# Mapping SPH data on Eulerian Grid for further evolution

I'm sure this is very important for anyone working in computational astrophysics. I have a .sph file & it has 10 columns containing

x, y, z, density, temp., velx, vely, velz, smoothing length, particle mass.


Data is in some strange units but I can take care of that. But, I don't know about other details. Anyone who may have worked with SPH code probably will know how to extract physically sensible data out of it.

I'm a novice in computational astrophysics & computation as a whole but know the physical equations (MHD, Radiative transport, etc...) very well. Any help would be highly appreciated.

The data in the SPH format is perfectly "physically sensible", you just need to know how to interpret it.

In the SPH formulation, you can compute any particle quantity $A$ at any given point using

$$A(\mathbf r) = \sum_j m_j \frac{A_j}{\rho_j} W(\|\mathbf r-\mathbf r_j\|,h_j).$$

Where $\mathbf r$ is the target point, e.g. a node on your grid, and $\mathbf r_j$ is the location of the $j$th particle, and $\rho_j$, $m_j$, and $h_j$ its density, mass, and smoothing length respectively.

The function $W(r,h)$ is the kernel function which is usually zero beyond $r>2h$. This means that for any target point $\mathbf r$, you only need to inspect particles where $\|\mathbf r - \mathbf r_j\| < 2h_j$.

The target quantity $A$ can be the velocity, temperature, density, whatever is stored at the particle level.

Most of this is described in the Wikipedia article on SPH. A good source for further details is Price's excellent review of SPH available here.

Note that if you're mapping the particle data to a regular grid, it makes much more sense to loop over the particles, not the grid points, as finding the grid points within range of a particle is much easier than finding the particles within range of a grid point.

• thanks a lot for the help. Sorry about returning to this page after so long. I figured out most of the subtleties in SPH data from the Bodenheimer etal book. I would like to add one more aspect of it which I still haven't figured out completely. It's Gather vs Scatter approach to get the physical data at a point in space. Which one is better in what kind of condition etc. There is no pressing need for this but, hopefully someone can elaborate on this. – sceptic_one Feb 26 '14 at 17:42