[matthewshorter]

Hello,
I am working on a shock tube simulation as part of a research project. My current difficulty is getting a non oscillating value for p,T,U, and rho at the contact surface of the fluid domain. In the attached image you can see the small deviation in the plot. I have also attached the fvSchemes file. Currently, I am using gamma 1 interpolation but vanLeer and vanAlbada give similar results, with gauss linear and superbee causing the solver to crash. I have read the original paper on CentralFoam by Greenshields etal. and they briefly mentioned that the contact region had dubious accuracy. I am observing excellent results for shock velocity and strength, but have concerns regarding impact of the oscillations around contact surface affecting rest of simulation.

I am somewhat confused as a limiter is supposed to make sure that the fields are behaving monotonically throughout the domain. Is the numerical error/oscillation caused by the discontinuity inevitable or can I mitigate it by changing the solver settings? This is currently in OF 3.0.

fluxScheme Kurganov;

ddtSchemes
{
default Euler;
}

gradSchemes
{
// default Gauss;// linear;
default leastSquares 1;
}

divSchemes
{
default none;
div(tauMC) Gauss linear;
div(phi,k) Gauss linear;
div(phi,omega) Gauss linear;
}

laplacianSchemes
{
default Gauss linear corrected;
}

interpolationSchemes
{
default linear;
reconstruct(rho) Gamma 1;
reconstruct(U) GammaV 1;
reconstruct(T) Gamma 1;
}

snGradSchemes
{
default corrected;
}

In system: maxCo = 0.1

[schuyler]

What Courant number are you using? Decreasing Courant number and also increasing grid resolution could help.

Personally, I have had the most success with vanAlbada. I have some friends that have found Gamma 0.5 to work well.

[matthewshorter]

Hello,
Thank you for your response. I ran the case with gamma 0.5 and vanAlbada limiters with no improvement in the results. The current MaxCo value is set to 0.1, which is below the value of MaxCo = 0.2 that I have been using and the value I have seen used in other simulations. Currently, the shock tube has a pressure ratio of 145:1 across the diaphragm and consists of helium at 300k treated as an ideal gas. The tube is 4m long with 3200 elements (1D). I am still running a case with reduced courant number which for now appears slightly qualitatively better but that might just be wishful thinking.... I will report back next Monday.

[schuyler]

I happened to be writing a blog post about this topic when I saw your post. Here is a link to it. I finished it on the weekend. Let me know if it helps!

https://curiosityfluids.com/2016/07/18/shocktube-rhocentralfoam-tvd-schemes-test/

I think that using Gamma 1 like you are is a good choice. That or vanAlabada. I think if you continue to have issues you'll just have to use more cells and an even lower CFL.

Hopefully I helped... haha

Schuyler

[matthewshorter]

Thank you for your response and very helpful blog post. I did not examine results with the other schemes in detail but did find results supporting your finding of Gamma 1 being stable and consistent, with results at MaxCo = 0.1 and MaxCo = 0.01 in my case being relatively close to each other. Since gamma 1 is providing very good results compared to analytical solution and minimal oscillations, I think I will stick with that. If I have time I will take a look at vanAlbada and see how that behaves for similar courant no. and mesh resolution as gamma 1.