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TECHNICAL PAPERS

Truncation Error Analysis in Turbulent Boundary Layers

[+] Author and Article Information
A. Di Mascio

INSEAN, Via di Vallerano, 139, 00128, Rome, Italy

R. Paciorri, B. Favini

Department of Mechanics and Aeronautics, University of Rome “La Sapienza,” Via Eudossiana, 18, 00184, Rome, Italy

J. Fluids Eng 124(3), 657-663 (Aug 19, 2002) (7 pages) doi:10.1115/1.1478564 History: Received January 25, 1999; Revised February 06, 2002; Online August 19, 2002
Copyright © 2002 by ASME
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References

Roache,  P. J., 1997, “Quantification of Uncertainty in Computational Fluid Dynamics,” Annu. Rev. Fluid Mech., 29, pp. 123–160.
Jameson, A., Schmidt, W., and Turkel, E., 1981, “Numerical Solutions of the Euler Equations by Finite Volume Methods Using Runge-Kutta Time-Stepping Schemes,” AIAA Paper 81-1259.
Jameson, A., 1985, “Multigrid Algorithms for Compressible Flow Calculations” MAE Report 1743, Princeton University, Princeton, NJ.
Harten,  A., Engquist,  B., Osher,  S., and Chakravarthy,  S. R., 1987, “Uniformly High Order Accurate Essentially Non-Oscillatory Schemes,” J. Comput. Phys., 71, pp. 231–303.
Chorin,  A., 1967, “A Numerical Method for Solving Incompressible Viscous Flow Problems,” J. Comput. Phys., 2, pp. 12–26.
Brandt, A., 1984, “Multi-grid Techniques: 1984 Guide With Application to Fluid Dynamics,” The Weizmann Institute of Science, Rehovot (Israel).
Favini,  B., Broglia,  R., and Di Mascio,  A., 1996, “Multigrid Acceleration of Second Order ENO Schemes From Low Subsonic to High Supersonic Flows,” Int. J. Numer. Methods Fluids, 23, pp. 589–606.
Baldwin, B. S., and Lomax, H., 1978, “Thin Layer Approximation and Algebraic Model for Separated Turbulent Flows,” AIAA Paper 78-257.
Spalart,  P. R., and Allmaras,  S. R., 1994, “A One-Equation Turbulence Model for Aerodynamic Flows,” La Recherche Aérospatiale, 121, pp. 5–21.
Di Mascio, A., Broglia, R., and Favini, B., 1998, “Numerical Simulation of Free-Surface Viscous Flow by ENO-Type Schemes,” 3rd Int. Conf. on Hydrod., Oct. 1998, Seoul, Korea.
Schlichting, H., 1960, Boundary Layer Theory, McGraw-Hill, New York.
Vinokur,  M., 1983, “On One Dimensional Stretching Function of Finite Difference Calculations,” J. Comput. Phys., 50, pp. 215–234.
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Figures

Grahic Jump Location
Velocity profile and turbulent viscosity profile for the Spalart and Allmaras profile (solid line) and for the Baldwin and Lomax model (dashed line)
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Truncation error coefficients for the Spalart and Allmaras model (solid line) and for the Baldwin and Lomax model (dashed line)
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Numerical error coefficients for the Spalart and Allmaras model (solid line) and for the Baldwin and Lomax model (dashed line)
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Numerical error for λ+=30,Δy+=1.75 and ε4=1/64, 1/128, 1/256
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Numerical solution with the ENO scheme and the Spalart and Allmaras model on three mesh levels
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Numerical solution with the centered scheme (ε4=1/64) and the Baldwin and Lomax model on three mesh levels
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Numerical solutions with the centered scheme and varying ε4 and with the ENO scheme on a 16×16-G3 mesh
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Numerical solutions with the ENO scheme and mesh families G1 (left, top and middle) and G2 (left, bottom) and mesh families G3 (right, top and middle) and G4 (right, bottom) with Baldwin and Lomax model (top) and Spalart and Allmaras model (middle and bottom). Solid line: numerical solution. X : control points. Full circles: apparent convergence order. Bars: GCI.
Grahic Jump Location
Numerical solutions with the centered scheme (ε4=1/64) and mesh families G1 (left) and mesh families G3 (right) with Baldwin and Lomax model (top) and Spalart and Allmaras model (bottom). Solid line: numerical solution. X : control points. Full circles: apparent convergence order. Bars: GCI.

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