Euler solution using cartesian grid with a gridless least-squares boundary treatment

AIAA Journal

Volumn 43, Issue 2, 2005, Pages 246-255

  Koh, E P C ^a,c   Tsai, H M ^a,c   Liu, F ^b  

^a NATIONAL UNIVERSITY OF SINGAPORE   (Singapore)

^b UNIVERSITY OF CALIFORNIA   (United States)

^c NANYANG TECHNOLOGICAL UNIVERSITY   (Singapore)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTATIONAL COMPLEXITY; LEAST SQUARES APPROXIMATIONS; MATHEMATICAL MODELS; NUMERICAL ANALYSIS; PROBLEM SOLVING;

CARTESIAN GRIDS; COARSE GRIDS; EULER SOLUTIONS;

COMPUTATIONAL FLUID DYNAMICS;

EID: 13444310542     PISSN: 00011452     EISSN: None     Source Type: Journal    
DOI: 10.2514/1.6177     Document Type: Article

References (33)

1. Batina, J. T., "Unsteady Euler Algorithm with Unstructured Dynamic Mesh for Complex Aircraft Aerodynamic Analysis," AIAA Journal, Vol. 29, No. 3, 1991, pp. 327-333.
2. Weatherill, N. P., Hassan, O., Marchant, M. J., and Marcum, D. L., "Adaptive Inviscid Flow Solutions for Aerospace Geometries Using Efficiently Generated Unstructured Tetrahedral Meshes," AIAA Paper 93-3390, 1993.
3. Jameson, A., and Mavriplis, D., "Finite Volume Solution of the Two-Dimensional Euler Equations on a Regular Triangular Mesh," AIAA Journal, Vol. 24, No. 4, 1986, pp. 611-618.
4. Frink, N. T., and Pirzadeh, S. Z., "Tetrahedral Finite-Volume Solutions to the Navier-Stokes Equations on Complex Configurations," 10th International Conf. on Finite Elements in Fluids, Jan. 1998.
5. Meakin, R. L., "Automatic Off-Body Grid Generation for Domains of Arbitrary Size," AIAA Paper 2001-3105, June 2001.
6. Liu, F., Cai, J., Zhu, Y., Wong, A. S. F., and Tsai, H. M., "Calculation of Wing Flutter by a Coupled Fluid-Structure Method," Journal of Aircraft, Vol. 38, No. 2, 2001, pp. 334-342.
7. Meakin, R. L., "Object X-Rays for Cutting Holes in Composite Overset Structured Grids," AIAA Paper 2001-2537, June 2001.
8. Coirier, W. J., and Powell, K. G., "An Accuracy Assessment of Cartesian Mesh Approaches for the Euler Equations," Journal of Computational Physics, Vol. 117, No. 1, 1995, pp. 121-131.
9. Berger, M. J., and LeVeque, R. J., "An Adaptive Cartesian Mesh Algorithm for the Euler Equations in Arbitrary Geometries," AIAA Paper 89-1930, June 1989.
10. Clarke, D. K., Salas, M. D., and Hassan, H. A., "Euler Calculations for Multielement Airfoils Using Cartesian Grids," AIAA Journal, Vol. 24, No. 3, 1986, pp. 353-358.
11. Epstein, B., Luntz, A., and Nachson, A., "Multigrid Euler Solver About Arbitrary Aircraft Configurations, with Cartesian Grids and Local Refinement," AIAA Paper 89-1960, June 1989.
12. Tidd, D. M., Strash, D. J., Epstein, B., Luntz, A., Nachshon, A., and Rubin, T., "Multigrid Euler Calculations over Complete Aircraft," Journal of Aircraft, Vol. 29, No. 6, 1992, pp. 1080-1085.
13. Wu, Z. N., "Anisotropic Cartesian Grid Method for Viscous Flow Computation," Computational Fluid Dynamics Review 1998, edited by M. Hafez and K. Oshima, World Scientific, 1998.
14. Aftosmis, M. J., Berger, M. J., and Adomavicius, G., "A Parallel Multilevel Method for Adaptively Refined Cartesian Grids with Embedded Boundaries," AIAA Paper 2000-0808, Jan. 2000.
15. Zeeuw, D. D., and Powell, K. G., "An Adaptively Refined Cartesian Mesh Solver for the Euler Equations," Journal of Computational Physics, Vol. 104, No. 1, 1993, pp. 56-68.
