A hyperbolicity-preserving discontinuous stochastic Galerkin scheme for uncertain hyperbolic systems of equations

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:370

Article

Duerrwaechter, Jakob¹  Kuhn, Thomas¹  Meyer, Fabian²  Schlachter, Louisa³  Schneider, Florian³ 

[1] Univ Stuttgart, Inst Aerodynam & Gasdynam, Pfaffenwaldring 21, D-70569 Stuttgart, Germany

[2] Univ Stuttgart, Inst Angew Anal & Numer Simulat, Pfaffenwaldring 57, D-70569 Stuttgart, Germany

[3] TU Kaiserslautern, Fachbereich Math, Erwin Schrodinger Str, D-67663 Kaiserslautern, Germany

关键词: Uncertainty quantification;    Polynomial chaos;    Stochastic Galerkin;    Discontinuous Galerkin;    Hyperbolicity;    Multi-element;   

DOI  :  10.1016/j.cam.2019.112602

来源: Elsevier

【 摘 要 】

Intrusive Uncertainty Quantification methods such as stochastic Galerkin are gaining popularity, whereas the classical stochastic Galerkin approach is not ensured to preserve hyperbolicity of the underlying hyperbolic system. We apply a modification of this method that uses a slope limiter to retain admissible solutions of the system, while providing high-order approximations in the physical and stochastic space. This is done using a spatial discontinuous Galerkin scheme and a Multi-Element stochastic Galerkin ansatz in the random space. We analyze the convergence of the resulting scheme and apply it to the compressible Euler equations with various uncertain initial states in one and two spatial domains with up to three uncertainties. The performance in multiple stochastic dimensions is compared to the non-intrusive Stochastic Collocation method. The numerical results underline the strength of our method, especially if discontinuities are present in the uncertainty of the solution. (C) 2019 Elsevier B.V. All rights reserved.

【 授权许可】

Free