fluxcorrected

Flux Correction is a numerical technique used in computational fluid dynamics (CFD) and other areas of physics to address issues related to numerical diffusion and truncation errors in finite volume methods.

In finite volume methods, numerical flux functions are used to approximate the numerical flux across the faces of the control volumes. However, when solving hyperbolic systems of equations, the Taylor expansion of these numerical flux functions can lead to errors, particularly when dealing with waves that have structured elongated shapes such as refinement in one direction but evenly spaced in the other. This comes about due to the distortion of wave structures.

To correct for these errors, the Flux Corrected Transport (FCT) algorithm was developed. This algorithm traditionally works by adding an anti-diffusion term to the residual, set by subtracting a diffusion term calculated from a smoothed source term of the residual relative to the maximum absolute value of the original residual. This method aims to maintain temporal and spatial accuracy and also characterize advection operations across a defined face.

FCT has diverse applications in various fields, ranging from meteorology and oceanography to astrophysical modeling of fluids and radiation quantities. When dealing with certain non-linear partial differential equations, that can be seen to have general resultant discharge attributed either to granular or fluid pathways, Flux Correction in a form of stabilization may allow for more tangible probabilistic representation where necessary conditions for aggressive cancellations make non-physical emission evaluations to behave otherwise differently.