Browse > Article
http://dx.doi.org/10.5139/JKSAS.2004.32.9.001

Convergence and Stability Analysis of LU Scheme on Unstructured Meshes: Part I - Euler Equations  

Kim, Joo-Sung (한국과학기술원 항공우주공학과 대학원)
Kwon, Oh-Joon (한국과학기술원 항공우주공학과)
Publication Information
Journal of the Korean Society for Aeronautical & Space Sciences / v.32, no.9, 2004 , pp. 1-11 More about this Journal
Abstract
A comprehensive study has been made for the investigation of the convergence and stability characteristics of the LU scheme for solving the Euler equations on unstructured meshes. The von Neumann stability analysis technique was initially applied to a scalar model equation, and then the analysis was extended to the Euler equations. The results indicated that the convergence rate is governed by a specific combination of flow parameters. Based on this insight, it was shown that the LU scheme does not suffer any convergence deterioration at all grid aspect ratios, as long as the local time step is defined using an appropriate parameter combination.
Keywords
LU scheme; Von Neumann Stability Analysis; Scalar Convection Equation; Euler Equations; Unstructured Meshes;
Citations & Related Records
연도 인용수 순위
  • Reference
1 Sharov, D. and Nakahashi, K., "Reordering of 3-D Hybrid Unstructured Grids for Vectorized LU-SGS Navier-Stokes Computations," AIAA Paper 97-2102, 1997.
2 강희정, 권오준, "비정렬 적응격자를 이용한 로터 정지 비행 공력 해석," 한국항공우주학회지, 제28권, 제8호, 2000, pp. 1-7.
3 Buelow, P. E. O., Venkateswaran, S., and Merkle, C. L., "Grid Aspect Ratio Effects on the Convergence of Upwind Schemes," AIAA Paper 95-0565, 1995.
4 Whitfield, D. L. and Taylor, L. K., "Discretized Newton-relaxation Solution of High Resolution Flux-difference Split Schemes," AIAA Paper 91-1539, 1991.
5 Anderson, W. K. and Bonhaus, D. L., "An Implicit Upwind Algorithm for Computing Turbulent Flows on Unstructured Grids," Computers & Fluids, Vol. 23, No. 1, 1994, pp. 1-21.   DOI   ScienceOn
6 Ekici, K. and Lyrintzis, A. S., "Parallel Newton-Krylov Methods for Rotorcraft Aerodynamics," AIAA Paper 2001-2587, 2001.
7 Anderson, W. K., Thomas, J. L., and Whitfield, D. L., "Multigrid Acceleration of the Flux-Split Euler Equations," AIAA Journal, Vol. 26, No. 6, 1988, pp. 649-654.   DOI   ScienceOn
8 Hirsch, C., "Numerical Computation of Internal and External Flows," John Wiley & Sons, 1988.
9 Weiss, J. M., Maruszewski, J. P., and Smith, W. A., "Implicit Solution of Preconditioned Navier-Stokes Equations Using Algebraic Multigrid," AIAA Journal, Vol. 37, No. 1, 1999, pp. 29-36.   DOI   ScienceOn
10 Frink, N. T., "Assessment of an Unstructured Grid Method for Predicting 3-D Turbulent Viscous Flows," AIAA Paper 96-0292, 1996.
11 Venkatakrishnan, V., "c," ICASE Report, No. 95-28, 1995.
12 Strang, W. Z., Tomaro, R. F., and Grismer, M. J., "The Defining Methods of Cobalt60: A Parallel, Implicit, Unstructured Euler/Navier-Stokes Flow Solver," AIAA Paper 99-0786, 1999.
13 Wright, M. J., Candler, G. V., and Prampolini, M., "Data-Parallel Lower-Upper Relaxation Method for the Navier-Stokes Equations," AIAA Journal, Vol. 34, No. 7, 1996, pp. 1371-1377.   DOI   ScienceOn
14 Luo, H., Baum, J. D., and Lohner, R., "A Fast, Matrix-free Implicit Method for Compressible Flows on Unstructured Grids," J. Computational Physics, Vol. 146, 1998, pp. 664-690.   DOI   ScienceOn
15 Buelow, P.E.O., Venkateswaran, S., and Merkle, C. L., "Stability and Convergence Analysis of Implicit Upwind Schemes," Computers & Fluids, Vol. 30, 2001, pp. 961-988.   DOI   ScienceOn
16 Jespersen, D. C., "Design and Implementation of a Multigrid Code for the Euler Equations," Applied Mathematics and Computation, Vol. 13, 1983, pp. 357-374.   DOI   ScienceOn