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An Efficient Solver for Cumulative Density Function-based Solutions of Uncertain Kinematic Wave Models
- Source :
- Journal of Computational Physics, 2018
- Publication Year :
- 2019
-
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 kinematic wave model. The approach relies on Monte Carlo Simulations (MCS) of the fine-grained CDF equation of system state, as derived by the CDF method. This fine-grained CDF equation is solved via the method of characteristics. Each method of characteristics solution is far more computationally efficient than the direct solution of the kinematic wave model, and the MCS estimator of the CDF converges relatively quickly. We verify the accuracy and robustness of our procedure via comparison with direct MCS of a particular kinematic wave system, the Saint-Venant equation.<br />Comment: 19 pages, 6 figures, 3 tables
- Subjects :
- Mathematics - Numerical Analysis
Physics - Computational Physics
65M22, 65M25
Subjects
Details
- Database :
- arXiv
- Journal :
- Journal of Computational Physics, 2018
- Publication Type :
- Report
- Accession number :
- edsarx.1901.08520
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1016/j.jcp.2019.01.008