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From: Manav Bhatia <bhatiamanav@gm...>  20130514 18:37:59

> > > > > This is the Gaussian bump problem from the higherorder CFD workshop > > (http://dept.ku.edu/~cfdku/hiocfd/case_c1.1.html). You are correct that > away > > from the bump the boundary is straight, so linear elements should be > fine. I > > am looking at the entropy error, since the entropy is supposed to stay > > constant. The bumpboundary, infact, is adding to the entropyerror. I am > > able to drop down to 10^7 in the error L2 norm, and then it stagnates. > And > > I have a feeling that this is due to the loworder geometry. > > Oh yeah, I have heard of this spurious entropy production problem on > curved geometries. > > Are you really using Quad8's? Can you use Quad9's with the hierarchics? > > Can you modify the test problem slightly so the bump is a quadratic > function and verify convergence with higher p's? > > This is a great suggestion, John. I will try converting the geometry to second order. I have not tried Quad9, but what would that be any better than Quad8? > > Yes, I was considering this, and also the 25noded quad. However, I am > still > > considering if the effort might be worth it: Meaning that I may be able > to > > get theoretical order of convergence for this simpler benchmark problem, > but > > I don't know if any practical problem will benefit from a 16 or 25 noded > > quad. I am not sure if any mesh generator would give me elements with > these > > many nodes. > > You will probably have trouble viewing the solutions in Paraview too... > As it is, I am having trouble viewing results from higherorder elements in Paraview. I can output only the nodal data for viewing in Paraview, and so the higherorder information of the element solution gets lost. I haven't yet had the chance to look into improving this behavior. Roy: Just to clarify, I do get a reduction in error for higher order elemets after 10^7, but the rate of convergence is considerably lower than the p+1/2 theoretical order. I will try compiling with quad precision to see if that does something. I have played around with the solver parameters, and have also used direct solvers to flush out any potential problems form linear solvers. 
From: John Peterson <jwpeterson@gm...>  20130514 18:12:30

On Tue, May 14, 2013 at 11:54 AM, Manav Bhatia <bhatiamanav@...> wrote: > > > On Tue, May 14, 2013 at 12:59 PM, John Peterson <jwpeterson@...> > wrote: >> >> On Tue, May 14, 2013 at 9:25 AM, Manav Bhatia <bhatiamanav@...> >> wrote: >> > Hi, >> > >> > I am working on higherorder simulation using the hierarchich >> > function >> > on quad8s. >> > >> > My errorconvergence plots give me theoretical convergence for first >> > and second order p, but the error stagnates for p > 2. I am speculating >> > that this might be due to the lowerorder geometry, assuming that the x >> > and ycoordinates are interpolated using Lagrange functions associated >> > with >> > nodes of quad8. >> >> What does your domain look like? Unit square? If so I don't think >> there can be errors due to using even bilinear element maps, the >> Jacobians are linear in this case. >> > > This is the Gaussian bump problem from the higherorder CFD workshop > (http://dept.ku.edu/~cfdku/hiocfd/case_c1.1.html). You are correct that away > from the bump the boundary is straight, so linear elements should be fine. I > am looking at the entropy error, since the entropy is supposed to stay > constant. The bumpboundary, infact, is adding to the entropyerror. I am > able to drop down to 10^7 in the error L2 norm, and then it stagnates. And > I have a feeling that this is due to the loworder geometry. Oh yeah, I have heard of this spurious entropy production problem on curved geometries. Are you really using Quad8's? Can you use Quad9's with the hierarchics? Can you modify the test problem slightly so the bump is a quadratic function and verify convergence with higher p's? > Yes, I was considering this, and also the 25noded quad. However, I am still > considering if the effort might be worth it: Meaning that I may be able to > get theoretical order of convergence for this simpler benchmark problem, but > I don't know if any practical problem will benefit from a 16 or 25 noded > quad. I am not sure if any mesh generator would give me elements with these > many nodes. You will probably have trouble viewing the solutions in Paraview too...  John 
From: Roy Stogner <roystgnr@ic...>  20130514 18:11:45

