Temporal accuracy

ganesh

Dear Friends,

I am trying to establish the order of accuracy of the time discretisation procedure for my unsteady code. I use a BDF3 scheme so my design accuracy has to be 3. The test problem is the Sod shock tube problem in 2D and care is taken that the left and right boundaries do not come into play (in terms of reflections). I am having problems getting the design accuracy even on static grids. Specifically, I have the following questions.

1. BDF3 is not self--starting and therefore I used CN (Crank--Nicholson) for the first two iterations and start off BDF3. CN is second order accurate, what effect does this have on the temporal accuracy studies ? I have already tested CN2 for second order accuracy both on static/moving grids.

2. What is the best way to start-up BDF3 ?

3. Instead of any special start--up if the initial values are themselves used until values at the time level become available, will there be a detrimental effect on time accuracy ?

It is known that a single step with a large local error could be dominant over all the other steps taken to reach upto final time in an unsteady simulation, and I would like to know the opinion of those who have had experiences with BDF for unsteady flows.

Regards and thanks in advance,

Ganesh