On CFL evolution strategies for implicit upwind methods in linearized Euler equations

International Journal for Numerical Methods in Fluids

Volumn 59, Issue 1, 2009, Pages 1-18

  Bucker H M ^a   Pollul, B ^a   Rasch, A ^a  

^a RWTH AACHEN UNIVERSITY   (Germany)

Author keywords

ADIFOR; Automatic differentiation; CFL number; Euler equations; Implicit upwind methods; QUADFLOW; Sensitivity analysis

Indexed keywords

EVOLUTIONARY ALGORITHMS; HEURISTIC METHODS; LINEARIZATION; SENSITIVITY ANALYSIS;

ADIFOR; AUTOMATIC DIFFERENTIATION; CFL NUMBER; IMPLICIT UPWIND METHODS; QUADFLOW;

EULER EQUATIONS;

EID: 61749097963     PISSN: 02712091     EISSN: 10970363     Source Type: Journal    
DOI: 10.1002/fld.1798     Document Type: Article

References (37)

1. Knoll DA, Keyes DE. Jacobian-free Newton-Krylov methods: a survey of approaches and applications. Journal of Computational Physics 2004; 193(2):357-397.
2. Courant R, Friedrichs K. Supersonic Flow and Shock Waves. Springer: Berlin, 1978.
3. Brakhage K, Müller S. Algebraic-hyperbolic grid generation with precise control of intersection of angles. International Journal for Numerical Methods in Fluids 2000; 33:89-123.
4. Bramkamp F, Gottschlich-Müller B, Hesse M, Lamby P, Müller S, Ballmann J, Brakhage K, Dahmen W. H-adaptive multiscale schemes for the compressible Navier-Stokes equations - polyhedral discretization, data compression and mesh generation. In Flow Modulation and Fluid-Structure-Interaction at Airplane Wings, Ballmann J (ed.). Notes on Numerical Fluid Mechanics and Multidisciplinary Design, vol. 84. Springer: Berlin, 2003; 125-204.
5. Bramkamp F, Lamby P, Müller S. An adaptive multiscale finite volume solver for unsteady and steady state flow computations. Journal of Computational Physics 2004; 197(2):460-490.
6. Bramkamp FD. Unstructured h-adaptive finite-volume schemes for compressible viscous fluid flow. Ph.D. Thesis, RWTH Aachen University, 2003.
7. Luo H, Baum J, Löhner R. A fast, matrix-free implicit method for compressible flows on unstructured grids. Journal of Computational Physics 1998; 146(2):664-690.
8. McHugh PR, Knoll DA. Comparison of standard and matrix-free implementations of several Newton-Krylov solvers. AIAA Journal 1994; 32(12):394-400.
9. Meister A. Comparison of different Krylov subspace methods embedded in an implicit finite volume scheme for the computation of viscous and inviscid flow fields on unstructured grids. Journal of Computational Physics 1998; 140(2):311-345.
10. Meister A, Sonar T. Finite-volume schemes for compressible fluid flow. Surveys on Mathematics for Industry 1998; 8(1):1-36.
11. Meister A, Vömel C. Efficient preconditioning of linear systems arising from the discretization of hyperbolic conservation laws. Advances in Computational Mathematics 2001; 14(1):49-73.
12. Venkatakrishnan V. Implicit schemes and parallel computing in unstructured grid CFD. Technical Report 95-28, Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, 1995.
13. Moir IRM. Measurements on a two-dimensional aerofoil with high-lift devices. AGARD-AR-303: A Selection of Experimental Test Cases for the Validation of CFD Codes, vols 1 and 2. Advisory Group for Aerospace Research & Development, Neuilly-sur-Seine, France, 1994.
14. Kelley CT, Keyes DE. Convergence analysis of pseudo-transient continuation. SIAM Journal on Numerical Analysis 1998; 35(2):508-523.
15. Balay S, Buschelman K, Gropp WD, Kaushik D, Knepley MG, McInnes LC, Smith BF, Zhang H. PETSc Web page, 2001. http://www.mcs.anl.gov/petsc.
16. Balay S, Gropp WD, McInnes LC, Smith BF. Efficient management of parallelism in object oriented numerical software libraries. In Modern Software Tools in Scientific Computing, Arge E, Bruaset AM, Langtangen HP (eds). Birkhäuser: Basel, 1997; 163-202.
