Grid-characteristic numerical method on an irregular grid with extending the interpolation stencil

A grid-characteristic numerical method for solving a multidimensional transport equation on an unstructured grid with an order higher than one is proposed; this method does not use auxiliary points on edges and faces. The avoidance of auxiliary points on edges and faces simplifies the topology of the computational grid during its motion, which is important for solving dynamic problems of mechanics of deformable solids. To increase the approximation order, an analog of the grid stencil extension implemented for an unstructured grid is used. Results of testing the proposed numerical scheme for continuously differentiable, continuous, discontinuous solutions are presented.