Abstract
High-order non-reflecting boundary conditions in a generalized curvilinear coordinate system for solving the time-dependent Navier-Stokes equations in complex geometry have been developed based on the characteristic analysis and the modified Navier-Stokes equation. Viscous terms are taken into account to include the viscous effect near the wall. All boundary conditions are added implicitly to the equations of interior points to ensure the stability of this scheme. The computational results show that the non-reflecting boundary conditions are compatible to the sixth- or fourth-order compact central difference scheme and maintain a high-order accuracy for the global solution. The non-reflecting boundary conditions work surprisingly well without any artificial buffer or sponge. No visible reflected wave was found from either inflow, outflow, far-field, or solid surface. The computational solution is found quite accurate comparing with valid data.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Collis, S.S. and Lele, S.K. (1996) A computational approach to swept leading-edge receptivity, AIAA Paper 96-0180
Fasel, H. (1990) Numerical investigation of the three-dimensional development in boundary-layer transition, AIAA Journal, 28, pp.29–37
Guo, Y., Kleiser, L., and Adams, N. (1996) Comparison of temporal and spatial direct numerical simulation of compressible boundary-layer transition, AIAA Journal, 34(4), pp.683–690
Jiang, L., Shan, H, Liu, C. (1999) Direct numerical simulation of boundary-layer receptivity for subsonic flow around airfoil, The Second AFOSR International Conference on DNS/LES, Rutgers, New Jersey, June 7–9.
Kloker, M., Konzelmann, U., and Fasel, H. (1993) Outflow boundary conditions for spatial Navier-Stokes simulations of transition boundary layers, AIAA Journal, 31, pp.620–628
Lele, S. K. (1992) Compact finite difference schemes with spectral-like resolution. J. Comprit. Phys., 103, pp. 16–42
Liu, C., Liu, Z., and McCormick, S. (1993) Multigrid methods for flow transition in three-dimensional boundary layers with surface roughness, NASA Contractor Report 4540.
Liu, Z., and Liu, C. (1993) High order finite difference and multigrid methods for spatially evolving instability in a planar channel, J. Comp. Phys., 106, pp.92–100
Liu, C., and Liu, Z. (1995) Multigrid mapping and box relaxation for simulation of the whole process of flow transition in 3-D boundary layers. J. Comput. Phys., 119, pp.325–341
Liu, C. and Liu, Z. (1997) Direct Numerical Simulation for Flow Transition Around Airfoils, Proceedings of First AFOSR International Conference on DNS/LES, Louisiana Tech University, Ruston, Louisiana, August 4–8, 1997, pp.13–28, Edited by C. Liu, Z. Liu and L. Sakell.
Liu, Z., Xiong, G., and Liu, C. (1998) A contravariant velocity based implicit multilevel method for simulating the whole process of incompressible flow transition around Joukowsky airfoils, J. of Applied Mechanics and Engineering, 3(1), pp. 111–161
Poinsot, T. J., Lele, S. K. (1992) Boundary conditions for direct simulations of compressible viscous flows, J. Comput. Phys., 101, pp 104–129
Shan, H., Jiang, L., Zhao, W., and Liu, C. (1999) Large eddy simulation of flow transition in a supersonic flat-plate boundary layer. AIAA Paper 99-0425
Street, C. L., and Macaraeg, M. G. (1989) Spectral multi-domain for large-scale fluid dynamics simulations, Appl. Num. Math., 6, pp.123.
Thompson, K. W. (1987) Time dependent boundary conditions for hyperbolic systems, I, J. Comput. Phys., 68, pp.1–24
Thompson, K. W. (1990) Time dependent boundary conditions for hyperbolic systems, II, J. Comput. Phys., 89, pp.439–461
Visbal, M. R. and Gaitonde, D. V. (1998) High-order accurate methods for unsteady vortical flows on curvilinear meshes, AIAA Paper 98-0131
Whitfield, D. (1983) Three-dimensional unsteady Euler equation solutions using flux vector splitting, Mississippi State University Report.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1999 Springer Science+Business Media Dordrecht
About this paper
Cite this paper
Jiang, L., Shan, H., Liu, C., Visbal, M.R. (1999). Non-Reflecting Boundary Conditions for DNS in Curvilinear Coordinates. In: Knight, D., Sakell, L. (eds) Recent Advances in DNS and LES. Fluid Mechanics and its Applications, vol 54. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-4513-8_19
Download citation
DOI: https://doi.org/10.1007/978-94-011-4513-8_19
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-5924-4
Online ISBN: 978-94-011-4513-8
eBook Packages: Springer Book Archive