Numerical methods for a reliable prediction of water wave phenomena : uncertainty quantification for tsunami runup

Aim of this study is to present robust numerical methods for shallow water equations permitting to correctly predict long water-wave phenomena. A semi-intrusive and polynomialchaos based method are coupled with a residual based distribution scheme by considering several sources of uncertainties in the simulation of a long wave runup on a conical island. Stochastic results are assessed by comparing with Monte Carlo results. Numerical solutions are compared with experimental data by displaying a great sensitivity from physical and modelling uncertainties. Key-words: numerical analysis, uncertainty quantification, shallow water flows, tsunami runup, friction ∗ Research Scientist † Research Scientist ‡ Ph.D. student § Professor at Institut de Mathématiques de Bordeaux ha l-0 06 43 87 8, v er si on 1 23 N ov 2 01 1 Numerical methods for a reliable prediction of long water-wave phenomena Résumé : Aim of this study is to present robust numerical methods for shallow water equations permitting to correctly predict long water-wave phenomena. A semi-intrusive and polynomial-chaos based method are coupled with a residual based distribution scheme by considering several sources of uncertainties in the simulation of a long wave runup on a conical island. Stochastic results are assessed by comparing with Monte Carlo results. Numerical solutions are compared with experimental data by displaying a great sensitivity from physical and modelling uncertainties. Mots-clés : numerical analysis, uncertainty quantification, shallow water flows, tsunami runup, friction ha l-0 06 43 87 8, v er si on 1 23 N ov 2 01 1 Numerics and UQ for tsunami runup 3 Nomenclature J Jacobian Matrix f Residual value vector x Variable value vector F Force, N m Mass, kg ∆x Variable displacement vector α Acceleration, m/s Subscript i Variable number