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Shyam February 1, 2009 22:01

convergence of DG for Euler equations

I am developing a CFD code for unstructured grids based on spectral and DG methods. I used linear advection and Burger's eqn to get the order of convergence of the code. The scheme performed pretty good. But, when I use the same for Euler code, I am not able to get the designed order of error convergence. I used the advection of isentropic vortex for testing the Euler code. For the flux, I used HLL fluxes. Can anyone let me know what fluxes are recommended for the DG schemes of order > 3?

Also, in the HLL flux, the normal flux is something like

F_HLL = (SR*FL - SL*FR + SL*SR*(qR-qL))/(SR-SL)

I have used the fluxes FL and FR as the normal fluxes and qL and qR to be the original state variables (not transformed to normal coordinates). If I am wrong in this, please correct me.

Thanks, Shyam

Shyam February 2, 2009 04:19

Re: convergence of DG for Euler equations
Hi All,

I figured out that the code produces the desired order of accuracy if a more benign problem is chosen. When I chose the initial condition to be rho = 1 + 0.2 * sin(PI*(x+y)), u=0.7, v=0.2, p=1

the code produced the expected results. Still wondering why it struggles for advection of isentropic vortex.


jack February 7, 2009 01:48

Re: convergence of DG for Euler equations
i am a DG worker too MSN:

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