Stabilized FE simulation of prototype thermal-hydraulics problems with integrated adjoint-based capabilities
Abstract
A critical aspect of applying modern computational solution methods to complex multiphysics systems of relevance to nuclear reactor modeling, is the assessment of the predictive capability of specific proposed mathematical models. The understanding of numerical error, the sensitivity of the solution to parameters associated with input data, boundary condition uncertainty, and mathematical models is critical. Additionally, the ability to evaluate and or approximate the model efficiently, to allow development of a reasonable level of statistical diagnostics of the mathematical model and the physical system, is of central importance. In our study we report on initial efforts to apply integrated adjoint-based computational analysis and automatic differentiation tools to begin to address these issues. The study is carried out in the context of a Reynolds averaged Navier–Stokes approximation to turbulent fluid flow and heat transfer using a particular spatial discretization based on implicit fully-coupled stabilized FE methods. We present the initial results that show the promise of these computational techniques in the context of nuclear reactor relevant prototype thermal-hydraulics problems.
- Authors:
-
- Sandia National Lab. (SNL-NM), Albuquerque, NM (United States). Computational Mathematics Dept. and Dept. of Mathematics and Statistics
- Sandia National Lab. (SNL-NM), Albuquerque, NM (United States). Multiphysics Applications Dept.
- Sandia National Lab. (SNL-NM), Albuquerque, NM (United States). Computational Mathematics Dept.
- Sandia National Lab. (SNL-NM), Albuquerque, NM (United States). Optimization and UQ Dept.
- Publication Date:
- Research Org.:
- Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
- Sponsoring Org.:
- USDOE Office of Nuclear Energy (NE); USDOE Office of Science (SC)
- OSTI Identifier:
- 1338379
- Alternate Identifier(s):
- OSTI ID: 1329336
- Report Number(s):
- SAND2016-12353J
Journal ID: ISSN 0021-9991; 649724
- Grant/Contract Number:
- AC04-94AL85000; AC05-00OR22725
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Journal of Computational Physics
- Additional Journal Information:
- Journal Volume: 321; Journal Issue: C; Journal ID: ISSN 0021-9991
- Publisher:
- Elsevier
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 97 MATHEMATICS AND COMPUTING; Reynolds averaged Navier–Stokes; Stabilized finite elements; Adjoints; Sensitivities; Error-estimation; Uncertainty quantification
Citation Formats
Shadid, J. N., Smith, T. M., Cyr, E. C., Wildey, T. M., and Pawlowski, R. P. Stabilized FE simulation of prototype thermal-hydraulics problems with integrated adjoint-based capabilities. United States: N. p., 2016.
Web. doi:10.1016/j.jcp.2016.04.062.
Shadid, J. N., Smith, T. M., Cyr, E. C., Wildey, T. M., & Pawlowski, R. P. Stabilized FE simulation of prototype thermal-hydraulics problems with integrated adjoint-based capabilities. United States. https://doi.org/10.1016/j.jcp.2016.04.062
Shadid, J. N., Smith, T. M., Cyr, E. C., Wildey, T. M., and Pawlowski, R. P. Fri .
"Stabilized FE simulation of prototype thermal-hydraulics problems with integrated adjoint-based capabilities". United States. https://doi.org/10.1016/j.jcp.2016.04.062. https://www.osti.gov/servlets/purl/1338379.
@article{osti_1338379,
title = {Stabilized FE simulation of prototype thermal-hydraulics problems with integrated adjoint-based capabilities},
author = {Shadid, J. N. and Smith, T. M. and Cyr, E. C. and Wildey, T. M. and Pawlowski, R. P.},
abstractNote = {A critical aspect of applying modern computational solution methods to complex multiphysics systems of relevance to nuclear reactor modeling, is the assessment of the predictive capability of specific proposed mathematical models. The understanding of numerical error, the sensitivity of the solution to parameters associated with input data, boundary condition uncertainty, and mathematical models is critical. Additionally, the ability to evaluate and or approximate the model efficiently, to allow development of a reasonable level of statistical diagnostics of the mathematical model and the physical system, is of central importance. In our study we report on initial efforts to apply integrated adjoint-based computational analysis and automatic differentiation tools to begin to address these issues. The study is carried out in the context of a Reynolds averaged Navier–Stokes approximation to turbulent fluid flow and heat transfer using a particular spatial discretization based on implicit fully-coupled stabilized FE methods. We present the initial results that show the promise of these computational techniques in the context of nuclear reactor relevant prototype thermal-hydraulics problems.},
doi = {10.1016/j.jcp.2016.04.062},
journal = {Journal of Computational Physics},
number = C,
volume = 321,
place = {United States},
year = {Fri May 20 00:00:00 EDT 2016},
month = {Fri May 20 00:00:00 EDT 2016}
}
Web of Science
Works referenced in this record:
Galerkin Finite Element Approximations of Stochastic Elliptic Partial Differential Equations
journal, January 2004
- Babuska, Ivo; Tempone, Raúl; Zouraris, Georgios E.