16. Durbin, P. A., and Iaccarino, G., "An Approach to Local Refinement of Structured Grids," Journal of Computational Physics, Vol. 181, No. 2, 2002, pp. 639-653.
17. Ham, F. E., Lien, F. S., and Strong, A. B., "A Cartesian Grid Method with Transient Anisotropic Adaptation," Journal of Computational Physics, Vol. 179, No. 2, 2002, pp. 469-494.
18. Clarke, D. K., Salas, M. D., and Hassan, H. A., "Euler Calculations for Multi-Element Airfoils Using Cartesian Grids," AIAA Journal, Vol. 24, No. 3, 1986, pp. 353-358.
19. Ye, T., Mittal, R., Udaykumar, H. S., and Shyy, W., "An Accurate Cartesian Grid Method for Viscous Incompressible Flows with Complex Immersed Boundaries," Journal of Computational Physics, Vol. 156, No. 2, 1999, pp. 209-240.
20. "A Cartesian Multigrid Euler Code for Flow Around Arbitrary Configurations," MGAERO User's Manual, Ver. 3.1.4, Analytical Methods, Inc., Redmond, WA, 2001.
21. Forrer, H., and Jeltsch, R., "A Higher-Order Boundary Treatment for Cartesian-Grid Methods," Journal of Computational Physics, Vol. 140, No. 2, 1998, pp. 259-277.
22. Batina, J. T., "A Gridless Euler/Navier-Stokes Solution Algorithm for Complex-Aircraft Applications," AIAA Paper 93-0333, Jan. 1993.
23. Batina, J. T., "A Gridless Euler/Navier-Stokes Solution Algorithm for Complex Two-Dimensional Applications," NASA TM-107631, June 1992.
24. Sridar, D., and Balakrishnan, N., "An Upwind Finite Difference Scheme for Meshless Solvers," Journal of Computational Physics, Vol. 189, No. 1, 2003, pp. 1-29.
25. Liu, J. L., and Su, S. J., "A Potentially Gridless Solution Method for the Euler/Navier-Stokes Equations," AIAA Paper 96-0526, Jan. 1996.
26. Vanka, S. P., and Ploplys, N., "Meshless Methods for Navier-Stokes Equations Using Radial Basis Functions," Advances in Computational Engineering and Sciences, Vol. 2, ICES, 2000.
27. Subrata, R., and Fleming, M., "Nonlinear Subgrid Embedded Element-Free-Galerkin Method for Monotone CFD Solutions," Proceedings of the 3rd ASME/JSME Joint Fluids Engineering Conf., FEDSM99-7023, July 1999.
28. Belytschko, T., Lu, Y. Y., and Gu, L., "Element-Free Galerkin Methods," International Journal of Numerical Methods in Engineering, Vol. 37, No. 2, 1994, pp. 229-256.
29. Kirshman, D. J., and Liu, F., "A Gridless Boundary Condition Method for the Solution of the Euler Equations on Embedded Cartesian Meshes with Multigrid," Journal of Computational Physics, Vol. 201, No. 1, 2004, pp. 119-147.
30. Jameson, A., Schmidt, W., and Turkel, E., "Numerical Solutions of the Euler Equations By Finite Volume Methods Using Runge-Kutta Time-Stepping Schemes," AIAA Paper 81-1259, June 1981.
31. Jameson, A., "Transonic Flow Calculation for Aircraft," Numerical Methods in Fluid Dynamics, edited by F. Brezzi, Vol. 1127, Lecture Notes in Mathematics, Springer-Verlag, 1985, pp. 156-242.
32. Ray, T., and Tsai, H. M., "Some Issues in NURBS Representation of Airfoil Shapes for Optimization," 8th International Conf. on Numerical Grid Generation in Computational Field Simulations, June 2002.
33. Suddhoo, A., and Hall, I. M., "Test Cases for the Plane Potential Flow past Multi-Element Aerofoils," Aeronautical Journal, Vol. 89, Dec. 1985, pp. 403-414.