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Old   October 17, 2008, 12:56
Default 1D Lagrangian code
  #1
Matthew Hunt
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Hi,

I am trying to write a 1D Lagrangian hydrocode, my lagrangian co-ordinate is the mass of the cell. My equations are:

dv/dt-du/dh=0 du/dt+dp/dh=0 d/dt(e+1/2u^2)+d/dh(pu)=0

Where v is specific volume, p is pressure, u is velocity and e is internal energy/unit mass and I use an EoS to calculate pressure from e and v.

There are a few things which I need a but of clarification on. Firstly, do I use the initial mass distribution throughout the code? Will a predictor-corrector method work as a numerical method? When looking at the Sod shock tube problem what artificial viscosity method should I be using? I get large spikes near the shock front and oscillations near the expansion wave.

Any advice?
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Old   October 17, 2008, 15:08
Default Re: 1D Lagrangian code
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ag
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Do a google search on "Neumann artificial viscosity". He was one of the first people to create a working Lagrangian hydrocode (if I remember correctly).
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Old   October 17, 2008, 15:15
Default Re: 1D Lagrangian code
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Matthew Hunt
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I know many flux limiter methods which I can use, I have tried a few of these and they don't seem to work for some reason. Is there a non-shock problem I can try my code on to see if the actual code is working properly?

Mat
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Old   October 18, 2008, 09:32
Default Re: 1D Lagrangian code
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ag
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Just out of curiosity, how are you applying a flux limiter in a Lagrangian scheme where there is no advective flux? Or are you referring to a slope limiter? Either way, take a look at the Neumann artificial viscosity - as I recall it basically uses a pressure switch to control a 2nd-order pseudo-viscous term, and is fairly straight-forward to implement.
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Old   October 18, 2008, 17:24
Default Re: 1D Lagrangian code
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Matthew Hunt
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I have been reading the book, "difference methods for initial value problems." where the switch is velocity. I am using a flux limiter from a paper on artificial viscosity in more than 1 dimension, it was in the journal of computational physics. I can't remember the authors but it combines a quadratic and linear viscosity.

I can send you my code if you wish, it can be run in matlab/octave with ease.

Mat
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