Improvement of stability and accuracy for weighted essentially nonoscillatory scheme

AIAA Journal

Volumn 47, Issue 2, 2009, Pages 331-344

  Shen, Yiqing ^a,b   Zha, Gecheng ^a,b   Wang, Baoyuan ^a,b  

^a UNIVERSITY OF MIAMI   (United States)

^b Miami Wind   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ACCURATE FINITE DIFFERENCE SCHEMES; CONVERGENCE RATES; FINITE DIFFERENCE SCHEMES; GAUSS SEIDELS; HIGH-ORDER SCHEMES; LINE RELAXATIONS; NONOSCILLATORY; NUMERICAL DISSIPATIONS; OPTIMUM VALUES; SHOCK PROFILES; SMOOTH REGIONS; THIRD ORDERS; TIME-MARCHING; WALL BOUNDARY CONDITIONS; WALL SURFACES; WEIGHTED ESSENTIALLY NON-OSCILLATORY SCHEMES; WEIGHTED ESSENTIALLY NONOSCILLATORY;

BOUNDARY CONDITIONS;

SUPERSONIC FLOW;

EID: 60049085651     PISSN: 00011452     EISSN: None     Source Type: Journal    
DOI: 10.2514/1.37697     Document Type: Article

References (34)

1. Liu, X. D., Osher, S., and Chan, T., "Weighted Essentially Nonoscillatory Schemes," Journal of Computational Physics, Vol. 115, No. 1, 1994, pp. 200-212. doi:10.1006/jcph.1994.1187
2. Jiang, G. S., and Shu, C. W., "Efficient Implementation of Weighted ENO Schemes," Journal of Computational Physics, Vol. 126, No. 1, 1996, pp. 202-228. doi:10.1006/jcph.1996.0130
3. Titarev, V. A., and Toro, E. F., "Finite-Volume WENO Schemes for Three-Dimensional Conservation Laws," Journal of Computational Physics, Vol. 201, No. 1, 2004, pp. 238-260. doi:10.1016/j.jcp.2004.05.015
4. Zhou, T., Li, Y., and Shu, C. W., "Numerical Comparison of WENO Finite Volume and Runge-Kutta Discontinuous Galerkin Methods," Journal of Scientific Computing, Vol. 16, No. 2, 2001, pp. 145-171. doi:10.1023/A:1012282706985
5. Latini, M., Schilling, O., and Don, W. S., "Effects of WENO Flux W. S., "Effects of WENO Flux Reconstruction Order and Spatial Resolution on Reshocked Two-Dimensional Richtmyer-Meshkov Instability," Journal of Computational Physics, Vol. 221. No. 2, 2007, pp. 805-836. doi:10.1016/j.jcp.2006.06.051
6. Crnjaric-Zic, N., Vukovic, S., and Sopta, L., "Balanced Finite Volume WENO and Central WENO Schemes for the Shallow Water and the Open-Channel Flow Equations," Journal of Computational Physics, Vol. 200, No. 2, 2004, pp. 512-548. doi:10.1016/j.jcp.2004.04.012
7. Beaza, A., and Mulet, P., "Adaptive Mesh Refinement Techniques for High-Order Shock Capturing Schemes for Multi-Dimensional Hydrodynamic Simulations," International Journal for Numerical Methods in Fluids, Vol. 52, No. 4, 2006, pp. 455-471. doi:10.1002/fld.1191
8. Sjogreen, B., and Yee, H. C, "Low Dissipative High-Order Numerical Simulations of Supersonic Reactive Flows," International Journal for Numerical Methods in Fluids, Vol. 43, Nos. 10-11, 2003, pp. 1221-1238. doi:10.1002/fld.507
9. Shu, C. W., "Essentially Non-Oscillatory and Weighted Essentially Non-Oscillatory Schemes for Hyperbolic Conservation Laws," NASA CR-97-206253, Inst, for Computer Applications in Science and Engineering Rept. No. 97-65, Nov. 1997.
10. Van Leer, B., 'Towards the Ultimate Conservative Difference Scheme, III," Journal of Computational Physics, Vol. 23, No. 3, 1977, pp. 263-275. doi:10.1016/0021-9991(77)90094-8
11. Nichols, R. H., Tramel, R. W., and Buning, P. G., "Evaluation of Two High Order WENO Schemes," AIAA Paper 2007-3920, 2007.
12. Nichols, R. H., Tramel, R. W., and Buning, P. G., "Solver and Turbulence Model Upgrades to OVERFLOW 2 for Unsteady and High-Speed Applications," AIAA Paper 2006-2824, 2006.
13. Chen, Y. N., Yang, S. C, and Yang, J. Y., "Implicit Weighted Essentially Non-Oscillatory Schemes for the Incompressible Navier-Stokes Equations," International Journal for Numerical Methods in Fluids, Vol. 31, No. 4, 1999, pp. 747-765. doi:10.1002/(SICI)1097-0363(19991030)31: 4〈747::AIDFLD901〉 3.0.CO;2-F
14. Yang, J., Perng, Y., and Yen, R., "Implicit Weighted Essentially Non-Oscillatorv Schemes for the Compressible Navier-Stokes Equations," AIAA Journal, Vol. 39, No. 11, 2001, pp. 2082-2090. doi:10.2514/2.1231
