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Discontinuous Galerkin - Science topic

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I would like to know is there any solver for Discontinuous Galerkin method in 3D in OpenFoam of Foam Extend except HopeFoam?
Thanks a lot.
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Thank you very much for this information. Can you kindly give some idea when we expect its release?
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I would like to know if the SUPG method has any advantages over the least squares finite element method?
Thank you for your reply.
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Dear Zmour,
It can be better in term of diffusion convection reaction. My opinion is little different, the least-squares method has better control of the streamline derivative than the SUPG.
Ashish
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Hi!
I am introducing myself very new to Nektar++ (https://www.nektar.info/) opensource code. I installed the code according to the user guide manual. The installing process shows success.
-- Install configuration: "Release" -- Up-to-date: /home/bidesh/nektar++/build/dist/lib64/nektar++/cmake/Nektar++Libraries.cmake -- Up-to-date: /home/bidesh/nektar++/build/dist/lib64/nektar++/cmake/Nektar++Libraries-release.cmake -- Up-to-date: /home/bidesh/nektar++/build/dist/lib64/nektar++/cmake/Nektar++Config.cmake -- Up-to-date: /home/bidesh/nektar++/build/dist/lib64/nektar++/thirdparty/libblas.so -- Up-to-date: /home/bidesh/nektar++/build/dist/lib64/nektar++/thirdparty/libblas.so.3 ................................
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.............................. -- Up-to-date: /home/bidesh/nektar++/build/dist/include/nektar++/FieldUtils/ProcessModules/ProcessScaleInFld.h -- Up-to-date: /home/bidesh/nektar++/build/dist/include/nektar++/FieldUtils/ProcessModules/ProcessDOF.h -- Up-to-date: /home/bidesh/nektar++/build/dist/include/nektar++/FieldUtils/ProcessModules/ProcessInnerProduct.h -- Up-to-date: /home/bidesh/nektar++/build/dist/include/nektar++/FieldUtils/ProcessModules/ProcessGrad.h -- Up-to-date: /home/bidesh/nektar++/build/dist/include/nektar++/FieldUtils/ProcessModules/ProcessPrintFldNorms.h -- Up-to-date: /home/bidesh/nektar++/build/dist/include/nektar++/FieldUtils/ProcessModules/ProcessAddFld.h -- Up-to-date: /home/bidesh/nektar++/build/dist/include/nektar++/FieldUtils/ProcessModules/ProcessQCriterion.h -- Up-to-date: /home/bidesh/nektar++/build/dist/include/nektar++/FieldUtils/ProcessModules/ProcessAddCompositeID.h -- Up-to-date: /home/bidesh/nektar++/build/dist/include/nektar++/FieldUtils/ProcessModules/ProcessInterpPtsToPts.h -- Up-to-date: /home/bidesh/nektar++/build/dist/include/nektar++/FieldUtils/ProcessModules/ProcessInterpPoints.h -- Up-to-date: /home/bidesh/nektar++/build/dist/include/nektar++/FieldUtils/ProcessModules/ProcessC0Projection.h -- Up-to-date: /home/bidesh/nektar++/build/dist/include/nektar++/FieldUtils/ProcessModules/ProcessNumModes.h -- Up-to-date: /home/bidesh/nektar++/build/dist/include/nektar++/FieldUtils/Module.h -- Up-to-date: /home/bidesh/nektar++/build/dist/include/nektar++/FieldUtils/Field.hpp -- Up-to-date: /home/bidesh/nektar++/build/dist/include/nektar++/FieldUtils/FieldUtilsDeclspec.h -- Up-to-date: /home/bidesh/nektar++/build/dist/bin/Tester
ctest was successful too.
But when I am trying to run a tutorial such as : ADRSolver, "ADRSolver: command not found" is appearing.
I am not a pro either in C++ or linux, I am trying hard to understand those aswell.
If any member in this group is using nektar and willing to help me a bit, I shall be really helped.
Thank you, Bidesh.
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As Thomas Frank said, you should call the solver with its path name.
For example, for running IncNavierStokesSolver:
Nektar++-4.4.1/build/solvers/IncNavierStokesSolver conditions.xml
Here conditions.xml is your case file containing mesh and solver information.
