Abstract
Hyperbolic conservation laws are utilized to describe a variety of real-world applications, which require the consideration of the influence of uncertain parameters on the solution to the problem. To extend these models, one is often interested in including discontinuities in the state space to the flux function of the conservation law. This paper studies the solution of a stochastic nonlinear hyperbolic partial differential equation (PDE), whose flux function contains random spatial discontinuities. The first part of the paper defines the corresponding stochastic adapted entropy solution and required properties for existence and uniqueness are addressed. The second part contains the numerical simulation of the nonlinear hyperbolic problem as well as the estimation of the expectation of the problem via the multilevel Monte Carlo method.
Keywords
- Stochastic conservation laws
- Discontinuous flux function
- Stochastic entropy solution
- Jump-advection coefficient
- Uncertainty quantification
- Finite volume method
MSC (2010)
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Funded by Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy—EXC 2075—390740016.
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Brencher, L., Barth, A. (2020). Hyperbolic Conservation Laws with Stochastic Discontinuous Flux Functions. In: Klöfkorn, R., Keilegavlen, E., Radu, F.A., Fuhrmann, J. (eds) Finite Volumes for Complex Applications IX - Methods, Theoretical Aspects, Examples. FVCA 2020. Springer Proceedings in Mathematics & Statistics, vol 323. Springer, Cham. https://doi.org/10.1007/978-3-030-43651-3_23
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DOI: https://doi.org/10.1007/978-3-030-43651-3_23
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