Eulerian description

A description of motion and physical fields that assigns values to positions in the current spatial configuration, rather than tracking individual material points.

Lagrangian description: A description of motion and fields that follows individual material points as they move. It tracks the same material points that an Eulerian description observes at changing spatial positions.
Velocity field: A vector field assigning a velocity to each spatial position and time. It specifies how material moves through the positions where Eulerian fields are evaluated.
Computational fluid dynamics: The numerical simulation of fluid flow using discretized governing equations. Many flow solvers store velocity, pressure, and density at spatial grid locations.
Continuum mechanics: The study of the motion and deformation of matter modeled as continuous media. Eulerian description is one of its principal ways to represent motion and fields.
Material derivative: The rate of change of a field experienced by a moving material point. It converts spatially observed field changes into rates experienced by moving matter.
Substantial derivative: The time rate of change of a quantity following a moving fluid element. It combines local time variation with transport through spatial gradients.
Finite volume method: A numerical method that enforces conservation by balancing fluxes across control-volume boundaries. It updates spatially organized field values through fluxes across cell faces.
Configuration (continuum mechanics): A mapping that assigns each material point of a body a position in space at a given time. The current configuration supplies the spatial positions where fields are described.
Arbitrary Lagrangian–Eulerian method: A computational method that allows a mesh to move independently of both material and spatial coordinates. It blends fixed-spatial and material-following descriptions to handle moving boundaries.
Advection: The transport of a quantity by the bulk motion of a fluid or other medium. It accounts for field changes caused by matter moving across fixed spatial positions.

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