Article2016

Numerical Solution of Scalar Conservation Laws with Random Flux Functions

Siddhartha Mishra · Nils Henrik Risebro · Christoph Schwab · Svetlana A. Tokareva

42 citations0/0 files storedSIAM/ASA Journal on Uncertainty Quantification

No readable copy stored yet — this record is metadata only.

No open-access location is known for this record yet.

Literature note Cite in a project Citation map

Probabilistic and Robust Engineering Design Computational Fluid Dynamics and Aerodynamics Model Reduction and Neural Networks

Abstract

We consider scalar hyperbolic conservation laws in several space dimensions, with a class of random (and parametric) flux functions. We propose a Karhunen--Loève expansion on the state space of the random flux. For random flux functions which are continuously differentiable with respect to the state variable $u$, we prove the existence of a unique random entropy solution. Using a Karhunen--Loève spectral decomposition of the random flux into principal components with respect to the state variables, we introduce a family of parametric, deterministic entropy solutions on high-dimensional parameter spaces. We prove bounds on the sensitivity of the parametric and of the random entropy solutions on the Karhunen--Loève parameters. We also outline the convergence analysis for two classes of discretization schemes, the multilevel Monte Carlo finite volume method (MLMCFVM), developed in [S. Mishra and C. Schwab, Math. Comp., 81 (2012), pp. 1979--2018], [S. Mishra, C. Schwab, and J. Šukys, J. Comput. Phys., 231 (2012), pp. 3365--3388], and [S. Mishra, C. Schwab, and J. Šukys, Multi-level Monte Carlo finite volume methods for uncertainty quantification in nonlinear systems of balance laws, in Uncertainty Quantification in Computational Fluid Dynamics, Lecture Notes in Comput. Sci. Eng. 92, Springer, Heidelberg, 2013, pp. 225--294], and the stochastic collocation finite volume method (SCFVM) of [S. Tokareva, Stochastic Finite Volume Methods for Computational Uncertainty Quantification in Hyperbolic Conservation Laws, Ph.D. dissertation, ETH Diss. Nr. 21498, ETH Zürich, Zürich, Switzerland]. (A corrected version is attached.)

Paper brief

Loading…

Cite this work

Citation unavailable for this work.

BibTeX RIS CSL-JSON

No public copy is stored for this record, so only the metadata is cited.

Citations in this library

Citation map →

Stored only when both papers are in the corpus — 42 citations exist upstream.

References

2008Multilevel Monte Carlo Path Simulation 2006Karhunen–Loève approximation of random fields by generalized fast multipole methods 2011Multi-level Monte Carlo Finite Element method for elliptic PDEs with stochastic coefficients 2008Uncertainty quantification for systems of conservation laws 2006Long-term behavior of polynomial chaos in stochastic flow simulations 2012Sparse tensor multi-level Monte Carlo finite volume methods for hyperbolic conservation laws with random initial data 2010Intrusive Galerkin methods with upwinding for uncertain nonlinear hyperbolic systems 2012Multi-level Monte Carlo finite volume methods for nonlinear systems of conservation laws in multi-dimensions

Cited by

2018A hyperbolicity-preserving stochastic Galerkin approximation for uncertain hyperbolic systems of equations 2016Multi-level Monte Carlo finite volume methods for uncertainty quantification of acoustic wave propagation in random heterogeneous layered medium 2017A multilevel Monte Carlo finite difference method for random scalar degenerate convection–diffusion equations 2019A hyperbolicity-preserving discontinuous stochastic Galerkin scheme for uncertain hyperbolic systems of equations

Explore the map →

Papers that cite the same references — the relational fallback while embeddings are still backfilling.

Imported from OpenAlex (CC0) — nothing here is generated.