-point depends, increases"

Thanks in advance

YOGESH

the CFL number is defined as v*deltat/deltax where v is the speed of a disturbance or some characteristic speed in the flow, deltat is the time step and deltax is the grid size. the CFL number is the ratio of the distance travelled by the disturbance moving at speed v in time deltat to the grid spacing. for a given analysis the CFL number controls the size of your timestep relative to your grid size. your timestep should be small enough to allow a disturbance moving at speed v to be captured in your spatial stencil. your understanding of the concept is adequate but it'd be better to read up on the CFL number in a CFD text like John Anderson's Intro to CFD or Tannehill,Anderson and Pletcher's CFD book

In simple physical terms, the CFL (Courant Friedrich Levi) conditions makes sure that the speed of the numerical integration is larger than any speed in the flow. So that as information propagates in the flow, the integration can follow it (otherwise the info goes faster than the integration and it is lost). The info for example might be just the sound waves over a flow moving with a velocity v. So if v is the velocity of the flow and c is the sound velocity, usually one wants

the time step dt to be smaller than dx/(c+v),

where dx is the grid spacing and v denotes the absolute value of the velocity of the flow. This is then equivalent to saying that

the velocity in the flow (c+v) is smaller than the integration speed dx/dt;

or dx/dt larger than c+v.

I hope this physical interpretation from a Physicist helps.

Patrick