A second-order-accurate monotone implicit fluctuation splitting scheme for unsteady problems

Journal of Computational Physics

Volumn 208, Issue 1, 2005, Pages 1-33

  De Palma, P ^a   Pascazio, G ^a   Rossiello, G ^a   Napolitano, M ^a  

^a POLITECNICO DI BARI   (Italy)

Author keywords

Consistent mass matrix; Dual time stepping technique; Monotone solutions; Residual distribution method; Unsteady hyperbolic equations

Indexed keywords

CONSISTENT-MASS MATRICES; DUAL-TIME STEPPING TECHNIQUES; FLUCTUATION SPLITTING; HYPERBOLIC EQUATIONS; MONOTONE SOLUTION; RESIDUAL-DISTRIBUTION METHODS; SECOND ORDERS; SECOND-ORDER ACCURACY; UNSTEADY HYPERBOLIC EQUATION; UNSTEADY PROBLEMS;

COMPUTATIONAL METHODS;

EID: 19044379980     PISSN: 00219991     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jcp.2004.11.023     Document Type: Article

References (28)

1. P.L. Roe Characteristic-based schemes for the Euler equations Ann. Rev. Fluid Mech. 18 1986 337-365
2. E. Godlewski P. Raviart Hyperbolic systems of conservation laws Applied Mathematical Sciences 1995 Springer Berlin
3. B. Cockburn C.-W. Shu The local discontinuous Galerkin method for time-dependent convection-diffusion systems SIAM J. Numer. Anal. 35 6 1998 2440-2463
4. R. Struijs H. Deconinck P.L. Roe Fluctuation splitting schemes for the 2D Euler equations, VKI LS 1991-01 Computational Fluid Dynamics 1991 von Karman Institute Belgium
5. E. van der Weide H. Deconinck E. Issmann G. Degrez Fluctuation splitting schemes for multidimensional convection problems: An alternative to finite volume and finite element methods Comput. Mech. 23 2 1999 199-208
6. P.L. Roe, Fluctuations and signals - a framework for numerical evolution problems, in: Numerical Methods for Fluid Dynamics, Proceedings Conference, Reading, 1982, pp. 219-257
7. R. Struijs, H. Deconinck, P. De Palma, P.L. Roe, K.G. Powell, Progress on multidimensional upwind Euler solvers for unstructured grids, AIAA Paper 91-1550, 1991
8. P.L. Roe D. Sidilkover Optimum positive linear schemes for advection in two and three dimensions SIAM J. Numer. Anal. 29 6 1992 1542-1588
9. H. Deconinck P.L. Roe R. Struijs A multidimensional generalization of Roe's flux difference splitter for the Euler equations Comput. Fluids 22 1993 215-222
10. H. Deconinck R. Struijs H. Paillère L.A. Catalano P. De Palma M. Napolitano G. Pascazio Development of cell-vertex multidimensional upwind solvers for the compressible flow equations CWI Quart. 6 1 1993 1-28
11. L.A. Catalano P. De Palma G. Pascazio M. Napolitano Cell-vertex adaptive Euler method for cascade flows AIAA J. 33 12 1995 2299-2304
12. E. van der Weide, H. Deconinck, Positive matrix distribution schemes for hyperbolic systems, in: Computational Fluid Dynamics '96, 1996, pp. 747-753
13. A. Bonfiglioli, P. De Palma, G. Pascazio, M. Napolitano, An implicit fluctuation splitting scheme for turbomachinery flows, ASME J. Turbomach, in press (2005)
14. J. März, G. Degrez, Improving time accuracy for residual distribution schemes, von Karman Institute Project Report 1996-17, 1996
15. A. Ferrante, H. Deconinck, Solution of the unsteady Euler equations using residual distribution and flux corrected transport, von Karman Institute Project Report 1997-08, 1997
16. M.E. Hubbard P.L. Roe Compact high resolution algorithms for time dependent advection problems on unstructured grids Int. J. Numer. Methods Fluids 33 2000 711-736
17. Á. Csík, M. Ricchiuto, H. Deconinck, S. Poedts, Space-time residual distribution schemes for hyperbolic conservation laws, AIAA Paper 2001-2617, 2001
18. D. Caraeni L. Fuch Compact third-order multidimensional upwind scheme for Navier-Stokes simulations Theoret. Comput. Fluid Dynamics 15 2002 373-401
19. R. Abgrall M. Mezine Construction of second order accurate monotone and stable residual distribution schemes for unsteady flow problems J. Comput. Phys. 188 2003 16-55
20. R. Lohner K. Morgan M. Vahadati J.P. Boris D.L. Book FEM-FCT: Combining unstructured grids with high resolution Commun. Appl. Numer. Methods 4 1988 717-729
21. P. De Palma G. Pascazio M. Napolitano A second-order-accurate fluctuation splitting scheme for unsteady hyperbolic problems Notes on Numerical Fluid Mechanics vol. 78 2001 Springer New York pp. 103-116
22. H. Paillère, Multidimensional upwind residual distribution schemes for the Euler and Navier-Stokes equations on unstructured grids, Ph.D Thesis, Université Libre de Bruxelles, Belgium, 1995
23. A. Jameson, Time dependent calculations using multigrid with applications to unsteady flows past airfoils and wings, AIAA Paper 91-1596, 1991
24. M. Mezine, M. Ricchiuto, R. Abgrall, H. Deconinck, Monotone and stable residual distribution schemes on prismatic space-time elements for unsteady conservation laws, von Karman Institute Lecture Series 2003-05, 2003
25. E. van der Weide H. Deconinck Positive matrix distribution schemes for hyperbolic systems, with applications to the Euler equations Computational Fluid Dynamics '96 1996 Wiley New York pp. 747-753
26. P. De Palma G. Pascazio M. Napolitano A hybrid fluctuation splitting scheme for two-dimensional compressible steady flows in: M.M. Hafez J.J. Chattot (Eds.) Innovative Methods for Numerical Solution of Partial Differential Equations 2002 World Scientific New Jersey 305-333
27. K.R. Meadows, A. Kumar, M.Y. Hussaini, A computational study of the interaction between a vortex and a shock wave, AIAA Paper 89-1043, 1989
28. R.J. Le Veque Wave propagation algorithms for multidimensional hyperbolic systems J. Comput. Phys. 131 1997 327-353