[selig5576]

Hi,

I am currently building up a 2D hydrodynamics code. Specifically, I am numerically solving the 2D Euler equations in order to simulate Kelvin-Helmholtz instability. The boundary conditions are periodic, however I am running into issues when enforcing such conditions.

Given the governing equations






I define Q to be the left-hand side of the system of PDEs. As such in discrete form its a (nx,ny,4) array. Given we have periodic boundary conditions I set

Q(1,1:ny,1:4) = Q(nx,1:ny,1:4) (Q(1) = Q(n) in x)
Q(1:nx,1,1:4) = Q(1:nx,ny,1:4) (Q(1) = Q(n) in y)

With this implementation I am not getting the desired effects of the Kelvin-Helmholtz. I conclude the error is at the boundary due to the plot. I start my arrays at 1 so my boundaries are at 1 and nx.

subroutine BC (Q_out)
	implicit none
	real, dimension(nx,ny,4), intent(inout) :: Q_out
    
	Q_out(1,:,:) = Q_out(nx,:,:)
	Q_out(:,1,:) = Q_out(:,ny,:)
 	return
end subroutine

I am assuming a uniform grid and am using the Rusanov (Local Lax Friedrichs) flux discretization, so there shouldnt be any special treatment of ghost points needed. I have done periodic boundary conditions for non-systems of PDEs and the implementation is straight forward however, I am suspecting that I way of doing PBCs is not correct given I have a system.

NOTE 1: I can post my Fortran code if it will help.
NOTE 2: I have tested this code on various 2D Riemann problems and I get correct results.