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A high-fidelity numerical method for the simulation of compressible flows in cylindrical geometries. (English) Zbl 1354.76073

Summary: A wide range of flows of practical interest occur in cylindrical geometries. In order to simulate such flows, an available compact finite-difference simulation code [N. A. Adams, Theor. Comput. Fluid Dyn. 12, No. 2, 109–129 (1998; Zbl 0931.76033)] was adapted by introducing a mapping that expresses cylindrical coordinates as generalized coordinates. This formulation is conservative and avoids problems associated with the classical formulation of the Navier-Stokes equations in cylindrical coordinates. The coordinate singularity treatment follows and is modified for generalized coordinates. To retain high-order numerical accuracy, a Fourier spectral method is employed in the azimuthal direction combined with mode clipping to alleviate time-step restrictions due to a very fine grid spacing near the singularity at the axis (\(r = 0\)). An implementation of this scheme was successfully validated by a simulation of a tripolar vortex formation and by comparison with linear stability theory.

MSC:

76F65 Direct numerical and large eddy simulation of turbulence
76M20 Finite difference methods applied to problems in fluid mechanics
76N99 Compressible fluids and gas dynamics

Citations:

Zbl 0931.76033
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Full Text: DOI

References:

[1] Adams, Theoret. Comput. Fluid Dynamics 12 pp 109– (1998) · Zbl 0931.76033 · doi:10.1007/s001620050102
[2] Mohseni, J. Comput. Phys. 157 pp 787– (2000) · Zbl 0981.76075 · doi:10.1006/jcph.1999.6382
[3] Adams, J. Fluid Mech. 420 pp 47– (2000) · Zbl 1009.76043 · doi:10.1017/S0022112000001257
[4] Adams, J. Comput. Phys. 127 pp 27– (1996) · Zbl 0859.76041 · doi:10.1006/jcph.1996.0156
[5] Anderson, J. Comput. Phys. 2 pp 279– (1968) · Zbl 0159.57401 · doi:10.1016/0021-9991(68)90058-2
[6] J. B. Freund P. Moin S. K. Lele Compressibility effects in a turbulent annular mixing layer, Technical Report Report No. TF-72, FPC, Dept. of Mechanical Engineering, Stanford, CA, 1997.
[7] S. B. Müller F. Keiderling L. Kleiser Viscous compressible stability investigations in cylindrical coordinates, submitted to Proc. Appl. Math. Mech. , 2004. · Zbl 1354.76139 · doi:10.1002/pamm.200410215
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