Accuracy analysis and improvement for the cell-centered scheme with the quasi-one-dimensional reconstriction

We study the cell-centered finite-volume scheme with the quasi-one-dimensional reconstruction. For the model transport equation with a constant velocity, we prove that on translationally-invariant (TI) triangular meshes it possesses the second order of the truncation error and, if the solution is steady, the third order of the solution error. We offer the modification possessing the third order of the solution error on TI-meshes for unsteady solutions also and verify its accuracy on unstructured meshes.