Modification of Flux Corrector method for accuracy improvement on unsteady problems

In the paper we introduce the modification of Flux Corrector (FC) method for solving linearized Euler equations on unstructured simplicial meshes. The original FC method possesses the third order of accuracy only on steady solutions and the second order otherwise. Our modification does not change steady solutions of the FC method but has the third order on translationally-symmetric meshes for unsteady problems. Despite the second order of the scheme on arbitrary meshes for unsteady problems we show that the accuracy becomes significally better than in the original FC method.