Advektionsscheman

Advektionsscheman, or advection schemes, are numerical methods used to approximate the advection term in partial differential equations that describe the transport of scalars or vectors by a velocity field. They are central to computational fluid dynamics, meteorology, and oceanography, where quantities such as temperature, humidity, salinity, or pollutant concentration are advected by flows.

In discrete models, advection can be treated in Eulerian form on a fixed grid or in semi-Lagrangian/Lagrangian forms that follow characteristics. Conservative formulations ensure that the total quantity is preserved across cell interfaces, a requirement for physical fidelity.

Common approaches include first-order upwind schemes, which are robust but diffusive; higher-order linear schemes such as Lax-Friedrichs and Godunov methods; and high-resolution nonlinear schemes designed to reduce numerical diffusion while avoiding spurious oscillations, such as Flux-Corrected Transport (FCT), Total Variation Diminishing (TVD) schemes, ENO/WENO schemes, and MPDATA. Semi-Lagrangian schemes are widely used in weather prediction because they allow large time steps by interpolating values from departure points, though they rely on interpolation accuracy and can introduce numerical diffusion.

Key properties include stability criteria such as the CFL condition, accuracy, monotonicity, and the balance between numerical diffusion and dispersion. The choice of scheme depends on the problem, desired conservation properties, smoothness of the solution, and computational resources.

Advektionsscheman are integral to simulations of atmospheric transport, ocean circulation, pollutant dispersion, and climate modeling, influencing the fidelity of modeled transport processes and the interpretation of results.