A study of high-order grid-characteristic methods on unstructured grids

In this paper, grid-characteristic methods for solving hyperbolic systems using approximation with high-order interpolation on unstructured tetrahedral and triangular grids are studied. Interpolation methods of order from 1 through 5 inclusive are considered. One-dimensional finite difference schemes for these methods are presented. The stability of these schemes is investigated. The grid-characteristic methods on unstructured triangular and tetrahedral grids are successfully used in seismic prospecting, specifically under the Arctic shelf and permafrost conditions. They are also used to solve problems of seismics, dynamic deformation and destruction, and to study anisotropic composite materials.