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An optimal splitting technique is proposed for numerical solution of the Euler and Navier-Stokes equations for a compressible heat-conducting gas. This technique is common for original equations in the divergent and nondivergent form. Based on this splitting, a class of economical (in the number of operations per a grid node) difference schemes is proposed so that those schemes are implemented on fractional steps by the scalar sweep methods and have a large stability margin, but have a lesser number of sweep steps in their implementation.

Splitting algorithms for numerical solution of Euler and Navier–Stokes problems