If you have separate mesh file, then use:
Nektar++-4.4.1/build/solvers/IncNavierStokesSolver mesh.xml conditions.xml
Regards,
Sartaj Tanweer
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I need to simulate a 2-D problem with DGFEM. I have been advised to use C/C++ for a code that delivers quick and efficient results, however, I am not very comfortable with them, and my base code happens to be in MATLAB. Would Julia be a better choice than MATLAB, comparable to the performance of C/C++?
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Julia is faster than Matlab, but I think the speedness of solution is not the problem, the most important issue is to write a correct code especially for complicated models, so I do not recommend using C language if you are a beginner in it.
Julia/Python/Matlab/R language are similar in simplicity. Julia is the faster.
You can see the difference in this sheet
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We know that , In applied mathematics, discontinuous Galerkin methods (DG methods) form a class of numerical methods for solving differential equations. They combine features of the finite element and the finite volume framework and have been successfully applied to hyperbolic, elliptic, parabolic and mixed form problems arising from a wide range of applications . so i want to know ,What is the difference between the discontinuous Galerkin method(DGM) and discontinuous Galerkin finite elelment(DGFEMs) method?
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Give examples.
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Dear colleagues,
Using very short explanation, how to came up with the difference between Discontinuous Galerkin approach in FEM and Mixed FEM ?
regards and thanks, Egor
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Quickly, the
Mixed Finite Element method , a great reference is of course Brezzi and Fortin.
deals with elliptic problems where the unknowns belong to different functional spaces. As an example, take the incompressible Stokes problem where the unknowns are the velocity and the pressure. For a Dirichlet boudary condition problem it is known that u belongs to H^1_0 and the pressure p is in L^2_0. Two different spaces.
For the Mixed FEM the choice of elements, one for u and another for p, is of paramount importance. The choice must satisfy a compatibility condition which known as the discret inf-sup condition.
The Discontinuous Galerkin FEM proceeds as the regular Galerkin FEM , meaning project the continuous problem into a finite dimensional space of dimension n and seek the numerical solution to your problem as a linear combination. In regular FEM we impose continuity between the Finite elements, thsi condition is relaxed when we deal with the DGFEM.
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I cannot transform these two coupled equations to one equation (the technique we use in Timoshenko beam). 
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Yeah, actually it is pretty simple :). the point is that you should solve the weak form of the equation (the equation which includes integral). So, do not go for the differential form.
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I am trying to modify a CFD model applying the DG method, it's too difficult and I hope there are some programs that I can refer to
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I agree with all these proposed software. Besides you may also try the FEniCS software project , see
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There has been considerable interest in the past few years in DG methods - and rightfully so, owing to its success. The strongest claim for DG methods' superiority seems to be its ability to be parallelized on GPU architecture, due to the locality of the elements in the discretization. Although I see its value, I am curious what the possible pitfalls/limitations/issues exist in DG methods for CFD - say, in comparison to established techniques like FDM and FVM. FVM has strong support in the commercial space for complex geometries, yet higher order (HO) schemes seem to be challenging and/or expensive. FDM seems to suitable for HO and often used in academic research codes, but suffers in unstructured meshes and complex geometries. I am not too familiar with DG, unlike FVM/FDM, and most of the literature highlights the strengths of DG methods - Is there any reason today to prefer FVM or FDM over DG? I'm looking for discussions on cases where DG fails or performs poorly, the fundamental limitations behind it, and your future outlook for the scheme.
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The interest in DG methods for LES has experienced a dramatic growth over the last 5-10 years. I would argue this was originally due to the fact that the numerical results were surprisingly accurate, but now there is a much better understanding of why this is the case. Roughly speaking, the numerical dissipation properties in wavenumber space of DG methods are very well-suited for transition prediction and for LES of moderately-high-Reynolds number turbulence [1] (*). Not surprisingly, it has been acknowledged that the Riemann solver in DG methods (which is responsible for the numerical dissipation) plays the role of an implicit subgrid-scale model (see e.g. [2,3,4]) and this implicit model somehow behaves like a dynamic model (it vanishes for laminar flows, etc.)