17. Hänel D, Schwane R. An implicit flux-vector splitting scheme for the computation of viscous hypersonic flow. AIAA Paper 1989-0274, 1989.
18. Venkatakrishnan V. Convergence to steady state solutions of the Euler equations on unstructured grids with limiters. Journal of Computational Physics 1995; 118(1):120-130.
19. Batten P, Leschziner MA, Goldberg UC. Average-state Jacobians and implicit methods for compressible viscous and turbulent flows. Journal of Computational Physics 1997; 137(1):38-78.
20. van der Vorst HA. Bi-CGSTAB: a fast and smoothly converging variant of Bi-CG for the solution of nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 1992; 13(2):631-644.
21. Pollul B, Reusken A. Preconditioners for linearized discrete compressible Euler equations. Technical Report 247, IGPM, RWTH Aachen University, 2004.
22. Geuzaine P. An implicit upwind finite volume method for compressible turbulent flows on unstructured meshes. Ph.D. Thesis, Université de Liège, 1999.
23. Issman E, Degrez G, Deconinck H. Implicit upwind residual-distribution Euler and Navier-Stokes solver on unstructured meshes. AIAA Journal 1996; 34(10):2021-2028.
24. Vanderstraeten D, Csík A, Rose D. An expert-system to control the CFL number of implicit upwind methods. Technical Report TM 304, Universiteit Leuven, 2000.
25. Mulder W, van Leer B. Experiments with implicit upwind methods for the Euler equations. Journal of Computational Physics 1985; 59(2):232-246.
26. Delanaye M. Polynomial reconstruction finite volume schemes for the compressible Euler- and Navier-Stokes equations on unstructured adaptive grids. Ph.D. Thesis, Université de Liège, 1996.
27. Jones DJ. Reference test cases and contributors. AGARD-AR-211: Test Cases for Inviscid Flow Field Methods. Advisory Group for Aerospace Research & Development, Neuilly-sur-Seine, France, 1986.
28. Ballmann J. Flow modulation and fluid-structure-interaction at airplane wings - survey and results of the Collaborative Research Center SFB 401. DGLR 2002-009, 2002.
29. Ballmann J (ed.). Flow Modulation and Fluid-Structure-Interaction at Airplane Wings. Notes on Numerical Fluid Mechanics and Multidisciplinary Design, vol. 84. Springer: Berlin, 2003.
30. Griewank A. Evaluating Derivatives: Principles and Techniques of Algorithmic Differentiation. SIAM: Philadelphia, PA, 2000.
31. Rall LB. Automatic Differentiation: Techniques and Applications. Lecture Notes in Computer Science, vol. 120. Springer: Berlin, 1981.
32. Berz M, Bischof C, Corliss G, Griewank A (eds). Computational Differentiation: Techniques, Applications, and Tools. SIAM: Philadelphia, 1996.
33. Bücker HM, Corliss GF, Hovland PD, Naumann U, Norris B (eds). Automatic Differentiation: Applications, Theory, and Implementations. Lecture Notes in Computational Science and Engineering, vol. 50. Springer: Berlin, 2005.
34. Corliss G, Faure C, Griewank A, Hascoët L, Naumann U (eds). Automatic Differentiation of Algorithms: From Simulation to Optimization. Springer: New York, 2002.
35. Griewank A, Corliss G. Automatic Differentiation of Algorithms. SIAM: Philadelphia, 1991.
36. Bischof C, Carle A, Khademi P, Mauer A. Adifor 2.0: automatic differentiation of Fortran 77 programs. IEEE Computational Science and Engineering 1996; 3(3):18-32.
37. Bischof CH, Bücker HM, Hovland PD. On combining computational differentiation and toolkits for parallel scientific computing. In Euro-Par 2000 - Parallel Processing, Proceedings of the 6th International Euro-Par Conference, Bode A, Ludwig T, Karl W, Wismüller R (eds), Munich, Germany, August/September 2000. Lecture Notes in Computer Science, vol. 1900. Springer: Berlin, 2000; 86-94.