Stochastic finite volume method for uncertainty quantification of transient flow in gas pipeline networks

Tokareva, S.; Zlotnik, A.; Gyrya, V.

doi:10.1016/j.apm.2023.09.017

Stochastic finite volume method for uncertainty quantification of transient flow in gas pipeline networks

Journal Article · Thu Sep 26 00:00:00 EDT 2024 · Applied Mathematical Modelling

DOI:https://doi.org/10.1016/j.apm.2023.09.017· OSTI ID:2007357

^[1]; ^[1]; Gyrya, V. ^[1]

Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)

We develop a weakly intrusive framework to simulate the propagation of uncertainty in solutions of generic hyperbolic partial differential equation systems on graph-connected domains with nodal coupling and boundary conditions. The method is based on the Stochastic Finite Volume (SFV) approach and can be applied for uncertainty quantification (UQ) of the dynamical state of fluid flow over actuated transport networks. The numerical scheme has specific advantages for modeling intertemporal uncertainty in time-varying boundary parameters, which cannot be characterized by strict upper and lower (interval) bounds. We describe the scheme for a single pipe, and then formulate the controlled junction Riemann problem (JRP) that enables the extension to general network structures. In conclusion, we demonstrate the method's capabilities and performance characteristics using a standard benchmark test network.

View Accepted Manuscript (DOE)

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

Sponsoring Organization:: USDOE Laboratory Directed Research and Development (LDRD) Program; USDOE National Nuclear Security Administration (NNSA)

Grant/Contract Number:: 89233218CNA000001

OSTI ID:: 2007357

Alternate ID(s):: OSTI ID: 2369785

Report Number(s):: LA-UR--22-23349

Journal Information:: Applied Mathematical Modelling, Journal Name: Applied Mathematical Modelling Vol. 125; ISSN 0307-904X

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

References (29)

