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SPH for fluid dynamics
Dear Colleges,
I have a number of questions concerning practical implementation of Smoothed Particle Hydrodynamics for fluid dynamics. I would really appreciate if you can give me some useful hints or references.
First, how to set initial values for volumes or mass and density associated with a particle? So far, I've not found a satisfactory explanation how to do this.
Second, from my reading I can see that the imposition of incompressibility constrains is ‘a piece of art' in SPH. It seems that, historically, fluid is modeled as weakly compressible which leads to restrictions on the size of the time step. Recently, I've met a few references on incompressible SPH with additional Poisson equation for pressure . What is your opinion about this approach?
And the last question at the moment is the imposition of essential boundary conditions. As I can see there are two general ways to do this: 1) If the strong form of PDEs is used, then boundary (rigid body) particles apply forces (of different forms) on the fluid particles; 2) If the collocation (variational) form is used then such mechanisms as Lagrangian multipliers can be applied. What are the criteria to choose the technique?
Thank you in advance!
Olga
Quick Help
About setting initial values of mass and density:
e.g. density of water in ambient pressure and temperature is approximately 1000 and as you know in SPH each particle is representative of a part of space, so if you want to apply it in 2D in a programming language like fortran you can use:
DO I=1,N
M(I)=RO(I)*(LF**2)
END DO
where LF is initial distance between two fluid particles and I is iterative index for particles
about incompressibilty try this paper, it is nice
http://hessan.persiangig.com/document/Hosseini.pdf
Mu He
M.S. Student in Guilan university , Iran