A Lagrangian meshless method that models continua by particles carrying mass, momentum and state variables and computes field quantities through kernel-weighted interpolation (smoothing) over neighboring particles.

Principle

Approximate integral identities of continuum fields by sums over particles weighted by a compact support kernel; particle motion follows Lagrangian kinematics and conservation laws are enforced in discrete particle form.

Demonstration

Simulating free-surface fluid flow: initialize particles with mass and velocity, compute density and pressure at each particle by summing kernel-weighted contributions from neighbors, and advance particle positions using momentum equations discretized in particle form.

Misapplication

Using SPH with overly coarse or irregular particle distributions without corrective terms leads to tensile instability, spurious pressure oscillations, and poor enforcement of boundary conditions if kernels are not adjusted.

Consequence

When properly implemented with consistent kernels and stabilization, SPH naturally handles large deformations, free surfaces, and multiphase interfaces without remeshing, making it attractive for fluid-structure interaction and astrophysical flows.

Reversal

The opposite is Eulerian mesh-based CFD where fields are defined on fixed spatial grids; that approach avoids particle noise and certain instabilities but struggles with mesh entanglement and severe deformations without complex remeshing.

Boundary

Appropriate for problems with large deformation, free surfaces, or where mesh generation is difficult; less effective for steady-state problems requiring high-order boundary accuracy unless special boundary treatments and consistency corrections are applied.

Semantic Tension

Competes with grid-based CFD and other particle methods: SPH trades mesh tangling for particle noise and kernel-consistency issues; improvements (e.g., corrective kernels) attempt to reconcile particle convenience with numerical accuracy.

Synthesis

Smoothed Particle Hydrodynamics: a meshfree Lagrangian method that approximates continuum fields via kernel-weighted particle sums, enabling robust handling of large deformations and free surfaces at the cost of careful kernel and stability treatments.