Automatic resolution control for the finite-volume method, part 1: A-posteriori error estimates

Numerical Heat Transfer, Part B: Fundamentals

Volumn 38, Issue 3, 2000, Pages 237-256

  Jasak, H ^a   Gosman, A D ^b  

^a Computational Dynamics Ltd ^*  (United Kingdom)

^b IMPERIAL COLLEGE LONDON   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000583304     PISSN: 10407790     EISSN: 15210626     Source Type: Journal    
DOI: 10.1080/10407790050192753     Document Type: Article

References (32)

1. Z. Lilek and M. Peric, A Fourth-Order Finite Volume Method with Colocated Variable Arrangement, Comput. Fluids, vol. 24, no. 3, pp. 239-252, 1995.
2. M. J. Berger and J. Oliger, Adaptive Mesh Rehnement for Hyperbolic Partial Differential Equations, J. Comput. Phys., vol. 53, pp. 484-512, 1984.
3. M. J. Berger and P. Collela, Local Adaptive Mesh Rehnement for Shock Hydrodynamics, J. Comput. Phys., vol. 82, pp. 64-84, 1989.
4. M. J. Berger and A. Jameson, Adaptive Multigrid Method for the Euler Equations, Lect. Notes Phys., vol. 218, pp. 92-97, 1985.
5. H. A. Dwyer, Grid Adaptation for Problems in Fluid Dynamics, AIAA J., vol. 22, no. 12, pp. 1705-1712, 1984.
6. W. Speares and E. F. Toro, A High Resolution Algorithm for Time Dependent Shock Dominated Problems with Adaptive Mesh Rehnement, Z. Flugwiss. Weltraumforsch., vol. 19, pp. 267-281, 1995.
7. R. Ldhner, An Adaptive Finite Element Scheme for Transient Problems in CFD, Comput. Meth. Appl. Mech. Eng., vol. 61, pp. 323-338, 1987.
8. R. Ramakrishnan, K. S. Bey, and E. A. Thornton, Adaptive Quadrilateral and Triangular Finite Element Scheme for Compressible Flows, AIAA J., vol. 28, pp. 51-59, 1990.
9. M. J. Berger and A. Jameson, Automatic Adaptive Grid Rehnement for the Euler Equations, AIAA J., vol. 23, no. 4, pp. 561-568, 1985.
10. D. C. Catharell, A Solution-Adaptive-Grid Procedure for Transonic Flow Around Airfoils, Tech. Rep. 88020, Royal Aerospace Establishment, 1988.
11. W. Speares and E. F. Toro, A High-Resolution Algorithm for Time-Dependent Shock Dominated Problems with Adaptive Mesh Refinement, Z. Flugwiss. Weltraumforsch., vol. 19, no. 4, pp. 267-281, 1995.
12. T. Sonar, V. Hannemann, and D. Hempel, Dynamic Adaptivity and Residual Control in Unsteady Compressible Flow Computation, Math. Comput. Model., vol. 20, no. 10-11, pp. 201-213, 1994.
13. J. J. McGuirk, A. M. P. K. Taylor, and J. H. Whitelaw, The Assessment of Numerical Diffusion in the Upwind-Difference Calculations of Turbulent Recirculating Flows, in L. J. S. Bradbury, F. Durst, B. E. Launder, F. W. Schmidt, and J. H. Whitelaw (eds.), Selected Papers from the Third International Symposium on Turbulent Shear Flows, volume 3 of Turbulent Shear Flows, pp. 206-224, University of California, Davis, Sept. 9-11, 1981.
14. P. Tattersall and J. J. McGuirk, Evaluation of Numerical Diffusion Effects in Viscous Flow Calculation, Comput. Fluids, vol. 23, no. 1, pp. 177-209, 1994.
15. W. L. Chen, F. S. Lien, and M. Z. Leschziner, A Local Grid Refinement Scheme within a Multiblock Structured-Grid Strategy for General Flows, in 6th Int. Symp. On CFD, Lake Tahoe, CA, September 1995.
16. D. C. Haworth, S. H. El Tahry, and M. S. Huebler, A Global Approach to Error Estimation and Physical Diagnostics in Multidimensional Fluid Dynamics, Int. J. Numer. Meth. Fluids, vol. 17, no. 1, pp. 75-97, 1993.
17. S. Muzaferija and D. Gosman, Finite-Volume CFD Procedure and Adaptive Error Control Strategy for Grids of Arbitrary Topology, J. Comput. Phys., vol. 138, no. 2, pp. 766-787, 1997.
18. D. Ait-Ali-Yahia, W. G. Habashi, A. Tam, M.-G. Vallet, and M. Fortin, A Directionally Adaptive Methodology Using an Edge-Based Error Estimate on Quadrilateral Grids, Int. J. Numer. Meth. Fluids, vol. 23, pp. 673-690, 1996.
19. J. Dompierre, M.-G. Vallet, M. Fortin, Y. Bourgault, and W. G. Habashi, Anisotropic Mesh Adaptation: Towards a Solver and User Independent CFD, AIAA Paper 97-0861, 1997.
20. W. G. Habashi, J. Dompierre, and Y. Bourgault, Certifiable Computational Fluid Dynamics through Mesh Optimisation, AIAA J., vol. 36, no. 5, pp. 703-711, 1998.
21. S. Caruso, J. H. Ferziger, and J. Oliger, Adaptive Grid Techniques for Elliptic Flow Problems, Tech. Rep. TF-23, Thermosci. Div. Stanford Univ. Stanford, CA, 1985.
22. F. Moukalled and S. Acharya, A Local Adaptive Grid Procedure for Incompressible Flows with Multigridding and Equidistribution Concepts, Int. J. Numer. Meth. Fluids, vol. 13, no. 9, pp. 1085-1111, 1991.
23. M. C. Thompson and J. H. Ferziger, An Adaptive Multigrid Technique for the Incompressible Navier-Stokes Equations, J. Comput. Phys., vol. 82, pp. 94-121, 1989.
24. J. H. Ferziger and M. Peric, Further Discussion of Numerical Error in CFD, Int. J. Numer. Meth. Fluids, vol. 23, pp. 1-12, 1996.
25. H. Jasak, Error Analysis and Estimation in the Finite Volume Method with Applications to Fluid Flows, Ph.D. thesis, Imperial College, University of London, London, 1996.
26. S. Muzaferija, Adaptive Finite Volume Method for Flow Prediction Using Unstructured Meshes and Multigrid Approach, Ph.D. thesis, Imperial College, University of London, London, 1994.
27. J. H. Ferziger and M. Peric, Computational Methods for Fluid Dynamics, Springer-Verlag, Berlin-New York, 1995.
28. C. Helf and U. Kuster, A Finite Volume Method with Arbitrary Polygonal Control Volumes and High Order Reconstruction for the Euler Equations, in S. Wagner, E. H. Hirschel, J. Periaux, and R. Piva (eds.), Computational Fluid Dynamics, pp. 234-238, Wiley, New York, 1994.
29. J. O. Hinze, Turbulence, McGraw-Hill, New York, 1975.
30. R. L. Panton, Incompressible Flow, Wiley, New York, 1984.
31. H. Jasak and A. D. Gosman, Automatic Resolution Control for the Finite-Volume Method, Part 2: Adaptive Mesh Refinement, Numer. Heat Transfer B, vol. 38, no. 3, pp. 257-271, 2000.
32. H. Jasak and A. D. Gosman, Automatic Resolution Control for the Finite-Volume Method, Part 3: Turbulent Flow Applications, Numer. Heat Transfer B, vol. 38, no. 3, pp. 273-290, 2000.