Simulation of transient gas flows in networks Osiadacz, A. International Journal for Numerical Methods in Fluids, Vol. 4, Issue 1 https://doi.org/10.1002/fld.1650040103	journal	January 1984
A new model for gas flow in pipe networks Herty, M.; Mohring, J.; Sachers, V. Mathematical Methods in the Applied Sciences, Vol. 33, Issue 7 https://doi.org/10.1002/mma.1197	journal	July 2009
Numerical Approximation of Hyperbolic Systems of Conservation Laws Godlewski, Edwige; Raviart, Pierre-Arnaud Applied Mathematical Sciences https://doi.org/10.1007/978-1-4612-0713-9	book	January 1996
Polynomial Chaos Approach to Describe the Propagation of Uncertainties Through Gas Networks Gerster, Stephan; Herty, Michael; Chertkov, Michael Progress in Industrial Mathematics at ECMI 2018 https://doi.org/10.1007/978-3-030-27550-1_8	book	January 2019
Numerical Methods for Conservation Laws LeVeque, Randall J. Lectures in Mathematics. ETH Zürich https://doi.org/10.1007/978-3-0348-8629-1	book	January 1992
High Order SFV and Mixed SDG/FV Methods for the Uncertainty Quantification in Multidimensional Conservation Laws Tokareva, Svetlana; Schwab, Christoph; Mishra, Siddhartha Lecture Notes in Computational Science and Engineering https://doi.org/10.1007/978-3-319-05455-1_7	book	January 2014
High Order ENO and WENO Schemes for Computational Fluid Dynamics Shu, Chi-Wang High-Order Methods for Computational Physics https://doi.org/10.1007/978-3-662-03882-6_5	book	January 1999
On the propagation of statistical model parameter uncertainty in CFD calculations Barth, Timothy Theoretical and Computational Fluid Dynamics, Vol. 26, Issue 5 https://doi.org/10.1007/s00162-011-0221-2	journal	February 2011
ENO and WENO Schemes Zhang, Y. -T.; Shu, C. -W. Handbook of Numerical Analysis https://doi.org/10.1016/bs.hna.2016.09.009	book	January 2016
An explicit staggered-grid method for numerical simulation of large-scale natural gas pipeline networks Gyrya, Vitaliy; Zlotnik, Anatoly Applied Mathematical Modelling, Vol. 65 https://doi.org/10.1016/j.apm.2018.07.051	journal	January 2019
Modelling compressors, resistors and valves in finite element simulation of gas transmission networks Bermúdez, Alfredo; Shabani, Mohsen Applied Mathematical Modelling, Vol. 89 https://doi.org/10.1016/j.apm.2020.08.013	journal	January 2021
Shock detection and limiting with discontinuous Galerkin methods for hyperbolic conservation laws Krivodonova, L.; Xin, J.; Remacle, J. -F. Applied Numerical Mathematics, Vol. 48, Issue 3-4 https://doi.org/10.1016/j.apnum.2003.11.002	journal	March 2004
Roe solver with entropy corrector for uncertain hyperbolic systems Tryoen, J.; Le Maître, O.; Ndjinga, M. Journal of Computational and Applied Mathematics, Vol. 235, Issue 2 https://doi.org/10.1016/j.cam.2010.05.043	journal	November 2010
Stochastic modeling of random roughness in shock scattering problems: Theory and simulations Lin, G.; Su, C. -H.; Karniadakis, G. E. Computer Methods in Applied Mechanics and Engineering, Vol. 197, Issue 43-44 https://doi.org/10.1016/j.cma.2008.02.025	journal	August 2008
Predicting shock dynamics in the presence of uncertainties Lin, G.; Su, C. -H.; Karniadakis, G. E. Journal of Computational Physics, Vol. 217, Issue 1 https://doi.org/10.1016/j.jcp.2006.02.009	journal	September 2006
Uncertainty quantification for systems of conservation laws Poëtte, Gaël; Després, Bruno; Lucor, Didier Journal of Computational Physics, Vol. 228, Issue 7 https://doi.org/10.1016/j.jcp.2008.12.018	journal	April 2009
Intrusive Galerkin methods with upwinding for uncertain nonlinear hyperbolic systems Tryoen, J.; Le Maître, O.; Ndjinga, M. Journal of Computational Physics, Vol. 229, Issue 18 https://doi.org/10.1016/j.jcp.2010.05.007	journal	September 2010
Well-balanced and energy stable schemes for the shallow water equations with discontinuous topography Fjordholm, Ulrik S.; Mishra, Siddhartha; Tadmor, Eitan Journal of Computational Physics, Vol. 230, Issue 14 https://doi.org/10.1016/j.jcp.2011.03.042	journal	June 2011
Multi-level Monte Carlo finite volume methods for nonlinear systems of conservation laws in multi-dimensions Mishra, S.; Schwab, Ch.; Šukys, J. Journal of Computational Physics, Vol. 231, Issue 8 https://doi.org/10.1016/j.jcp.2012.01.011	journal	April 2012
Junction-Generalized Riemann Problem for stiff hyperbolic balance laws in networks: An implicit solver and ADER schemes Contarino, Christian; Toro, Eleuterio F.; Montecinos, Gino I. Journal of Computational Physics, Vol. 315 https://doi.org/10.1016/j.jcp.2016.03.049	journal	June 2016
Uncertainty quantification methodology for hyperbolic systems with application to blood flow in arteries Petrella, M.; Tokareva, S.; Toro, E. F. Journal of Computational Physics, Vol. 386 https://doi.org/10.1016/j.jcp.2019.02.013	journal	June 2019
Hyperbolic stochastic Galerkin formulation for the p-system Gerster, Stephan; Herty, Michael; Sikstel, Aleksey Journal of Computational Physics, Vol. 395 https://doi.org/10.1016/j.jcp.2019.05.049	journal	October 2019
Finite volume methods for hyperbolic conservation laws Morton, K. W.; Sonar, T. Acta Numerica, Vol. 16 https://doi.org/10.1017/S0962492906300013	journal	April 2007
Sparse tensor multi-level Monte Carlo finite volume methods for hyperbolic conservation laws with random initial data Mishra, S.; Schwab, Ch. Mathematics of Computation, Vol. 81, Issue 280 https://doi.org/10.1090/S0025-5718-2012-02574-9	journal	April 2012
Multiresolution analysis for stochastic hyperbolic conservation laws Herty, M.; Kolb, A.; Müller, S. IMA Journal of Numerical Analysis https://doi.org/10.1093/imanum/drad010	journal	March 2023
Monotonicity Properties of Physical Network Flows and Application to Robust Optimal Allocation Misra, Sidhant; Vuffray, Marc; Zlotnik, Anatoly Proceedings of the IEEE, Vol. 108, Issue 9 https://doi.org/10.1109/JPROC.2020.3014069	journal	September 2020
Model Reduction and Optimization of Natural Gas Pipeline Dynamics Zlotnik, Anatoly; Dyachenko, Sergey; Backhaus, Scott ASME 2015 Dynamic Systems and Control Conference, Volume 3: Multiagent Network Systems; Natural Gas and Heat Exchangers; Path Planning and Motion Control; Powertrain Systems; Rehab Robotics; Robot Manipulators; Rollover Prevention (AVS); Sensors and Actuators; Time Delay Systems; Tracking Control Systems; Uncertain Systems and Robustness; Unmanned, Ground and Surface Robotics; Vehicle Dynamics Control; Vibration and Control of Smart Structures/Mech Systems; Vibration Issues in Mechanical Systems https://doi.org/10.1115/DSCC2015-9683	conference	January 2016
Fast Iterative Solution of the Optimal Transport Problem on Graphs Facca, Enrico; Benzi, Michele SIAM Journal on Scientific Computing, Vol. 43, Issue 3 https://doi.org/10.1137/20M137015X	journal	January 2021
Stability analysis of a hyperbolic stochastic Galerkin formulation for the Aw-Rascle-Zhang model with relaxation Gerster, Stephan; Herty, Michael Mathematical Biosciences and Engineering, Vol. 18, Issue 4 https://doi.org/10.3934/mbe.2021220	journal	January 2021

Similar Records

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

Journal Article · Thu Feb 28 23:00:00 EST 2019 · Journal of Computational Physics · OSTI ID:1499352

Adaptive Uncertainty Quantification for Stochastic Hyperbolic Conservation Laws

Journal Article · Wed Apr 02 00:00:00 EDT 2025 · SIAM/ASA Journal on Uncertainty Quantification · OSTI ID:2556812

A flexible uncertainty quantification method for linearly coupled multi-physics systems

Journal Article · Sun Sep 01 00:00:00 EDT 2013 · Journal of Computational Physics · OSTI ID:22230788

Related Subjects

97 MATHEMATICS AND COMPUTING
Gas pipeline
Graphs
Hyperbolic conservation law
Mathematics
Semi-intrusive method
Uncertainty quantification

Stochastic finite volume method for uncertainty quantification of transient flow in gas pipeline networks

Citation Formats

References (29)

Similar Records

Related Subjects