Question about Discontinous Galerkin Method

phy4me · January 25, 2014, 11:27

Hi,

I use the DG to solve the 1d shallow water.
I want to know how calculate the state value in the Riemann solver ( Roe for example ). If I use the formula in attachments i have minor oscillation but if i use Uh=U0 the result is good.

What is the right ?

Thanks in advance

cfdnewbie · January 25, 2014, 12:23

What is written there in the equation is just the solution representation, i.e. the basis functions times your DOF. For the input into the flux functions, you should evaluate U on the boundaries, then calculate the fluxes from that.
Are you using a modal or a nodal basis? If you are using a modal basis, u0 would be (I'm guessing here) the value of your first Legendre polynomial, i.e. the mean value. That will give you a first order approximation of your fluxes, and thus result in a globally first order method. The correct way to do is indeed to evaluate the basis fully at the location it is needed.

I recommend you do a convergence study for a simple model problem (Burgers, linear advection etc) first to make sure you got everything right.

phy4me · January 25, 2014, 13:19

Thanks for your response,

I use here a legendre polynomial basis, I think that are modal approach ( if it lagrange basis here is nodal ... right ? ). In the case when I use the fully basis, osciallations are generated in the solution in same problems ( Haudraulic jump for example ).

Here, what I want know is how evaluate the physical state to calculate the flux at each edge.

Thanks,

cfdnewbie · January 25, 2014, 13:21

You do that evaluation the full basis / full expansion at the location where you need it. If you are getting oscillations (for a smooth problem), then you will need to check your code. If you are talking about non-smooth problems, then oscillations are to be expected if you don't use any form of limiting.

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January 25, 2014, 12:23		#2
cfdnewbie Senior Member cfdnewbie Join Date: Mar 2010 Posts: 557 Rep Power: 20	What is written there in the equation is just the solution representation, i.e. the basis functions times your DOF. For the input into the flux functions, you should evaluate U on the boundaries, then calculate the fluxes from that. Are you using a modal or a nodal basis? If you are using a modal basis, u0 would be (I'm guessing here) the value of your first Legendre polynomial, i.e. the mean value. That will give you a first order approximation of your fluxes, and thus result in a globally first order method. The correct way to do is indeed to evaluate the basis fully at the location it is needed. I recommend you do a convergence study for a simple model problem (Burgers, linear advection etc) first to make sure you got everything right.

January 25, 2014, 13:19		#3
phy4me Member C. Ziyad Join Date: Oct 2010 Posts: 37 Rep Power: 15	Thanks for your response, I use here a legendre polynomial basis, I think that are modal approach ( if it lagrange basis here is nodal ... right ? ). In the case when I use the fully basis, osciallations are generated in the solution in same problems ( Haudraulic jump for example ). Here, what I want know is how evaluate the physical state to calculate the flux at each edge. Thanks,

January 25, 2014, 13:21		#4
cfdnewbie Senior Member cfdnewbie Join Date: Mar 2010 Posts: 557 Rep Power: 20	You do that evaluation the full basis / full expansion at the location where you need it. If you are getting oscillations (for a smooth problem), then you will need to check your code. If you are talking about non-smooth problems, then oscillations are to be expected if you don't use any form of limiting.