On some methods for the numerical simulation of flows with complex structure

The paper considers the development of efficient difference schemes for application to compressible viscous heat-conducting gas flows. Particular consideration is given to the problem of shock wave localization in the numerical simulation of such flows. The methods presented are essentially efficient in the computation of flows of complex structure, where singular zones and elements are present (e.g., shock waves and transitions, contact strips, boundary layers, double and triple shock configurations, etc.).