An efficient solver for cumulative density function-based solutions of uncertain kinematic wave models

Ming Cheng; Akil Narayan; Yi Qin; Peng Wang; Xinghui Zhong; Xueyu Zhu

doi:10.1016/j.jcp.2019.01.008

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An efficient solver for cumulative density function-based solutions of uncertain kinematic wave models

Journal article

Peer reviewed

An efficient solver for cumulative density function-based solutions of uncertain kinematic wave models

Ming Cheng, Akil Narayan, Yi Qin, Peng Wang, Xinghui Zhong and Xueyu Zhu

Journal of computational physics, Vol.382, pp.138-151

04/01/2019

DOI: 10.1016/j.jcp.2019.01.008

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https://arxiv.org/pdf/1901.08520View

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Abstract

We develop a numerical framework to implement the cumulative density function (CDF) method for obtaining the probability distribution of the system state described by a stochastic kinematic wave model. The approach relies on the computation of the fine-grained CDF equation of system state, as derived by the CDF method, via the method of characteristics. Due to its linearity, the fine-grained CDF equation is solved far more efficiently than the direct simulation of the kinematic wave model. Since the ensemble mean of the fine-grained CDF solutions is the probability distribution of the original system state, the proposed scheme requires less realizations than direct Monte Carlo simulations (MCS) of the kinematic model and thus converges relatively quickly. We verify the accuracy and effectiveness of our procedure via comparisons with direct MCS of several examples, including a particular kinematic wave system, the Saint-Venant equation. •Numerical framework of the cumulative density function (CDF) method for the stochastic kinematic wave model.•Computation of the fine-grained CDF equation from the CDF formulation via method of characteristics.•Numerically more efficient than direct simulation of the nonlinear kinematic wave model at each realization.•Less realizations are needed than direct simulation of the stochastic kinematic wave model for a desired accuracy.

Kinematic wave model

Uncertainty quantification

Cumulative density function/probabilistic density function method

Saint-Venant equation

Details

Title: Subtitle: An efficient solver for cumulative density function-based solutions of uncertain kinematic wave models
Creators: Ming Cheng - LMIB & School of Mathematics and System Sciences, Beihang University, Beijing, China
Akil Narayan - Department of Mathematics, and Scientific Computing and Imaging (SCI) Institute, The University of Utah, Salt Lake City, UT, USA
Yi Qin - LMIB & School of Mathematics and System Sciences, Beihang University, Beijing, China
Peng Wang - LMIB & School of Mathematics and System Sciences, Beihang University, Beijing, China
Xinghui Zhong - School of Mathematical Sciences, Zhejiang University, Hangzhou, China
Xueyu Zhu - Department of Mathematics, University of Iowa, Iowa City, IA, USA
Resource Type: Journal article
Publication Details: Journal of computational physics, Vol.382, pp.138-151
DOI: 10.1016/j.jcp.2019.01.008
ISSN: 0021-9991
eISSN: 1090-2716
Publisher: Elsevier Inc
Grant note: DOI: 10.13039/501100001809, name: National Natural Science Foundation of China, award: 11571028; name: National Key Research and Development Program of China, award: 2017YFB0701700; DOI: 10.13039/501100010871, name: Recruitment Program of Global Experts; DOI: 10.13039/100000181, name: AFOSR, award: FA9550-15-1-0467; DOI: 10.13039/501100001809, name: National Natural Science Foundation of China, award: 11871428; name: Creative Research Groups of NSFC, award: 11621101; DOI: 10.13039/501100010871, name: Recruitment Program of Global Experts; DOI: 10.13039/100000893, name: Simons Foundation, award: 504054
Language: English
Date published: 04/01/2019
Academic Unit: Mathematics
Record Identifier: 9983986099602771

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