If it's the right method for your problem, it's another question all together. So, as far as what you can do with it, I believe that it's past the point that you can put into question whether is valid or not to use SPH. There are things that SPH simply sucks, it's true, like simulating Schrödinger Equation (via Madelung's Eqiation), but many other methods also suck, so that's no problem intrinsic to SPH.
This problems, in my view, are not entirely gratutious, part of the point of creating SPH was exactly that: to be able to deal with boundary-free and higly deformable boundaries that you find in explosion and astrophysical simulations (2 of the first real-life applications of the SPH method).Īs for actual fluids, there is all kinds of simulations done with it: Atmospheric Dynamics, High-Explosives Design, Galactic Evolution, Astrophysics, Relativistic Heavy-Ion Collisions/QGP dynamics, you name it. You end up needing either to include 'ghost particles' which constitute and 'softly' enforce the boundary conditions, or to put it by brute force on the external potential.
Other problems relate to the construction of the kernels, like the limitation of 1st order reproducibility, which is necessary to assure positivity of you reference density.Īlso, SPH always had problems with dealing with boundaries, there is no natural way (as far as I know) to include boundary conditions directly on SPH formalism.
The Idea of SPH is that once you put that Smoothing Kernel, you are killing small wavelenght components of the function you are approximating, so, you it's not too different from grid methods, but you do it on a 'smoother' way.
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