# Can Smoothed-Particle Hydrodynamics (SPH) be used to simulate porous media flow and deformation?

I am trying to use Smoothed-Particle Hydrodynamics (SPH) to study fluid flow in and around porous media. The aim is to observe how it causes erosion and failure. For this, from my understanding, there needs to be a proper consideration of all the processes at all scales. However, with SPH when problems of bigger scales are considered, i believe there is an averaging over increasing spatial scales and thus loss of information of processes happening in the sub-particle scale. Ex: if the discretization is such that each particle represents 5 liters of fluid or 1 cubic meter of porous media, aren't the processes within these volumes lost to us? Even though they may be considered at the equation level, aren't they difficult to visualize?

To summarize, the use of SPH is primarily to model a continuum using particle discretization, but if it is so coarse such that averaging effects from continuum mechanics need to be considered to account for sub-particle contributions, isn't it redundant to still be using this method for the problem?

• That's true of any computational method though. Finite volume can only resolve the physics at levels resolvable on the grid, everything smaller is averaged away. Finite element can only resolve the physics at the level of the interpolating nodes in the polynomial, smaller than that is lost. Same for finite difference. All methods can only resolve the number of points you give it -- SPH is no different. SPH is always averaging unless you are simulating the atoms themselves as each particle. Commented Aug 20, 2013 at 15:21

The example I am most familiar with is the formation of stars from gas. The simulation particles I deal with are $10^{8}$-$10^{10}$ times too large to resolve the formation of individual stars but we want to resolve this process, so instead when a collection of gas particles achieves conditions ($T,P,\rho$, etc.) correct for star formation, some fraction of gas particles are converted to star particles according to an explicit prescription coded into the simulation. I don't know much about porous media, but I could imagine perhaps some mechanism that dissipates momentum below the scale of the SPH particles; perhaps it would be appropriate to add this in explicitly as a sub-resolution process.