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Numerical simulation of transient turbulent flows by the vorticity-vector potential formulation. (English) Zbl 0732.76058

Summary: A new eighth-order accurate method is presented for simulating directly turbulent shear flows. In the present method the vorticity-vector potential formulation is adopted in order to satisfy the equation of continuity automatically. The Poisson equations for the vector potentials are discretized also with eighth-order accurate method and the higher- order multi-grid method is employed. The accuracy and efficiency of the present Poisson solver are inspected in detail. The present method is, at the outset, applied to computations of cubic cavity flow and the result shows a striking agreement with that use the pseudo-spectral method. After having shown that the present method predicts accurately the three- dimensional instability of plane Poiseuille flow, the numerical simulation of the transient turbulent flow in a plane channel is dealt with in the \(65^ 3\) grid. The result shows an excellent agreement with that using the pseudo-spectral method; so the present computational method is suitable for the numerical simulation of shear flow turbulences.

MSC:

76M20 Finite difference methods applied to problems in fluid mechanics
76F10 Shear flows and turbulence
65N40 Method of lines for boundary value problems involving PDEs
65N55 Multigrid methods; domain decomposition for boundary value problems involving PDEs

Software:

TURBIT
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References:

[1] Moin, P.; Kim, J., Numerical investigation of turbulent channel flow, J. Fluid Mech., 118, 341 (1982) · Zbl 0491.76058
[2] Kim, J.; Moin, P.; Moser, R. D., Turbulence statistics in fully developed channel flow at low Reynolds number, J. Fluid Mech., 177, 133 (1987) · Zbl 0616.76071
[3] Zang, T. A.; Krist, S. A.; Erlebacher, G.; Hussaini, M. Y., Nonlinear structures in the later stages of transition, AIAA Paper 87-1204 (1987)
[4] Orszag, S. A.; Kells, K. C., Transition to turbulence in plane Poiseuille and plane Couette flow, J. Fluid Mech., 96, 159 (1980) · Zbl 0418.76036
[5] Deardorff, J. W., Subgrid scale model for finite difference simulations of turbulent flows in a plane channel and annuli, J. Comput. Phys., 18, 376 (1975)
[6] Groetzbach, G.; Schumann, U., Direct numerical simulation of turbulent velocity, pressure and temperature fields in channel flows, (Turbulent Shear Flows I (1979), Springer: Springer Berlin), 370
[7] Tokunaga, H.; Satofuka, N.; Miyagawa, H., Direct simulation of shear flow turbulence in a plane channel by sixth order accurate method of lines with new sixth order accurate multi-grid Poisson solver, Lect. Notes Phys., 264, 617 (1986)
[8] Satofuka, N., Method of lines approach to the numerical solution of fluid dynamic equations, Lect. Notes Phys., 264, 57 (1986)
[9] Ku, H. C.; Hirsh, R. S.; Taylor, T. D., A pseudo-spectral method for solution of the three dimensional incompressible Navier-Stokes equations, J. Comput. Phys., 70, 439 (1987) · Zbl 0658.76027
[10] Goda, K., A multi-step technique with implicit difference schemes for calculations of two or three dimensional cavity flows, J. Comput. Phys., 30, 76 (1979) · Zbl 0405.76017
[11] Takami, H.; Kuwahara, K., Numerical study of three-dimensional flow within a cubic cavity, J. Phys. Soc. Japan, 37, 1695 (1974)
[12] Aziz, K.; Hellums, J. D., Numerical solution of the three-dimensional equations of motion for laminar natural convection, Phys. Fluids, 10, 314 (1967) · Zbl 0158.23402
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