Hostname: page-component-76fb5796d-2lccl Total loading time: 0 Render date: 2024-04-26T08:44:55.143Z Has data issue: false hasContentIssue false
  • English
  • Français

All Speed and High-Resolution Scheme Applied to Three-Dimensional Multi-Block Complex Flowfield System

Published online by Cambridge University Press:  05 May 2011

Uzu- Kuei Hsu ,
Chang- Hsien Tai  and
Chien- Hsiung Tsai
Uzu- Kuei Hsu*
Affiliation:
Department of Aircraft Maintenance and Repair, Air Force Institute of Technology, Kaohsiung, Taiwan 820, R. O. C.
Chang- Hsien Tai*
Affiliation:
Department of Vehicles Engineering, National Pingtung University of Science and Technology, Neipu Shiang, Pingtung, Taiwan 912, R.O.C.
Chien- Hsiung Tsai*
Affiliation:
Department of Vehicles Engineering, National Pingtung University of Science and Technology, Neipu Shiang, Pingtung, Taiwan 912, R.O.C.
*
* Professor
** Research Assistant
** Research Assistant
Get access

Abstract

The improved numerical approach is implemented with preconditioned Navier-Stokes solver on arbitrary three-dimensional (3-D) structured multi-block complex flowfield. With the successful application of time-derivative preconditioning, present hybrid finite volume solver is performed to obtain the steady state solutions in compressible and incompressible flows. This solver which combined the adjective upwind splitting method (AUSM) family of low-diffusion flux-splitting scheme with an optimally smoothing multistage scheme and the time-derivative preconditioning is used to solve both the compressible and incompressible Euler and Navier-Stokes equations. In addition, a smoothing procedure is used to provide a mechanism for controlling the numerical implementation to avoid the instability at stagnation and sonic region. The effects of preconditioning on accuracy and convergence to the steady state of the numerical solutions are presented. There are two validation cases and three complex cases simulated as shown in this study. The numerical results obtained for inviscid and viscous two-dimensional flows over a NACA0012 airfoil at free stream Mach number ranging from 0.1 to 1.0E-7 indicates that efficient computations of flows with very low Mach numbers are now possible, without losing accuracy. And it is effectively to simulate 3-D complex flow phenomenon from compressible flow to incompressible by using the advanced numerical methods.

Keywords

preconditioningfinite volumemulti-block
Type
Articles
Information
Journal of Mechanics , Volume 20 , Issue 1 , March 2004 , pp. 13 - 25
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2004

