On the solution of hyperbolic equations using unstructured grids

The article concerns with the numerical solution of hyperbolic equations on nonregular difference meshes. We discuss the construction of control volume and projectional schemes providing the quasimonotonous solution resolved with appropriately good accuracy. The comparison of the developed and some known schemes is implemented by solving 2D model problems formulated for the linear transport equation. We consider also the properties of a new algorithm designed for the implementation of explicit difference schemes on unstructured grids. In this algorithm it is unnecessary to store simultaneously the main mesh functions related to “upper” and “ower” time levels.