Regarding implementation, theoretically, the potential of DG methods for the incoming computing architectures such as GPUs is huge (**), but one needs to be clever and think out of the box. For example, state-of-the-art algorithms that are great for CPUs (pseudo-time marching, Jacobi-Newton-GMRES, etc.) can be extremely inefficient for GPUs. With the right choice of algorithms (some of them perhaps need to be new), and for some applications, however, the speedup in terms of "accuracy vs. time-to-solution" and "accuracy vs. energy consumption" with DG methods could be massive (as massive as the uncertainty on whether this potential will ever be realized in practice).
(*) The numerical dissipation properties of DG methods are arguably beneficial for LES but not for RANS-type simulations. Since DG methods are more expensive than 2nd-order FV, and there is little or no benefit in the RANS setting, that's probably why the use of DG methods in CFD was so marginal in the past.
(**) This is true not only for DG but also for the majority of high-order methods.
[1] P. Fernandez, R. Moura, G. Mengaldo, J. Peraire, Non-modal analysis of spectral element methods: Towards accurate and robust large-eddy simulations, arXiv preprint arXiv:1804.09712
[2] A.D. Beck, D. Flad, C. Tonhäuser, G. Gassner, C.-D. Munz, On the Influence of Polynomial De-aliasing on Subgrid Scale Models, Flow Turbul. Combust. 97 (2) (2016) 475–511.
[3] P. Fernandez, N.C. Nguyen, J. Peraire, On the ability of discontinuous Galerkin methods to simulate under-resolved turbulent flows, arXiv preprint arXiv:1810.09435
[4] J. Manzanero, E. Ferrer, G. Rubio, E. Valero, On the role of numerical dissipation in stabilising under-resolved turbulent simulations using discontinuous Galerkin methods, arXiv preprint arXiv:1805.10519
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Hi
There is many types of high order methods such as DG, Nodal DG, Spectral element, Spectral difference, Huynh Flux Reconstruction and so on.
Which method do you prefer and why?
Each of them have advantages and disadvantages but which of them do you think is most suitable for industrial applications in future?
Best Regards
Alireza
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Tapan K. Sengupta
you are right! However, the community is incredible interested on that issue even more than the true physics. That has lead a sour taste after attending recent conferences. I have seen a bunch of non-sense results but with very high order and beautiful colors. The sad true is that funding agencies are pumping a bunch of money on those projects. Particularly, I prefer using a low order numerical scheme since I am working with compressible flows, thus with discontinuities. Working with ENO is really like a lottery. You end up adding so many uncertainties with the different method for reconstructing the fluxes that I have no idea if the real physics is captured. Of course, people leading the field do not want to discuss much about that.
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Hello everyone,
In my DG-FEM model for solving a set of elliptic equations I use a collocation manner to evaluate the nonlinear product terms, which is known to cause aliasing errors. I know some de-aliasing methods like the mild nodal filter used by Fischer and Mullen (2001) which are best suited for nodal DG methods (e.g. working on LGL nodes), but I was wondering if anyone knows a de-aliasing method specially developed for modal DG formulation?
Regards,
Mohammad
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Dear Mounir,
Thanks for the answer. I've read it indeed and it's a good paper, no clues on modal representation though.
Cheers
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some mesh generator software called as finite element mesh generator. is there any difference between finite element and finite volume mesh generators? if so can we use them interchangeably? and what effect has this choice?
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thanks for answering.
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It seems that 'P3dc' element in FreeFem++ does not support third order derivatives in the code. The third order derivative is very necessary for the weak formulation.
Can someone please help me how to overcome these shortcomings?
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Ok, I understand.
I see two ways of bypassing this problem:
_you can create interpolation matrices and variational matrices as mentioned, but using these matrices are a bit technical to handle.
_introduce an auxiliary variable U in P1dc and its dual V and modify your weak formulation in a way such that Laplacian(U)=u and Laplacian(V)=v and use U,V when you need a third-order derivative. Not sure that it works but worth trying.
