I am running PyFR with very high order p = 6 or even higher with ILES method. But simulation blowed up but it is ok for lower polynomial order like 2 or 3. So I am thinking if it is the problem with quadrature rule and quadrature degree I chose for Pyramids elements. If I am right, I used gauss-legendre for solution points and witherden-vincent for quadrature points (I guess witherden-vincent is the only option for quadrature points right?). But could you tell me the formula to calculate the number of points that witherden-vincent need based on polynomial order? It seems it is not the same as what one can find from shape.py.
The witherden-vincent quadrature points are calculated based on this paper: https://doi.org/10.1016/j.camwa.2015.03.017
And the exact implementation of the search can be found in the polyquad repo under the PyFR organisation on githiub.
I wouldn’t have thought that the points would be the cause of this error. Are you decreasing the time step size as you increases the polynomial order?
@WillT’s suggestion about making sure you reduce dt as you increase p (on a fixed mesh) is important. RE: the quadrature rules, an important point is to ensure that you have more quadrature points than solution points. What quad-deg are you using for the witherden-vincent points on pyramids? How many quadrature points does this give you? And how does this compare to the number of solution points you have at your given p?
Thanks for rapid replies. I did reduced time step and run it with adaptive time integration method. Maybe I will try even smaller time step later. But I am thinking, as @p.vincent said, one has to use more quadrature points than solution points. I am running p=5, which gives 91 gauss-lagendre solution points. But the maximum quadrature degree in the quadrature file is d10 with 83 points. So I am thinking if this is the problem.
I think that is likely the problem (or at least part of the problem). Could you try generating some higher strength rules with more points using Polyquad, and then use them?
Ok, I will try and report back. Thanks again!
This is likely the issue. Please e-mail me and I will send you a set of rules up to degree 20 for the pyramid.
Sorry for the late response. After increasing quadrature degree from files that Freddie sent to me, our simulation can run pretty well. Thanks again for helping.
I will work on getting these rules (along with some of their counterparts for other element types) mainlined.