Adjoint Error Estimation and Grid Adaptation for Functional Outputs: Application to Quasi-One-Dimensional Flow

Journal of Computational Physics

Volumn 164, Issue 1, 2000, Pages 204-227

  Venditti, David A ^a   Darmofal, David L ^a  

^a Massachusetts Institute of Technology   (United States)

Author keywords

Adjoint; Error estimation; Functional output; Grid adaptation

Indexed keywords

COMPUTATIONAL FLUID DYNAMICS; ERRORS;

ADAPTIVE STRATEGY; ADJOINT FORMULATION; ADJOINTS; ESTIMATED ERROR; ESTIMATION PROCEDURES; FUNCTIONAL OUTPUTS; GRID ADAPTATION; QUASI-ONE-DIMENSIONAL FLOW; SIMULATION ERROR; UNIFORM GRIDS;

FINITE VOLUME METHOD;

EID: 0000238006     PISSN: 00219991     EISSN: None     Source Type: Journal    
DOI: 10.1006/jcph.2000.6600     Document Type: Article

References (30)

1. Ainsworth M., Oden J. T. A posteriori error estimation in finite element analysis. Comput. Meth. Appl. Mech. Eng. 142:1997;1.
2. Babuška I., Miller A. The post-processing approach in the finite element method - Part 1: Calculation of displacements, stresses and other higher order derivatives of the displacements. Int. J. Numer. Meth. Eng. 20:1984;1085.
3. Baker T. J. Mesh adaptation strategies for problems in fluid dynamics. Finite Elements Anal. Design. 25:1997;243.
4. Becker R., Rannacher R. Weighted A Posteriori Error Control in Finite Element Methods. 1994.
5. Braack M., Rannacher R. Adaptive Finite Element Methods for Low-Mach-Number Flows with Chemical Reactions. 30th Computational Fluid Dynamics. 1999.
6. Elliot J., Peraire J. Aerodynamic Optimization on Unstructured Meshes with Viscous Effects. 1997.
7. Giles M. B. Analysis of the accuracy of shock-capturing in the steady quasi-1D Euler equations. Comput. Fluid Dyn. J. 5:1996;247.
8. M. B. Giles, On adjoint equations for error analysis and optimal grid adaptation in CFD, in, Computing the Future II: Advances and Prospects in Computational Aerodynamics, edited by, M. Hafez and D. A. Caughey, Wiley, New York, 1998.
9. Giles M. B., Pierce N. A. Adjoint Equations in CFD: Duality, Boundary Conditions and Solution Behavior. 1997.
10. Hétu J. F., Pelletier D. H. Fast, adaptive finite element scheme for viscous incompressible flows. AIAA J. 30:1992;2677.
11. Hirsch C. Numerical Computation of Internal and External Flows. Computational Methods for Inviscid and Viscous Flows. 2:1992.
12. Jameson A., Pierce N. A., Martinelli L. Optimum Aerodynamic Design Using the Navier-Stokes Equations. 1997.
13. Johnson C., Rannacher R. On Error Control in CFD. 1994.
14. L. Machiels, J. Peraire, and, A. T. Patera, A posteriori finite element bounds for the incompressible Navier-Stokes equations: Application to a natural convection problem, submitted for publication.
15. Nielsen E. J., Anderson W. K. Aerodynamic Design Optimization on Unstructured Meshes Using the Navier-Stokes Equations. 1998.
16. E. Onate, and, G. Bugeda, Mesh optimality criteria for adaptive finite element computations, in, The Mathematics of Finite Elements and Applications, edited by, J. R. Whiteman, Wiley Chichester, England, 1994, p, 121.
17. Peraire J., Patera A. T. Asymptotic a posteriori finite element bounds for the outputs of noncoercive problems: The Helmholtz and Burgers equations. Comput. Meth. Appl. Mech. Eng. 171:1999;77.
18. Peraire J., Vahdati M., Morgan K., Zienkiewicz O. C. Adaptive remeshing for compressible flow computations. J. Comput. Phys. 72:1987;449.
19. Pierce N. A., Giles M. B. Adjoint recovery of superconvergent functionals from PDE approximations. SIAM Rev. 42:2000;247.
20. Richardson L. F. The approximate arithmetic solution by finite differences of physical problems involving differential equations with application to stresses in a masonry dam. Trans. Roy. Soc. London Ser. A. 210:1910;307.
21. Richardson L. F. The deferred approach to the limit. Trans. Roy. Soc. London Ser. A. 226:1927;299.
22. Roe P. L. Approximate Riemann solvers, parameter vectors, and difference schemes. J. Comput. Phys. 43:1981;357.
23. Shapiro A. H. The Dynamics and Thermodynamics of Compressible Fluid Flow. 1:1953.
24. van Albada G. D., van Leer B., Roberts W. W. A comparative study of computational methods in cosmic gas dynamics. Astron. Astrophys. 108:1982;95.
25. van Leer B. Towards the ultimate conservative difference scheme. V. A second order sequel to Godunov's method. J. Comput. Phys. 32:1979;101.
26. Venditti D. A., Darmofal D. L. Grid Adaptation for Functional Outputs of 2-D Compressible Flow Simulations. 2000.
27. Warren G. P., Anderson W. K., Thomas J. T., Krist S. L. Grid Convergence for Adaptive Methods. 1991.
28. Wu J., Zhu J. Z., Szmelter J., Zienkiewicz O. C. Error estimation and adaptivity in Navier-Stokes incompressible flows. Comput. Mech. 6:1990;259.
29. Zienkiewicz O. C., Zhu J. Z. A simple error estimation and adaptive procedure for practical engineering analysis. Int. J. Numer. Meth. Eng. 24:1987;337.
30. Zienkiewicz O. C., Zhu J. Z. The superconvergent patch recovery and a posteriori error estimates. Part 1: The recovery technique. Int. J. Numer. Meth. Eng. 33:1992;1331.