EulerianModelle

EulerianModelle are mathematical and computational frameworks in which physical fields are represented at fixed points in space rather than by following individual particles. The term is used in German-language literature for Eulerian models and reflects the Eulerian description of continua. In these models, quantities such as velocity, temperature, species concentration, and density are described as functions of time and spatial location on a stationary grid or network.

Applications and domains: They are widely used in fluid dynamics, meteorology, oceanography, environmental engineering, combustion, and traffic or crowd dynamics. In atmospheric and ocean models, they solve sets of conservation equations for mass, momentum, energy, and chemical species on a fixed grid.

Formulation and methods: The governing equations are typically advection-diffusion-reaction systems expressed in a fixed (Eulerian) frame. Numerical solution employs grid-based discretization methods such as finite volume, finite difference, or finite element schemes, combined with explicit or implicit time stepping. Boundary and initial conditions are imposed on the fixed domain.

Advantages and limitations: Eulerian models facilitate coupling with chemical mechanisms, radiation transport, and boundary conditions, and are well suited for large-scale and multi-physics simulations. However, they can suffer from numerical diffusion and grid dependence, require careful treatment of advection schemes, and may miss sub-grid-scale processes unless supplemented by turbulence models or subgrid closures; high computational resources are often needed for fine resolution.

Examples and related concepts: Notable examples include atmospheric chemistry transport models like GEOS-Chem, weather and ocean general circulation models, urban air quality simulations, and some macroscopic traffic-flow models. They are contrasted with Lagrangian models that track moving parcels, and with hybrid Eulerian-Lagrangian methods.