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September 29, 2005, 01:50 
2D Riemann problem

#1 
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Dear Friends,
Can anyone suggest the boundary conditions for 2D riemann problems? For a specific configuration wherein 4 shocks appear and interact, I get the shock curving at the boundary, while I have seen that in many simulations by others the shock is normal at the boundary. Regards, Ganesh 

September 29, 2005, 08:53 
Re: 2D Riemann problem

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By boundary do you mean a wall ? If so you should treat it in the same way as you treat subsonic inflow or subsonic outflow conditions. This is because the component of velocity normal to the wall is zero (no penetration condition). I prefer to treat it as outflow as I then only have to specify one condition (U=0).
Scott 

September 29, 2005, 23:14 
Re: 2D Riemann problem

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The boundary in this case is an artificial boundary meant to truncate the computational domain. There is no rigorous way of deriving such boundary conditions. What most people do is to extrapolate from inside the computational domain. You may have to limit the extrapolated values if there are shocks nearby.


September 30, 2005, 13:53 
Re: 2D Riemann problem

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Dear Friends,
I am in fact using extrapolation from the interior with limiting for shocks. The problem does not arise if the initial conditions are such that either one of the velocity components u or v is zero or both are zero in the four quadrants. ( Actually in this case, the normal velocity on the boundary actually vanishes and this makes things easy). However, when one of the quadrants does have a nonzero u and v, then I experience the problem of shock being not normal to the boundary. I have seen people using theextrapolation bc, but they seem to get normality at the boundary. Any suggestions ? Regards, Ganesh 

October 1, 2005, 02:38 
Re: 2D Riemann problem

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You could try a Neumanntype boundary condition,
du/dn = 0 for all the flow quantities. Or you could do a constrained least squares interpolation, ie., fit a polynomial such that the Neumann condition is satisfied either exactly or in a leastsquares sense (penalty function approach). 

October 3, 2005, 02:33 
Re: 2D Riemann problem

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Dear Praveen,
Thankyou for the suggestion on VN boundary condition, it does work. However, what I had to do was to revert to first order accuracy(constant poly. recons.) ie U_boundary = U_(cell centoid of the cell sharing the boundary face). I was wondering if I could do the same with second order accuacy. Least squares is a possibility, but will it wok effectively ? Regards, Ganesh 

October 3, 2005, 04:40 
Re: 2D Riemann problem

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You can try to interpolate to the cell face by satisfying Neumann bc and then compute the flux using the interpolated values. Of course this will be extra work since you have to define a stencil for the cell face. You may have to limit the interpolated values especially if there are shocks. I have used a minmax type of limiting in such situations, ie., if the interpolate exceeds the interval {min, max} then chop it to the endpoint of the interval. Its not a nice way to solve but it works.
PS: If you are in IISc, Bangalore, you can talk to Keshav Malagi who has recently solved 2D Riemann problem. 

October 3, 2005, 05:55 
Re: 2D Riemann problem

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Dear Praveen,
Thanks for the suggestions. I am in IISc and I shall talk to Keshav regarding the 2D Reimann problem. Regards, Ganesh 

October 3, 2005, 07:58 
Re: Keshav Malagi

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Praveen,
Am interested Keshav Malagi work. can you introduce his URL or his department......i really need to get in touch with him. Thanks. 

October 3, 2005, 08:09 
Re: 2D Riemann problem

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Ganesh,
I came across a report for boundary conditions. You can email me at shukla_apoorv1975@yahoo.co.uk. I have to did it up and will forward it to you. Hope it helps. Regards A.S. 

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