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Following the article "On positivity-preserving high order discontinuous Galerkin schemes for compressible Euler equations on rectangular meshes" of Zhang and Shu, JCP 2010.
They claim that: 
"It can be easily verified that p is a concave function of w=(rho,rho u,rho E) if rho ≥ 0."
This is true according to Jensen's inequality, where W is the conservative variables vector and rho is the density.
"Define the set of admissible states by G = {w|rho>0 and
p =(gamma − 1)(E − (1/2)(m2/r))>0},
then G is a convex set."
How is it possible to conclude that G is a convex set based on the first sentence?
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Hi, If you use the finite volume methods, it is enough to use some simple controls on fluxes for positivity preserving.
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I am doing DG calculation with deal.II for Pn equations in neutral particle transport, which is essentially a hyperbolic system. I am wondering if anyone knows a way of doing slope limiting and reconstruction for Q1 element (1, x, y, xy) with preserving the diffusion limit (or asymptotic preserving (AP) in CFD community). There are several AP schemes I know for limiting (e.g. the double minmod limiter). The difficulty is to be AP for the reconstruction. I just don't a decent scheme to be AP with the existence of xy component the Q1 element.
Someone suggests I do the limiting with AP scheme and when reconstructing, use P1 element (1, x, y), which is easy to implement. Yet it is not proved to be AP and therefore not desired.
I asked here just because the most papers on reconstruction in applied math and CFD communities are about P1 element. I just cannot find a thorough description on the algorithms.
Thanks in advance!
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I do not know exactly what you mean by AP reconstruction, but some years ago in the paper
we proposed a FCT based limiting technique for DG methods that worked well for scalar transport. Maybe this could help, although I am not sure it complies with the asymptotic preserving requirements you need.
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Several projects I have are about developing least square finite element (LSFEM) discretization to neutron transport equation. One of the days, my adviser asked me about the benefits of developing the methods over using discontinuous Galerkin (DG). I got stuck. My only answer at that time was less dof counts since continuous basis function can be used. But the fact I have now is when faced with material discontinuity and induced solution discontinuity, DG is much more efficient to gain a decent solution to such a hyperbolic system without involving much more dofs than LSFEM, actually. So I got confused. What is the intention that people use LSFEM for hyperbolic problems? Thanks in advance.
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Standard Galerkin approaches are in fact unstable for convection dominated problems. Therefore, a stabilisation needs to be introduced. Using LSqFEM provides you with a positive definite symmetric (or coercive) discrete problem to be solved, and is therefore a stable approach. In fact, you can use LSqFEM to provide a stable formulation for most difficult problems, but at the cost of a much increased condition number which makes the resulting equations more difficult to solve.
Streamline Upwind Petrov-Galerkin or other stabilised methods introduce additional upwind dissipation and are therefore loose accuracy. They may be seen - in case of a purely convective problem - as a linear combination of CG and LSqFEM. DGM on the other hand retains full precision and is stable for pure convection problems.
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Hi fellows,
I'm preparing numerical model with large deformation and I believe that EFG (meshless method) will suit my needs. However, I found no practical/useful information on how model this using LS-Dyna.
Does anyone have an example or simple tutorial on this matter?
Thank you very much!
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Dear Ji and Riccardo, thank you for you answer! (It took me months to realize that it was answered due to my midterm report... =/ ).
I'll try to use it as Riccardo suggested and will inform the results.
Thank you again!
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The locally conservative method with time step or with out for heat and fluid flow in one dimension (for example water is passing through a circular pipe).
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Hi Hayder, you can looking for related work in the followin source code, don't miss the FEM code avaliable in the mentioned sourse code as I know you are interesting with FEM 
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I am solving acoustic wave equation in frequency domain by Galerkin's weighted residual method. How can I implement absorbing boundary conditions/PML in the formulation?
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Sorry, I overlooked that. I thought you are working on the explicit form. I am not very sure how to formulate pml in week form. Maybe the attached doc can help a little bit.
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I need a resource that clearly explains different methods such as Galerkin method and the collocation method and an accuracy comparison between them.
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You may also follow the first chapter of Boundary elements—an introductory course, by CA Brebbia and J Dominguez.