Goal-oriented error control of stochastic system approximations using metric-based anisotropic adaptations

JOURNAL OF COMPUTATIONAL PHYSICS

卷:374

Article

Van Langenhove, J.¹  Lucor, D.²  Alauzet, F.³  Belme, A.¹ 

[1] Sorbonne Univ, CNRS, UMR 7190, Inst Jean le Rond dAlembert, F-75005 Paris, France

[2] Univ Paris Saclay, LIMSI, CNRS, Campus Univ Bat 508,Rue John von Neumann, F-91405 Orsay, France

[3] INRIA Saclay, Project Gamma3, F-91126 Palaiseau, France

关键词: Uncertainty quantification;    Error estimation;    Adjoint;    Riemannian metric;    Simplex stochastic collocation;    Anisotropic mesh adaptation;   

DOI  :  10.1016/j.jcp.2018.07.044

来源: Elsevier

【 摘 要 】

The simulation of complex nonlinear engineering systems such as compressible fluid flows may be targeted to make more efficient and accurate the approximation of a specific (scalar) quantity of interest of the system. Putting aside modeling error and parametric uncertainty, this may be achieved by combining goal-oriented error estimates and adaptive anisotropic spatial mesh refinements. To this end, an elegant and efficient framework is the one of (Riemannian) metric-based adaptation where a goal-based a priori error estimation is used as indicator for adaptivity. This work proposes a novel extension of this approach to the case of aforementioned system approximations bearing a stochastic component. In this case, an optimization problem leading to the best control of the distinct sources of errors is formulated in the continuous framework of the Riemannian metric space. Algorithmic developments are also presented in order to quantify and adaptively adjust the error components in the deterministic and stochastic approximation spaces. The capability of the proposed method is tested on various problems including a supersonic scramjet inlet subject to geometrical and operational parametric uncertainties. It is demonstrated to accurately capture discontinuous features of stochastic compressible flows impacting pressure-related quantities of interest, while balancing computational budget and refinements in both spaces. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free