Combined finite element-finite volume solution of compressible flow

The paper is concerned with numerical modelling of inviscid as well as viscous gas flow. The method is based on upwind flux vector splitting finite volume schemes on various types of unstructured grids. In the case of viscous flow we apply a combined method using the finite volume scheme for the discretization of inviscid first order terms of the system and the finite element approximation of viscous dissipative terms. Special attention is paid to higher order schemes and suitable adaptive strategy for a precise resolution of shock waves. Moreover, we summarize the convergence results obtained for a model nonlinear scalar conservation law equation with a diffusion term. Some computational results are presented. In this paper only two-dimensional flow is treated, but the extension to the three-dimensional case is possible.