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 Ronak Gupta April 16, 2013 11:01

Bow Shock Capturing

Hi,
I have run a code for computation of inviscid supersonic flow around cylinder using a finite volume approach. The bow shock is very much in the final mach number plot. Can someone please tell me if a finite volume method has shock capturing ability implicitly in it or is there something I am missing? The computation is done using a forward time stepping procedure for inviscid Euler equation.
Ronak

 SergeAS April 19, 2013 10:08

Which shock-capturing method are you used ?

PS: Take a look http://en.wikipedia.org/wiki/Shock_capturing_method

 Ronak Gupta April 19, 2013 12:02

shock capturing

I have a used a simple finite volume discretization with forward step for time integration. Euler equations have been used in their conserved state. My question is does the above said finite volume discretization have the ability to capture shock. I read in a paper that a finite volume discretization in conserved state captures shock as a weak solution.,Is that the reason?

 FMDenaro April 19, 2013 13:29

Quote:
 Originally Posted by Ronak Gupta (Post 420980) Hi, I have run a code for computation of inviscid supersonic flow around cylinder using a finite volume approach. The bow shock is very much in the final mach number plot. Can someone please tell me if a finite volume method has shock capturing ability implicitly in it or is there something I am missing? The computation is done using a forward time stepping procedure for inviscid Euler equation. Ronak
Discretizations of the Euler equation with FV are compatible with singularity when derived from the integral form of the equations.
But the "capture" of a physically admissable shock is not ensured by FV if the entropy condition is not verified, too. Monotone scheme ensures the pysical capturing but you need to work with several formulations (TVD, ENO/WENO)

 Ronak Gupta April 19, 2013 19:03

U(1,:) = U(1,:) - dtA.*R(1,:);

U is the Euler vector. Above is the forward step for time integration. R is flux calculated across various edges of the traingular grid. There is no other term added during the process. Will the above method capture shock.? The output has the bow shock clearly visible .

 FMDenaro April 20, 2013 04:02

Quote:
 Originally Posted by Ronak Gupta (Post 421863) U(1,:) = U(1,:) - dtA.*R(1,:); U is the Euler vector. Above is the forward step for time integration. R is flux calculated across various edges of the traingular grid. There is no other term added during the process. Will the above method capture shock.? The output has the bow shock clearly visible .
This instruction says nothing ... the key is in the type of flux reconstruction used in R

 Ronak Gupta April 22, 2013 02:51

The Euler flux evaluation is evaluated specifically as an HLLE flux function. Brief lookup told me that HLLE flux construction is a type of Riemann solver. Can an HLLE flux construction be used for capturing shock in gas dynamics problems?

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