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Weiss, J. M., Maruszewski, J. P. and Smith, W. A., “Implicit Solution of The Navier-Stokes Equations on unstructured Meshes,” AIAA Journal, Vol.37, No. 1, pp. 29–36 (1999).CrossRefGoogle Scholar
2., Sharov, and Nakahashi, K., “Low Speed Preconditioning and LU-SGS Scheme for 3-D Viscous Flow Computations on Unstructured Grids,” 36th Aerospace Sciences Meeting & Exhibit, AIAA paper 98–0614–CP, pp. 1–10 (1998).CrossRefGoogle Scholar
3.Turkel, E., “Preconditioned Methods for Solving the Incompressible and Low Speed Compressible Equations.” Journal of Computational Physics, Vol.72, pp. 277–298 (1987).CrossRefGoogle Scholar
4.Choi, Y.-H. and Merkle, C. L., “The Application of Preconditioning in Viscous Flows,” J. Comp. Phys., Vol.105, pp. 207–223 (1993).CrossRefGoogle Scholar
5.van Leer, B., Lee, W. T. and Roe, P., “Characteristic Time-Stepping Local Preconditioning of the Euler Equations,” AIAA paper 91–1552–CP (1991).CrossRefGoogle Scholar
6.Venkateswaran, S., Weiss, J. M. and Merkle, C. L., “Propulsion-Related Flowfields Using The Preconditioned Navier-Stokes Equations,” Technical Report AIAA–92–3437, AIAA/ASME/SAE/ASEE 28th Joint Propulsion Conference, Nashville, TN, July (1992).CrossRefGoogle Scholar
7.Weiss, J. M. and Smith, W. A., “Preconditioning Applied to Variable and Constant Density Time- Accurate Flows on Unstructured Meshes,” AIAA paper 94–2209 (1994).CrossRefGoogle Scholar
8.Weiss, J. M. and Smith, W. A., “Preconditioning Applied to Variable and Constant Density Flows,” AIAA Journal., Vol.33, No. 4, pp. 2050–2057 (1995).CrossRefGoogle Scholar
9.Dailey, L. D. and Pletcher, R. H., “Evaluation of Multigrid Acceleration for Preconditioned Time-Accurate Navier-Stokes Algorithms,” Computers and Fluids Journal, Vol.25, No. 8, pp. 791–811 (1996).CrossRefGoogle Scholar
10.Anderson, W. K., Rausch, R. D. and Bonhaus, D. L., “Implicit/Multigrid Algorithms for Incompressible Turbulent Flows on Unstructured Grids,” Journal of Computational Physics, Vol.128, pp. 391–408 (1996).CrossRefGoogle Scholar
11.Weiss, J. M., Maruszewski, J. P. and Smith, W. A., “Implicit Solution of The Navier-Stokes Equations on unstructured Meshes,” Implicit Solution of Preconditioned Navier-Stokes Equations Using Algebraic Multigrid,” AIAA Journal, Vol.37, No. 1, pp. 29–36(1999).CrossRefGoogle Scholar
12.Liou, M. S., “Program towards an Improved CFD Method: AUSM+,” AIAA Paper 95–1701–CP (1995).CrossRefGoogle Scholar
13.van Leer, B., “Upwind-Difference Methods for Aerodynamic Problems Governed by the Euler Equations,” Proceedings of Large-scale Computations in Fluid Mechanics, Lectures in Applied Mathematics, Vol.22, pp. 327–336 (1985).Google Scholar
14.Mulder, W. and van Leer, B., “Experiments with implicit upwind methods for the Euler equations,” Journal of Computational Physics, Vol.59, pp. 232–246 (1985)CrossRefGoogle Scholar
15.van Albada, G. D., van Leer, B. and Roberts, J. W. W., “A Comparative Study of Computational Methods in Cosmic Gas Dynamic,” Astronomy and Astrophysics, Vol.108, pp. 76–85 (1982).Google Scholar
16.Fromm, E., “A method for reducing dispersion in convective difference scheme,” Journal of Computational Physics, Vol.3, pp. 413–437 (1968).CrossRefGoogle Scholar
17.Tai, C. H., Sheu, J. H. and van Leer, B., “Optimally Multi-Stage Schemes for the Euler Equations with Residual Smoothing,” Journal of AIAA, Vol.33, No. 6, pp. 1008–1016 (1995).CrossRefGoogle Scholar
18.Guillard, H. and Viozat, C., “On the behavior of upwind schemes in the low Mach number limit,” Computers & Fluids, Vol.28, pp. 63–86 (1999).CrossRefGoogle Scholar
19.Swanson, R. C., Radespiel, R. and Turkel, E., “On Some Numerical Dissipation Schemes,” Journal of Computational Physics, Vol.147, pp. 518–544 (1998).CrossRefGoogle Scholar
20.Lee, D., “Design Criteria for Local Euler Preconditioning. Journal of Computational Physics,” Vol.144, pp. 423–459(1998).CrossRefGoogle Scholar
21.Bern, P., Steady and unsteady solutions of the Navier-Stokes equations for flows about airfoils at low speeds. AIAA paper, 91–1773 (1991).CrossRefGoogle Scholar
22.Tai, C. H., Miao, J. M. and Chen, J.J., “Numerical Simulation of the Flow Structure Around Connect-Truck,” Bulletin of National Pingtung University of Science and Technology, Vol.10, No. 2, pp. 119–130(2001).Google Scholar
23.Yoganathan, A. P., Corcoran, W. H. and Harrison, E. C., “Pressure Drops Across Prosthetic Aotic Heart Valves under Steady and Pulsatile Flow— in Vitro Measurement,” Journal of Biomechanics, Vol.12, pp. 153–164 (1979).CrossRefGoogle Scholar
24.Nichols, W. W. and O'Rourke, M. F., “McDonald's Blood Flow in Arteries,” 3rd ed., Lea & Febiger, Philadelphia, PA (1990).Google Scholar
25.Sutera, S. P. and Mehrjard, M. N., “Deformation and Fragmentation of Human RBC in Turbulence Shear Flow,” Biophys. J., Vol.15, pp. 1–10 (1975).CrossRefGoogle Scholar