Efficient formulation for schemes with quasi-one-dimensional reconstruction of variables

In this paper we use a class of schemes with quasi-1D reconstruction of variables for solving hyperbolic systems on unstructured meshes. We consider both vertex-centered and cell-centered schemes. We suggest a new formulation which helps to reduce the computational cost while preserving the quality of computations. Also shown are the results of computational experiments for the linearized Euler equations on various meshes.