- SIAM Journal on Numerical Analysis, Vol. 42, Issue 2
A Taxonomy of Consistently Stabilized Finite Element Methods for the Stokes Problem
journal, January 2004
- Barth, Teri; Bochev, Pavel; Gunzburger, Max
- SIAM Journal on Scientific Computing, Vol. 25, Issue 5
An optimal control approach to a posteriori error estimation in finite element methods
journal, May 2001
- Becker, Roland; Rannacher, Rolf
- Acta Numerica, Vol. 10
Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations
journal, September 1982
- Brooks, Alexander N.; Hughes, Thomas J. R.
- Computer Methods in Applied Mechanics and Engineering, Vol. 32, Issue 1-3
Approaches for Adjoint-Based A Posteriori Analysis of Stabilized Finite Element Methods
journal, January 2014
- Cyr, Eric C.; Shadid, John; Wildey, Tim
- SIAM Journal on Scientific Computing, Vol. 36, Issue 2
Choosing the Forcing Terms in an Inexact Newton Method
journal, January 1996
- Eisenstat, Stanley C.; Walker, Homer F.
- SIAM Journal on Scientific Computing, Vol. 17, Issue 1
Fast and reliable methods for determining the evolution of uncertain parameters in differential equations
journal, April 2006
- Estep, D.; Neckels, D.
- Journal of Computational Physics, Vol. 213, Issue 2
Estimating the error of numerical solutions of systems of reaction-diffusion equations
journal, January 2000
- Estep, Donald J.; Larson, Mats G.; Williams, Roy D.
- Memoirs of the American Mathematical Society, Vol. 146, Issue 696
A new finite element formulation for computational fluid dynamics: V. Circumventing the babuška-brezzi condition: a stable Petrov-Galerkin formulation of the stokes problem accommodating equal-order interpolations
journal, November 1986
- Hughes, Thomas J. R.; Franca, Leopoldo P.; Balestra, Marc
- Computer Methods in Applied Mechanics and Engineering, Vol. 59, Issue 1
Performance of fully coupled algebraic multilevel domain decomposition preconditioners for incompressible flow and transport
journal, January 2006
- Lin, Paul T.; Sala, Marzio; Shadid, John N.
- International Journal for Numerical Methods in Engineering, Vol. 67, Issue 2
A parallel fully coupled algebraic multilevel preconditioner applied to multiphysics PDE applications: Drift-diffusion, flow/transport/reaction, resistive MHD
journal, September 2010
- Lin, Paul T.; Shadid, John N.; Tuminaro, Raymond S.
- International Journal for Numerical Methods in Fluids, Vol. 64, Issue 10-12
Near field characteristics of swirling flow past a sudden expansion
journal, December 2007
- Mak, H.; Balabani, S.
- Chemical Engineering Science, Vol. 62, Issue 23
Graph-Based Software Design for Managing Complexity and Enabling Concurrency in Multiphysics PDE Software
journal, November 2012
- Notz, Patrick K.; Pawlowski, Roger P.; Sutherland, James C.
- ACM Transactions on Mathematical Software, Vol. 39, Issue 1
Large-scale stabilized FE computational analysis of nonlinear steady-state transport/reaction systems
journal, February 2006
- Shadid, J. N.; Salinger, A. G.; Pawlowski, R. P.
- Computer Methods in Applied Mechanics and Engineering, Vol. 195, Issue 13-16
Efficient parallel computation of unstructured finite element reacting flow solutions
journal, September 1997
- Shadid, John; Hutchinson, Scott; Hennigan, Gary
- Parallel Computing, Vol. 23, Issue 9
Performance of fully coupled domain decomposition preconditioners for finite element transport/reaction simulations
journal, May 2005
- Shadid, J. N.; Tuminaro, R. S.; Devine, K. D.
- Journal of Computational Physics, Vol. 205, Issue 1
Towards a scalable fully-implicit fully-coupled resistive MHD formulation with stabilized FE methods
journal, October 2010
- Shadid, J. N.; Pawlowski, R. P.; Banks, J. W.
- Journal of Computational Physics, Vol. 229, Issue 20
Scalable implicit incompressible resistive MHD with stabilized FE and fully-coupled Newton–Krylov-AMG
journal, June 2016
- Shadid, J. N.; Pawlowski, R. P.; Cyr, E. C.
- Computer Methods in Applied Mechanics and Engineering, Vol. 304
Differential equation-based wall distance computation for DES and RANS
journal, September 2003
- Tucker, P. G.
- Journal of Computational Physics, Vol. 190, Issue 1
On a multilevel preconditioning module for unstructured mesh Krylov solvers: two-level Schwarz
journal, March 2002
- Tuminaro, R. S.; Tong, C. H.; Shadid, J. N.
- Communications in Numerical Methods in Engineering, Vol. 18, Issue 6
The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations
journal, January 2002
- Xiu, Dongbin; Karniadakis, George Em
- SIAM Journal on Scientific Computing, Vol. 24, Issue 2
Works referencing / citing this record:
Dimension reduction in magnetohydrodynamics power generation models: Dimensional analysis and active subspaces: GLAWS
journal, August 2017
- Glaws, Andrew; Constantine, Paul G.; Shadid, John N.
- Statistical Analysis and Data Mining: The ASA Data Science Journal, Vol. 10, Issue 5
Dimension reduction in MHD power generation models: dimensional analysis and active subspaces
preprint, January 2016
- Glaws, Andrew; Constantine, Paul G.; Shadid, John
- arXiv