Uncertainty quantification methodology for hyperbolic systems with application to blood flow in arteries

Petrella, Marco; Tokareva, Svetlana; Toro, Eleuterio F.

doi:10.1016/j.jcp.2019.02.013

Title: Uncertainty quantification methodology for hyperbolic systems with application to blood flow in arteries

Journal Article · Fri Mar 01 00:00:00 EST 2019 · Journal of Computational Physics

DOI:https://doi.org/10.1016/j.jcp.2019.02.013· OSTI ID:1499352

^[1];

^[2]; Toro, Eleuterio F. ^[3]

Federal Inst. of Technology, Zurich (Switzerland). Dept. of Mathematics
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Univ. of Trento (Italy). Lab. of Applied Mathematics, DICAM

We present a Stochastic Finite Volume - ADER (SFV-ADER) methodology for Uncertainty Quantification (UQ) in the general framework of systems of hyperbolic balance laws with uncertainty in parameters. The resulting method is weakly intrusive, meaning that deterministic solvers need minor modifications to include random contributions, and has no theoretical accuracy barrier. An illustration of the second-order version for the viscous Burgers equation with uncertain viscosity coefficient is first given in detail, under different deterministic initial conditions; the attainment of the theoretically expected convergence rate is demonstrated empirically; results and features of our scheme are discussed. We then extend the SFV-ADER method to a non-linear hyperbolic system with source terms that models one-dimensional blood flow in arteries, assuming uncertainties in a set of parameters of the problem. Results are then compared with measurements in a well-defined 1:1 experimental replica of the network of largest arteries in the human systemic circulation. For a 99%-confidence level, severe influence of parameter fluctuations is seen in pressure profiles, while secondary effects on flow rate profiles become visible, particularly in terminal branches. In conclusion, results suggest that the proposed methodology could successfully be applied to other physical problems involving hyperbolic balance laws.

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Research Organization:: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)

Sponsoring Organization:: USDOE

Grant/Contract Number:: 89233218CNA000001

OSTI ID:: 1499352

Report Number(s):: LA-UR-18-27216

Journal Information:: Journal of Computational Physics, Vol. 386, Issue C; ISSN 0021-9991

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 4 works

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