Roe solver with entropy corrector for uncertain hyperbolic systems

Journal of Computational and Applied Mathematics

Volumn 235, Issue 2, 2010, Pages 491-506

  Tryoen, J ^a   Le Maitre O ^b   Ndjinga, M ^c   Ern, A ^a  

^a UNIVERSITÉ PARIS EST   (France)

^b CNRS   (France)

^c CEA SACLAY   (France)

Author keywords

Conservation laws; Entropy correction; Galerkin projection; Hyperbolic systems; Roe solver; Stochastic spectral methods; Uncertainty quantification

Indexed keywords

CONSERVATION LAW; GALERKIN PROJECTIONS; HYPERBOLIC SYSTEM; ROE SOLVER; SPECTRAL METHODS; UNCERTAINTY QUANTIFICATIONS;

EIGENVALUES AND EIGENFUNCTIONS; EULER EQUATIONS; GALERKIN METHODS; JACOBIAN MATRICES; SPECTROSCOPY; STOCHASTIC SYSTEMS;

ENTROPY;

EID: 77955708943     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cam.2010.05.043     Document Type: Conference Paper

References (15)

1. R. Ghanem, and P. Spanos Stochastic Finite Elements: A Spectral Approach 2003 Dover
2. G. Lin, C.-H. Su, and G.E. Karniadakis Stochastic modeling of random roughness in shock scattering problems: theory and simulations Comput. Methods Appl. Mech. Engrg. 197 4344 2008 3420 3434
3. R. Abgrall, A simple, flexible and generic deterministic approach to uncertainty quantifications in non linear problems: application to fluid flow problems, Rapport de recherche INRIA, 00325315, 2008.
4. L. Ge, K.F. Cheung, and M.H. Kobayashi Stochastic solution for uncertainty propagation in nonlinear shallow-water equations J. Hydraul. Eng. 2008 1732 1743
5. G. Poette, B. Desprs, and D. Lucor Uncertainty quantification for systems of conservation laws J. Comput. Phys. 228 7 2009 2443 2467
6. D. Gottlieb, and D. Xiu Galerkin method for wave equations with uncertain coefficients Commun. Comput. Phys. 3 2 2008 505 518
7. G. Lin, C.-H. Su, and G.E. Karniadakis Predicting shock dynamics in the presence of uncertainties J. Comput. Phys. 217 1 2006 260 276
8. J. Tryoen, O. Le Matre, M. Ndjinga, and A. Ern Intrusive Galerkin methods with upwinding for uncertain nonlinear hyperbolic systems J. Comput. Phys. 229 2010 6485 6511
9. M. Deb, I. Babuka, and J. Oden Solution of stochastic partial differential equations using Galerkin finite element techniques Comput. Methods Appl. Mech. Engrg. 190 48 2001 6359 6372
10. O. Le Matre, H. Najm, R. Ghanem, and O. Knio Multi-resolution analysis of Wiener-type uncertainty propagation schemes J. Comput. Phys. 197 2 2004 502 531
11. X. Wan, and G.E. Karniadakis Multi-element generalized polynomial chaos for arbitrary probability measures SIAM J. Sci. Comput. 28 3 2006 901 928 (electronic)
12. B. Debusschere, H. Najm, P. Pbay, O. Knio, R. Ghanem, and O. Le Matre Numerical challenges in the use of polynomial chaos representations for stochastic processes SIAM J. Sci. Comput. 26 2 2004 698 719
13. A. Harten High resolution schemes for hyperbolic conservation laws J. Comput. Phys. 49 3 1983 357 393
14. P. Roe Some contributions to the modelling of discontinuous flows Large-scale Computations in Fluid Mechanics, Part 2 La Jolla, Calif., 1983 Lectures in Appl. Math. vol. 22 1985 Amer. Math. Soc. Providence, RI 163 193
15. F. Dubois, and G. Mehlman A non-parameterized entropy correction for Roe's approximate Riemann solver Numer. Math. 73 2 1996 169 208