SPH and LBM, two “particle-based” methods? Well…

When we talk about our products to CFD engineers, there comes a point when we describe the technology inside. One of our solvers is based on the Smoothed Particle Hydrodynamics (SPH) method, which is a "particle-based" CFD method. At such point, we are often answered something like:

Ah yes! I think I know particle-based methods: I've already heard about the LBM methods...

The SPH and the LBM methods both deal with a concept of particles. However, the underlying concept for those two methods is totally distinct.

Smoothed Particle Hydrodynamics (SPH)

Moving particles are used to discretize the continuous space domain. This actually defines a particle-based method.

Indeed, rather than using mesh cells as volume discretization elements like usual mesh-based methods do, the SPH method relies on particles as discretization elements. SPH and other particle-based methods are thus meshless.

Note that those particles are individually tracked: they have their own position, velocity and size. They carry – like mesh cells in traditional CFD – the state variables of the fluid parcel they discretize: velocity, density, pressure, temperature…

Thanks to its Lagrangian nature, such methods are well-suited for simulating flows involving sharp and complex interfaces: multiphase and free-surface flows, atomization and coalescence, moving and deforming bodies, Fluid-Structure Interaction (FSI) and solid contact…

Lattice-Boltzmann Methods (LBM)

LBM deal with particles as a statistical concept: instead of considering all physical atoms/molecules, statistics is made on microscopic particles whose position and velocity lie on a lattice grid.

When solving the Boltzmann equations, the discrete nature of the fluid matter is considered, including atoms/molecules collisions and free stream. At such mesoscopic scale, individual microscopic atoms/molecules are not individually tracked, but statistics is considered. Macroscopic variables (as velocity or pressure) can then be reconstructed from those statistics.

Whatever the method, the continuous range of possible positions cannot be handled numerically, and a discretization is required. For LBM-based solvers, this translates in lining up all physical atoms/molecules onto admissible particles, whose position and velocity lie on a lattice grid.

Note that, those statistical particles are not individually identified nor tracked over time, they have no size and are not the support of the space discretization. However, they are the unitary elements for an extremely efficient statistical enumeration, making the LBM method very competitive on industrial problems, such as aerodynamics and aeroacoustics.

Brief sum-up

I hope this short article has shed the light on the alternative concepts of particles that are involved within the SPH and the LBM methods. Hopefully, the next CFD engineer I will talk about "particle-based method" will answer:

Ah yes! I think I know particle-based methods: They use discrete particles to describe the continuous domain. Not to be confused with LBM methods, which uses a mesh to account for microscopic discrete particles distribution.

Do not hesitate to react and share your experience on this duality.