Multidimensional Minimal Stencil Supported Second Order Accurate Upwind Schemes for Solving Hyperbolic and Euler systems

We present the construction and the theoretical background of a new class of explicit schemes. These schemes are based on minimal variable stencils that implies both high resolution and the simplicity of difference boundary conditions. The minimal stencil principle is formulated for the case of multidimensional systems. The selection of the stencil is based on the asymptotic analysis of solutions of difference equations. The presented method combines well-known elements (the flux splitting, the minmod-type switch) with new constructions such as the special basic first order accurate scheme, the smoothing of switches and other. The abilities of the method are illustrated by numerical examples.