Journal
JOURNAL OF SCIENTIFIC COMPUTING
Volume 67, Issue 3, Pages 1198-1218Publisher
SPRINGER/PLENUM PUBLISHERS
DOI: 10.1007/s10915-015-0124-2
Keywords
Uncertainty quantification; Hyperbolic balance laws; Well-balanced schemes; Generalized polynomial chaos; Stochastic Galerkin
Categories
Funding
- NSF DMS [1107291, 1107291: RNMS KI-Net]
- National Science Foundation of China [91330203]
- AFOSR
- DOE
- Division Of Mathematical Sciences
- Direct For Mathematical & Physical Scien [1107291] Funding Source: National Science Foundation
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We propose a generalized polynomial chaos based stochastic Galerkin methods for scalar hyperbolic balance laws with random geometric source terms or random initial data. This method is well-balanced (WB), in the sense that it captures the stochastic steady state solution with high order accuracy. The framework of the stochastic WB schemes is presented in details, along with several numerical examples to illustrate their accuracy and effectiveness. The goal of this paper is to show that the stochastic WB scheme yields a more accurate numerical solution at steady state than the non-WB ones.
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