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DG method with periodic boundary conditions.

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I am solving the incompressible Euler equations in 2d in vorticity-streamfunction formulation. The vorticity equation is
w_t + grad.(Uw)=0 where U is the velocity and w is the vorticity. To solve the vorticity equation, I am using DG method and the flux is the upwind flux. For periodic boundary condition, how do I modify the flux?

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