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Three-dimensional compressible-incompressible turbulent flow simulation using a pressure-based algorithm. (English) Zbl 1237.76086
Summary: In this work, we extend a finite-volume pressure-based incompressible algorithm to solve three-dimensional compressible and incompressible turbulent flow regimes. To achieve a hybrid algorithm capable of solving either compressible or incompressible flows, the mass flux components instead of the primitive velocity components are chosen as the primary dependent variables in a SIMPLE-based algorithm. This choice warrants to reduce the nonlinearities arose in treating the system of conservative equations. The use of a new Favre-averaging like technique plays a key role to render this benefit. The developed formulations indicate that there is less demand to interpolate the fluxes at the cell faces, which is definitely a merit. To impose the hyperbolic behavior in compressible flow regimes, we introduce an artificial hyperbolicity in pressure correction equation. We choose $$k-\omega$$ turbulence model and incorporate the compressibility effect as a correction. It is shown that the above considerations grant to achieve a robust algorithm with great capabilities in solving both flow regimes with a reasonable range of Mach number applications. To evaluate the ability of the new pressure-based algorithm, three test cases are targeted. They are incompressible backward-facing step problem, compressible flow over a wide range of open to closed cavities, and compressible turbulent flow in a square duct. The current results indicate that there are reliable agreements with those of experiments and other numerical solutions in the entire range of investigation.

##### MSC:
 76M12 Finite volume methods applied to problems in fluid mechanics 76F50 Compressibility effects in turbulence 76F60 $$k$$-$$\varepsilon$$ modeling in turbulence
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