Constants def

sebastianb

Hi.

I'm working with dualSPHysics and I have two questions about the part in XML-File which is called .

1. What means gamma?
2. What means eps?

Thanks for answers.

Sebastian

SLongshaw

Hi sebastianb.

1) "Gamma" refers to the gamma variable used in Tait's equation of state, which is used in DualSPHysics to relate density to pressure (http://en.wikipedia.org/wiki/Tait_equation)
2) "eps" refers to the controlling coefficient used in Monaghan's XSPH formulations that DualSPhysics CAN employ. If this is zero then the XSPH correction won't be applied, otherwise it determines the effect that the XSPH formulations have. There are many papers out there on the meaning of XSPH.

Regards,

Stephen

sebastianb

Hi Stephen.

1) Ok but how do you get "7"? I expected "3.5"
2) of course, sorry

Sebastian

Alex

Gamma=7 in the ocean !!!!!!!!

sebastianb

Hello again.

I have to say sorry, but I don't understand this.
Stephen you linked to wikipedia, but I don't really understand that.
Is the "gamma" the compressibility of the fluid (seewater)?

Maybe you can explain me gamma in words? I think that wolud be very helpful.
Thanks

Sebastian

SLongshaw

Well, (very) simply put, gamma refers to the compressibility of the fluid. As DualSPHysics implements a weakly compressible method, it uses an equation of state to relate density to pressure (an incompressible method does not do this but has to deal with other more difficult problems).

It has been found that the value for gamma within the Tait equation of state that creates the best likeness to sea-water (whilst maintaining stability) is 7. This value can be slightly lower or even slightly higher, but I suspect at 3.5 things simply won't work, the fluid will be far too compressible.

I linked the wiki page as it is a neat description of the Tait EOS. If you look you'll see that gamma is the power in the equation, therefore the larger the value of gamma, the larger the effect a change in density has on pressure, i.e. the fluid becomes less compressible as gamma increases.

Can I recommend you look through some seminal SPH papers as the methods employed by DualSPHysics in this regard would be considered quite fundamental.

Regards,

Stephen

EDIT: In fact perhaps a good document for you would the SPHysics user guide as it provides a neat description of the SPH stuff (which DualSPHysics is simply a GPU/multi-threaded CPU implementation of) https://wiki.manchester.ac.uk/sphysics/images/SPHysics_v2.2.000_GUIDE.pdf. The Tait EOS is described in tis document in SPH terms.

sebastianb

Hi Stephen.

So now I have to thank you a lot, I understood it.

Thanks!!!