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# Discontinuous Galerkin - Science topic

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Questions related to Discontinuous Galerkin

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.

I would like to know if the SUPG method has any advantages over the least squares finite element method?

Thank you for your reply.

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.

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++?

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?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

I cannot transform these two coupled equations to one equation (the technique we use in Timoshenko beam).

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

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.

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

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

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?

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?

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?

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!

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.

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!

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).

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?

I need a resource that clearly explains different methods such as Galerkin method and the collocation method and an accuracy comparison between them.