Achieving higher-order time accuracy for dynamic unstructured mesh fluid flow simulations: Role of the GCL

17th AIAA Computational Fluid Dynamics Conference

Volumn , Issue , 2005, Pages

  Mavriplis, Dimitri J ^a   Yang, Zhi ^a  

^a UNIVERSITY OF WYOMING   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

MESH GENERATION; ORDINARY DIFFERENTIAL EQUATIONS; RUNGE KUTTA METHODS; TWO PHASE FLOW;

DEPENDENT VARIABLES; DISCRETIZED EQUATIONS; GEOMETRIC CONSERVATION LAWS; GRID COORDINATES; INVISCID FLOW PROBLEMS; SMOOTH FUNCTIONS; TIME INTEGRATORS; UNSTRUCTURED MESHES;

COMPUTATIONAL FLUID DYNAMICS;

EID: 85085403570     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.2514/6.2005-5114     Document Type: Conference Paper

References (22)

1. Hirsch, C., Numerical Computation of Internal and External Flows, Volume I: Fundamentals of Numerical Discretization, Wiley, New York, NY, 1988.
2. Melson, N. D., Sanetrik, M. D., and Atkins, II. L., "Time-accurate Navier-Stokes calculations with multigrid acceleration, " 6th Copper Mountain Conf. on Multigrid Methods, 1993, pp. 423-439, NASA Conference Publication 3224.
3. Venkatakrishnan, V. and Mavriplis, D. J., "Implicit method for the computation of unsteady flows on unstructured grids, " Proceedings of the 12th AIAA CFD Conference, San Diego CÃ, June 1995, AIAA Paper 95-1705-CP.
4. Mousseau, V. A., Knoll, D. A., and Rider, W. J., "Physics-based preconditioning and the Newton-Krylov method for non-equilibrium radiation diffusion, " Journal of Computational Physics, Vol. 160, No. 2, 2000, pp. 743-765.
5. Kennedy, C. A. and Carpenter, M. II., "Additive Runge-Kutta schemes for convection diffusion reaction equations, " NASA TM-2001-211038.
6. Hijl, II., Carpenter, M. II., Vatsa, V. N., and Kennedy, C. A., "Implicit time integration schemes for the unsteady incompressible Navier-Stokes Equations: laminar flow, " Journal of Computational Physics, Vol. 179, No. 1, 2002, pp. 313-329.
7. Jothiprasad, G., Mavriplis, D. J., and Caughey, D. A., "Iligher-order time integration schemes for the unsteady Navier Stokes equations on unstructured meshes, " Journal of Computational Physics, Vol. 191, 2003, pp. 542-566.
8. Thomas, P. D. and Lombard, C. K., "Geometric Conservation Law and its Application to Flow Computations on Moving Grids, " AIAA Journal, Vol. 17, No. 10, 1979, pp. 1030-1037.
9. Gordnier, R. E. and Melville, R. B., "Transonic Flutter Simulations Using an Implicit Aeroelastic Solver, " AIAA Journal of Aircraft, Vol. 37, No. 5, 2000, pp. 872-879.
10. Zhang, II., Reggio, M., Trepanier, J. Y., and Camarero, R., "Discrete form of the GCL for moving meshes and its implementation in CFD schemes, " Computers and Fluids, Vol. 22, 1993, pp. 9-23.
11. Nkonga, B. and Guillard, II., "Godonuv type method on non-structured meshes for three-dimensional moving boundary problems, " Comp. Methods Appl. Mech. Engrg., Vol. 113, 1994, pp. 183-204.
12. Lesoinne, M. and Farhat, C., "Geometric conservation laws for flow problems with moving boundaries and deformable meshes, and their impact on aeroelastic computations, " Computer Methods in Applied Mechanics and Engineering, Vol. 134, 1996, pp. 71-90.
13. Koobus, B. and Farhat, C., "Second-order time-accurate and geometrically conservative implicit schemes for flow computations on unstructured dynamic meshes, " Computer Methods in Applied Mechanics and Engineering, Vol. 170, 1999, pp. 103-129.
14. Guillard, II. and Farhat, C., "On the significance of the geometric conservation law for flow computations on moving meshes, " Computer Methods in Applied Mechanics and Engineering, Vol. 190, 2000, pp. 1467-1482.
15. Geuzaine, P., Grandmont, C., and Farhat, C., "Design and analysis of ALE schemes with provable second-order time-accuracy for inviscid and viscous flow simulations, " Journal of Computational Physics, Vol. 191, 2003, pp. 206-227.
16. Visbal, M. R. and Gaitonde, D. V., "On the use of high-order flnite-difference schemes on curvilinear deforming meshes, " Journal of Computational Physics, Vol. 181, 2002, pp. 155-185.
17. Yang, Z. and Mavriplis, D. J., "Unstructured Dynamic Meshes with Iligher-order Time Integration Schemes for the Unsteady Navier-Stokes Equations, " AIAA Paper 2005-1222.
18. Butcher, J. C., Numerical methods for ordinary differential equations, Wiley, Chicester, UK, 2003.
19. Smith, R. W. and Wright, J. A., "An implicit edge-based ALE method for the incompressible Navier Stokes equations, " Int. J. Numer. Meth. Fluids, Vol. 43, 2003, pp. 253-278.
20. Lambert, J. D., Numerical methods for ordinary differential systems, Wiley, Chicester, UK, 1991.
21. Baker, T. J., "Mesh Movement and Metamorphosis, " Engineering with Computers, Vol. 18, No. 3, 2002, pp. 188-198.
22. Nielsen, E. J. and Anderson, W. K., "Recent Improvements in Aerodynamic Optimization on Unstructured Meshes, " AIAA Journal, Vol. 40, No. 6, June 2002, pp. 1155-1163.