Continuum particle models

Computational methods represent continuous materials as particles that carry physical properties such as mass, velocity, and stress. They update particle motion and interactions to approximate continuum behavior.

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Smoothed-particle hydrodynamics: A mesh-free method that estimates continuum fields by smoothing values over neighboring particles. It computes density, pressure, and other fields directly from nearby particles.
Continuum mechanics: The study of material behavior under forces, treating matter as continuously distributed. The particles approximate fields and laws defined by continuum mechanics.
Free-surface flow: Fluid motion with a boundary exposed to another fluid or to the atmosphere. Particles can follow a moving fluid boundary without a fitted mesh.
Finite element method: A numerical method that divides a domain into elements to approximate solutions of field equations. It typically organizes continuum calculations around a mesh rather than particles alone.
Material point method: A computational method that tracks material points while using a background grid to solve governing equations. It combines moving material carriers with a temporary grid for calculations.
Conservation laws: Physical principles stating that quantities such as mass, momentum, and energy remain conserved in closed systems. Particle updates must preserve the balances governing the represented material.
Impact mechanics: The study of forces and deformation during collisions and other short-duration contacts. Large transient deformations can make particle-based simulation advantageous.
Finite volume method: A numerical method that enforces conservation over finite control volumes. Its fixed or moving cells provide a contrasting way to preserve material balances.
Peridynamics: A continuum theory that models material interactions through finite-distance forces rather than spatial derivatives. Its nonlocal force law handles discontinuities that challenge local continuum equations.
Kernel function: A weighting function used to average or interpolate values over a region. Kernel weights let mesh-free methods estimate smooth fields from particle samples.