Coupled heat transfer problems associated with flows of viscous compressible fluids in a cavity bounded by stationary and rotating walls subject to forced convection are considered. The discretization of the equations describing the fluid flow and a temperature distribution in a solid body, the implementation of a simplified method for calculating the temperature fluid field based on the integration of the temperature equation with the frozen velocity field, the automatic generation of unstructured meshes in the domain occupied by the fluid, and other details of numerical implementation are discussed. The multigrid method and the generalized minimal residual method are used to solve the system of linear algebraic equations obtained after the discretization of Reynolds-averaged Navier-Stokes equations. The possibilities of the approach developed are illustrated by the example of solving some model problems. The results of speeding up the computational algorithm obtained for the full and simplified methods to solve the problem are compared with the results of using various methods of solving linear systems.

Keywords: coupled heat transfer, fluid dynamics, finite element method, finite volume method, unstructured mesh

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