 Consider the 1D semi-discrete scheme below,

where, formula_2 and formula_3 represent edge fluxes for the "ith" cell.If these edge fluxes can be represented by "low" and "high" resolution schemes, then a flux limiter can switch between these schemes depending upon the gradients close to the particular cell, as follows,

where

and formula_9 represents the ratio of successive gradients on the solution mesh, i.e.,

The limiter function is constrained to be greater than or equal to zero, i.e., formula_11.Therefore, when the limiter is equal to zero (sharp gradient, opposite slopes or zero gradient), the flux is represented by a "low resolution scheme".