Fluxlimited

Flux limiting is a numerical technique used in computational fluid dynamics (CFD) to improve the accuracy and stability of solutions involving advection or convection processes. It is employed primarily in high-resolution schemes to prevent non-physical oscillations, such as Gibbs phenomena, which can occur near sharp gradients or discontinuities like shock waves.

The fundamental concept of flux limiting involves modifying the numerical fluxes—quantities representing the transfer of conserved quantities like mass, momentum, or energy—based on local solution gradients. This adjustment ensures that the numerical scheme remains bounded and produces physically realistic results without excessive smearing of sharp features.

Flux limiters function by blending high-order, accurate schemes with more diffusive, stable ones. When the solution is smooth, the limiter permits higher-order schemes to maintain accuracy. Near sharp gradients or discontinuities, the limiter reduces the scheme's order to prevent spurious oscillations, effectively "limiting" the flux in regions where non-physical behavior might arise.

Common flux limiters include the Minmod, Superbee, and Van Leer limiters, each with different trade-offs between sharp feature preservation and numerical stability. The choice of limiter can influence the accuracy and computational efficiency of the simulation.

Overall, flux limiting is a critical component in modern CFD methods for achieving reliable, high-fidelity simulations of complex flows. Its proper application ensures that numerical solutions remain both physically plausible and stable across a range of flow conditions.