On Tue, 14 May 2013, Manav Bhatia wrote: > This is the Gaussian bump problem from the higherorder CFD workshop ( > http://dept.ku.edu/~cfdku/hiocfd/case_c1.1.html). You are correct that away > from the bump the boundary is straight, so linear elements should be fine. > I am looking at the entropy error, since the entropy is supposed to stay > constant. The bumpboundary, infact, is adding to the entropyerror. I am > able to drop down to 10^7 in the error L2 norm, and then it stagnates. And > I have a feeling that this is due to the loworder geometry. Hmm... the loworder geometry should definitely be hurting your convergence rate here, but it shouldn't be giving you a rate of *zero*. Usually when you start to converge but then stagnate it means you're hitting some previouslynegligible epsilon. I've never seen anything but a penalty BC parameter cause stagnation at a *relative* error as high as 1e7 though. Usually the second limitation I run into is insufficiently tight solver tolerances, and the third is FP roundoff error. From our point of view I don't want to discourage you from the QUAD16 idea, but I don't think it's likely to be the cause of your problem, and it would probably be easy for you to check your solver parameters or to recompile with quad precision before going to the effort of adding a new geometric element to libMesh.  Roy 
From: Manav Bhatia <bhatiamanav@gm...>  20130514 17:54:36

On Tue, May 14, 2013 at 12:59 PM, John Peterson <jwpeterson@...>wrote: > On Tue, May 14, 2013 at 9:25 AM, Manav Bhatia <bhatiamanav@...> > wrote: > > Hi, > > > > I am working on higherorder simulation using the hierarchich > function > > on quad8s. > > > > My errorconvergence plots give me theoretical convergence for first > > and second order p, but the error stagnates for p > 2. I am speculating > > that this might be due to the lowerorder geometry, assuming that the x > > and ycoordinates are interpolated using Lagrange functions associated > with > > nodes of quad8. > > What does your domain look like? Unit square? If so I don't think > there can be errors due to using even bilinear element maps, the > Jacobians are linear in this case. > > This is the Gaussian bump problem from the higherorder CFD workshop ( http://dept.ku.edu/~cfdku/hiocfd/case_c1.1.html). You are correct that away from the bump the boundary is straight, so linear elements should be fine. I am looking at the entropy error, since the entropy is supposed to stay constant. The bumpboundary, infact, is adding to the entropyerror. I am able to drop down to 10^7 in the error L2 norm, and then it stagnates. And I have a feeling that this is due to the loworder geometry. > What exact solution are you using for testing the convergence? > > > I am considering adding higher order quads to get x and > > y interpolation using higherorder Lagrange functions. Any thoughts on > how > > easy/difficult this might be? > > You are talking about QUAD16? It shouldn't be too hard but we would > need to come to a consesus on node numbering for this element. > > Yes, I was considering this, and also the 25noded quad. However, I am still considering if the effort might be worth it: Meaning that I may be able to get theoretical order of convergence for this simpler benchmark problem, but I don't know if any practical problem will benefit from a 16 or 25 noded quad. I am not sure if any mesh generator would give me elements with these many nodes. Manav 
From: John Peterson <jwpeterson@gm...>  20130514 17:00:02

On Tue, May 14, 2013 at 9:25 AM, Manav Bhatia <bhatiamanav@...> wrote: > Hi, > > I am working on higherorder simulation using the hierarchich function > on quad8s. > > My errorconvergence plots give me theoretical convergence for first > and second order p, but the error stagnates for p > 2. I am speculating > that this might be due to the lowerorder geometry, assuming that the x > and ycoordinates are interpolated using Lagrange functions associated with > nodes of quad8. What does your domain look like? Unit square? If so I don't think there can be errors due to using even bilinear element maps, the Jacobians are linear in this case. What exact solution are you using for testing the convergence? > I am considering adding higher order quads to get x and > y interpolation using higherorder Lagrange functions. Any thoughts on how > easy/difficult this might be? You are talking about QUAD16? It shouldn't be too hard but we would need to come to a consesus on node numbering for this element.  John 
From: Manav Bhatia <bhatiamanav@gm...>  20130514 15:25:26

Hi, I am working on higherorder simulation using the hierarchich function on quad8s. My errorconvergence plots give me theoretical convergence for first and second order p, but the error stagnates for p > 2. I am speculating that this might be due to the lowerorder geometry, assuming that the x and ycoordinates are interpolated using Lagrange functions associated with nodes of quad8. I am considering adding higher order quads to get x and y interpolation using higherorder Lagrange functions. Any thoughts on how easy/difficult this might be? Thanks, Manav 