hi guys who can tell me the advantage of Discontinunous galerkin method, has anyone already used this method in hypersonic flow?

It was good for handling of shock because it contains the characters of FVM as well as those of FEM. It's pretty close to the FVM in some sensors.

Some nice things I can remember about DGFEM, randomly listed.

High order schemes are easy to construct in a systematic way.

Order or accuracy can be varied from element to element (p-refinement)

Easier to use for hybrid approaches like RANS-LES since model can be varied from element to element.

hp-refinement is possible leading to use of optimal grid sizes

Very small stencil, each elements has to communicate with its immediately adjacent elements only. Good for parallellization. Simple communication pattern.

Fixed stencil irrespective of order of accuracy

Finite volume comes out as a low order version of DGFEM

Complex geometry - unstructured grids can be used

Discontinuous shape functions

* Upwind fl‚ux formulae can be used

* Conservative on each element

* Shock capturing scheme

* Any type(s) of element

* Hanging nodes OK - Cartesian grids

Block-diagonal mass matrix - decoupled between elements

No mass lumping required

Simple communication pattern: Good parallelizability