TY - GEN
T1 - Uncertainty propagation for systems of conservation laws, high order stochastic spectral methods
AU - Poëtte, G.
AU - Després, B.
AU - Lucor, D.
PY - 2011/1/1
Y1 - 2011/1/1
N2 - The application of the stochastic Galerkin-generalized Polynomial Chaos approach (sG-gPC) (Wiener, Am. J. Math. 60:897-936, 1938; Cameron and Martin, Ann. Math. 48:385-392, 1947; Xiu and Karniadakis, SIAM J. Sci. Comp. 24(2):619-644, 2002) for Uncertainty Propagation through NonLinear Systems of Conservation Laws (SLC) is known to encounter several difficulties: dimensionality (see, e.g., Nobile et al., SIAM J. Numer. Anal. 46(5):2309-2345, 2008; Blatman and Sudret, C. R. Méc. 336:518-523, 2008; Witteveen and Bijl, Comp. Struct. 86(23-24):2123-2140, 2008), non linearities (see, e.g., Debusshere et al., J. Sci. Comp. 26:698-719, 2004; Witteveen and Bijl, 47th AIAA Aerospace Sciences Meeting and Exhibit, 2006-2066, 2006), discontinuities (see Wan and Karniadakis, SIAM J. Sci. Comp. 27(1-3), 2006; Lin et al., J. Comp. Phys. 217:260-276, 2006; Le Maître and Knio, J. Comp. Phys. 197:28-57, 2004; Le Maitre et al., J. Comp. Phys. 197:502-531, 2004; Abgrall, Rapport de Recherche INRIA, 2007). In this paper, we first illustrate on a simple SLC (p-system) the difficulties occuring when dealing with non linearities and discontinuities. We will then present a new non adaptive high order uncertainty propagation method based on the entropy of the system of conservation laws, efficient on NonLinear systems and discontinuous solutions. Convergence tests are performed and spectral convergence is reached.
AB - The application of the stochastic Galerkin-generalized Polynomial Chaos approach (sG-gPC) (Wiener, Am. J. Math. 60:897-936, 1938; Cameron and Martin, Ann. Math. 48:385-392, 1947; Xiu and Karniadakis, SIAM J. Sci. Comp. 24(2):619-644, 2002) for Uncertainty Propagation through NonLinear Systems of Conservation Laws (SLC) is known to encounter several difficulties: dimensionality (see, e.g., Nobile et al., SIAM J. Numer. Anal. 46(5):2309-2345, 2008; Blatman and Sudret, C. R. Méc. 336:518-523, 2008; Witteveen and Bijl, Comp. Struct. 86(23-24):2123-2140, 2008), non linearities (see, e.g., Debusshere et al., J. Sci. Comp. 26:698-719, 2004; Witteveen and Bijl, 47th AIAA Aerospace Sciences Meeting and Exhibit, 2006-2066, 2006), discontinuities (see Wan and Karniadakis, SIAM J. Sci. Comp. 27(1-3), 2006; Lin et al., J. Comp. Phys. 217:260-276, 2006; Le Maître and Knio, J. Comp. Phys. 197:28-57, 2004; Le Maitre et al., J. Comp. Phys. 197:502-531, 2004; Abgrall, Rapport de Recherche INRIA, 2007). In this paper, we first illustrate on a simple SLC (p-system) the difficulties occuring when dealing with non linearities and discontinuities. We will then present a new non adaptive high order uncertainty propagation method based on the entropy of the system of conservation laws, efficient on NonLinear systems and discontinuous solutions. Convergence tests are performed and spectral convergence is reached.
UR - https://www.scopus.com/pages/publications/78651562560
U2 - 10.1007/978-3-642-15337-2_27
DO - 10.1007/978-3-642-15337-2_27
M3 - Conference contribution
AN - SCOPUS:78651562560
SN - 9783642153365
T3 - Lecture Notes in Computational Science and Engineering
SP - 293
EP - 305
BT - Spectral and High Order Methods for Partial Differential Equations - Selected Papers from the ICOSAHOM'09 Conference
T2 - 8th International Conference on Spectral and High Order Methods, ICOSAHOM'09
Y2 - 22 June 2009 through 26 June 2009
ER -