I work with FD implicit Crank Nicolson schema. I have problem with appearance of such oscillation, especially if I use a small element in order to get a better accuracy

Could someone tell me how to solve this oscillation.

thanks

arief

Arief :

Your question is kind of confusing because you mention using a Crank-Nicholson scheme which is a time-integration scheme, then you say you get oscillations when you use smaller mesh size. You could be experiencing several kinds of problems : maybe you are just going over the CFL characterizing the stability of your schemes, or otherwise maybe it is an aliasing problem or it could be odd-even point decoupling if you are using tensorized finite-diference schemes. You don't even mention if you are computing compressible or incompressible flow. If you want help you need to give all the necessary information regarding your code, boundary and initial conditions, etc...

There is a section of Dale A. Anderson's book dedicated to the method (7-3.3 Crank-Nicolson and Fully Implicit Method),including a warning on stability. It is in the Chapter seven on Numerical methods for Boundary Layer Type Equations. The name of the book is Computational Fluid Mechanics and Heat Transfer(Hemisphere Publishing 1984).