A second order Space discretization reduces the damping and give a high amplitude and high frequency solution.

What should I expect from Second order time discretization such as crank nicolson method over the first order discretization solution

Thanks aditya

You should expect an improvement in your solution, unless you are solving a steady problem in which case I'm not sure if there is a big improvement

Dear Aditya,

Second order temporal discretisation does not offer much for steady state problems, because you are driving your temporal terms to zero. However, for time -dependent flows where your require time accurate computations, the temoral order of accuracy becomes equally important as the spatial order of accuracy. The easy way to view the advantage is to have an analogy with the higher order spatial discretisation procedure. Second order time discretisation procedure do to the temporal scale what second order spatial discretisation procedures do to the spatial scale. The choice of the temporal scheme also depends on its stability. Thus, for a typical unsteady problem involving pitching airfoils or moving shocks, second order temporal discretisation such as the Crank Nicholson or the Three point Backward difference is employed. If you want to visually get an idea of how time accurate computations are important, you can see for yourself that in case of a pitching airfoil, a first order time accurate scheme would not predict the hysterisis loop correctly, while a second order accurate scheme does, and for aeroelastic problems where flutter predictions are of concern, first order temporal accuracy would result in erroneous predictions.

Hope this helps

Regards,

Ganesh

If you want to visually get an idea of how time accurate computations are important, you can see for yourself that in case of a pitching airfoil, a first order time accurate scheme would not predict the hysterisis loop correctly, while a second order accurate scheme does, and for aeroelastic problems where flutter predictions are of concern, first order temporal accuracy would result in erroneous predictions

Not strictly true. Provided the time step is small enough the first order scheme will be just as good but more expensive (provided the solution is time step converged). But generally speaking, for a given time step (rather than a time-step converged solution) we would expect better accuracy.