15. Cadiou, A., and Tenaud, C, "Implicit WENO Shock Capturing Scheme for Unsteady Flows, Application to One-Dimensional Euler Equations," International Journal for Numerical Methods in Fluids, Vol. 45, No. 2, 2004, pp. 197-229. doi:10.1002/fld.685
16. Yuan, L., "Comparison of Implicit Multigrid Schemes for Three-Dimensional Incompressible Flows," Journal of Computational Physics, Vol. 177, No. 1, 2002, pp. 134-155. doi:10.1006/jcph.2002.7007
17. Shen, Y. Q., Wang, B. Y., and Zha, G. C, "Comparison Study of Implicit Gauss-Seidel Line Iteration Method for Transonic Flows," AIAA Paper 2007-4332, June 2007.
18. Zhang, S. H., and Shu, C. W., "A New Smoothness Indicator for the WENO Schemes and Its Effect on the Convergence to Steady State Solutions," Journal of Scientific Computing, Vol. 31, Nos. 1-2, 2007, pp. 273-305. doi:10.1007/s10915-006-9111-y
19. Henrick, A. K., Aslam, T. D., and Powers, J. M., "Mapped Weighted Essentially Non-Oscillatory Schemes: Achiving Optimal Order Near Critical Points," Journal of Computational Physics, Vol. 208, No. 1, 2005, pp. 206-227. doi:10.1016/j.jcp.2005.02.006
20. Pantano, C, Deiterding, R., Hill, D. J., and Pullin, D. 1., "A Low Numerical Dissipation Patch-Based Adaptive Mesh Refinement Method for Large-Eddy Simulation of Compressible Flows," Journal of Computational Physics, Vol. 221, No. 1, 2007, pp. 63-87. doi:10.1016/j.jcp.2006.06.011
21. Taylor, E. M., and Martin, M. P., "Stencil Adaptation Properties of a WENO Scheme in Direct Numerical Simulations of Compressible Turbulence," Journal of Scientific Computing, Vol. 30, No. 3, 2007, pp. 533-554. doi:10.1007/s10915-006-9126-4
22. Taylor, E. M., Wu, M., and Martin, M. P., "Optimization of Nonlinear Error for Weighted Non-Oscillatory Methods in Direct Numerical Simulations of Compressible Turbulence," Journal of Computational Physics, Vol. 223, No. 1, 2007, pp. 384-397. doi:10.1016/j.jcp.2006.09.010
23. Piraux, J., and Lombard, B., "A New Interface Method for Hyperbolic Problems with Discontinuous Coefficients: One-Dimensional Acoustic Example," Journal of Computational Physics, Vol. 168, No. 1, 2001, pp. 227-248. doi:10.1006/jcph.2001.6696
24. Jameson, A., "Time Dependent Calculations Using Multigrid with Application to Unsteady Flows past Airfoils and Wings," AIAA Paper91-1596, 1991.
25. Lee, S., Lele, S. K., and Moin, P., "Interaction of Isotropic Turbulence with Shock Waves: Effect of Shock Strength," Journal of Fluid Mechanics, Vol. 340, 1997, pp. 225-247. doi:10.1017/S0022112097005107
26. Moin, P., and Mahesh, K., "Direct Numerical Simulation: A Tool in Turbulence Research," Annual Review of Fluid Mechanics, Vol. 30, Jan. 1998, pp. 539-578. doi:10.1146/annurev.fluid.30.1.539
27. Baldwin, B., and Lomax, H., "Thin Layer Approximation and Algebraic Model for Separated Turbulent Flows," AIAA Paper 78-257, 1978.
28. Shen, Y. Q., Wang.B. Y., andZha, G. C, "Implicit WENO Scheme and High Order Viscous Formulas for Compressible Flows," AIAA Paper 2007-4431, June 2007.
29. Roe, P., "Approximate Riemann Solvers, Parameter Vectors, and Difference Schemes," Journal of Computational Physics, Vol. 43, No. 2, 1981, pp. 357-372. doi:10.1016/0021-9991(81)90128-5
30. Hu, Z., and Zha, G.-C, "Calculations of 3D Compressible Flows Using an Efficient Low Diffusion Upwind Scheme," International Journal for Numerical Methods in Fluids, Vol. 47, No. 3, 2005, pp. 253-269. doi:10.1002/fld.810
31. Hu, Z. J., "Parallel Computation of Fluid-Structural Interactions Using High Resolution Upwind Schemes," Ph.D. Thesis, Dept. of Mechanical and Aerospace Engineering, Univ. of Miami, Coral Gables, FL, May 2005.
32. Chen, X., and Zha, G.-C., "Fully Coupled Fluid-Structural Interactions Using an Efficient High Solution Upwind Scheme," Journal of Fluids and Structures, Vol. 20, No. 8, 2005, pp. 1105-1125. doi:10.1016/j.jfluidstructs.2005.02.011
33. White, F. M., Viscous Fluid Flows, 2nd ed. McGraw-Hill, New York, 1991
34. Mason, M. L., and Putnam, L. E., "The Effect of Throat Contouring on Two-Dimensional Converging-Diverging Nozzles at Static Conditions," NASA, TP 1704, 1980.