A Multidimensional fluctuation splitting scheme for the three dimensional Euler equations
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 33 (1999) no. 6, p. 1241-1259
@article{M2AN_1999__33_6_1241_0,
     author = {Bastin, J\'er\^ome and Rog\'e, Gilbert},
     title = {A Multidimensional fluctuation splitting scheme for the three dimensional Euler equations},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {Dunod},
     volume = {33},
     number = {6},
     year = {1999},
     pages = {1241-1259},
     zbl = {0968.76034},
     mrnumber = {1736898},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_1999__33_6_1241_0}
}
Bastin, Jérôme; Rogé, Gilbert. A Multidimensional fluctuation splitting scheme for the three dimensional Euler equations. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 33 (1999) no. 6, pp. 1241-1259. http://www.numdam.org/item/M2AN_1999__33_6_1241_0/

[1] R. Abgrall and J. L. Montagné, Généralisation du schéma d'Osher pour le calcul d'écoulements de mélanges de gaz à concentrations variables et de gaz réels. La Recherche Aérospatiale No. 4 (1989) 1-13. | MR 1040786 | Zbl 0688.76049

[2] V. Billey, Résolution des équations d'Euler par des méthodes d'éléments finis, application aux écoulements 3D de Vaérodynamique Ph. D. thesis, Université Pierre et Marie Curie (1984).

[3] A. Bonfigholi, E. Van Der Weide and H. Deconinck, Study of 3D hypersonic flow using unstructured grid solvers based on multidimensional upwinding. von Karman Institute for Fluid Dynamics report (1996).

[4] H. Deconinck, Ch. Hirsch and J. Peuteman, Characteristic decomposition methods for the multidimensional Euler equations. Lect Notes Phys. 264, Springer-Verlag (1986). | Zbl 0624.76088

[5] H. Deconinck, H. Paillère, R. Struijs and P. L. Roe, Multidimensional upwind schemes based on fluctuation splitting for Systems of conservation laws. J. Comput. Mech. 11 (1993) 323-340. | Zbl 0771.76048

[6] H. Deconinck, P. L. Roe and R. Struijs, A multidimensional generalization of Roe's flux difference splitter for the Euler equations J. Comput. and Fluids 22 (1993) 215-222. | MR 1231645 | Zbl 0790.76054

[7] C. Faure and Y. Papegay, Odyssée Version 1.6. The User's Reference Manual Rapport INRIA 0211 (1997).

[8] A. Jameson and W. Schmidt, Some recent developments in numerical methods for transonic flows. Comput. Methods Appl. Mech. Engrg. 51 (1985) 467-493, North Holland. | MR 822753 | Zbl 0608.76049

[9] H. Paillère, Multidimensional upwind residual distribution schemes for the Euler and Navier-Stokes equations on unstructured grids. Ph. D. thesis, Université Libre de Bruxelles (1995).

[10] H. Paillère, H. Denoninck and E. Der Weide, Upwind residual distribution methods for compressible flow an alternative to finite volume and finite element methods. von Karman Institute for Fluid Dynamics, presented at the 28th CFD Lecture Series (1997).

[11] J. Peraire, J. Peiro, L. Formaggia, K. Morgan and O. C. Zienkiewicz, Finite element Euler computations in three dimensions. Internat J. Numer. Methods Engrg. 26 (1988) 2135-2159. | Zbl 0665.76073

[12] P. L. Roe, Discrete models for the numerical analysis of time-dependent multidimensional gas dynamics J. Comput. Phys. 63 (1986) 458-476. | MR 835826 | Zbl 0587.76126

[13] P. L. Roe Linear advection schemes on triangular meshes. Technical report, Cranfield Institute of Technology, CoA 8720 (1987).

[14] M. Rudgyard, Cell-vertex methods for steady inviscid flow. VKI LS 1993-04, Computational Fluid Dynamics (1993).

[15] Y. Saad and M. H. Schultz, GMRES: A generalized minimal residual algorithm for Solving Nonsymmetric Linear Systems. SIAM J. Sci. Statist. Comput. 7 (1986) 856-869. | MR 848568 | Zbl 0599.65018

[16] V. Selmin, A Multistage method for the solution of the Euler Equations on Unstructured Grids, in Proceedings of the fifth International Symposium on Numerical Methods in Engineering; Vol. 2, R. Gruber, J. Pénaux and R. P. Shaw Eds, Springer-Verlag, Berlin, Heidelberg (1989) 449-454.

[17] D. Sidilkover, Multidimensional upwinding and multigrid, in 12th AIAA CFD Conference, San Diego, Paper 95-1759 (1995).

[18] D. Sidilkover and P. L. Roe, Unification of some advection schemes in two dimensions. Technical Report 95-10, ICASE (1995).

[19] D. Sidilkover, Numerical solution to steady-state problems with discontinuities. Ph. D. thesis, The Weizmann Institute of science, Rehovot, Israel (1989).

[20] R. Struijs, H. Deconinck, P. De Palma, P. L. Roe and K. G. Powell, Progress on multidimensional upwind Euler solvers for unstructured grids. AIAA-91-1550 (1991).

[21] R. Struijs, H. Deconinck and P. L. Roe, Fluctuation Spitting Schemes for the 2D Euler Equations. VKI LS 1991-01, Computational Fluid Dynamics (1991).

[22] B. Van Leer, W. T. Lee and P. Roe, Characteristic Time-Stepping or Local Preconditionning of the Euler Equations, in AIAA l0th Computational Fluid Dynamics Conference (1991), AIAA-91-1552-CP.