Modification of Flux Correction method for accuracy improvement on unsteady problems

In the paper we introduce a new modification of the Flux Correction method (we name it Unsteady Flux Correction scheme) for solving convection-dominant problems on unstructured simplicial meshes. The original Flux Correction method possesses the third order of accuracy on steady solutions and the second order otherwise. Our modification does not degrade steady solutions of the Flux Correction method and, in addition, enjoys the third order on translationally-invariant meshes for unsteady problems. On arbitrary unstructured meshes for unsteady problems we show that the accuracy of Unsteady Flux Correction scheme is significantly higher than of the original (steady) Flux Correction method in terms of error values.