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Title: A tightly-coupled domain-decomposition approach for highly nonlinear stochastic multiphysics systems

Abstract

Multiphysics simulations often involve nonlinear components that are driven by internally generated or externally imposed random fluctuations. When used with a domain-decomposition (DD) algorithm, such components have to be coupled in a way that both accurately propagates the noise between the subdomains and lends itself to a stable and cost-effective temporal integration. We develop a conservative DD approach in which tight coupling is obtained by using a Jacobian-free Newton–Krylov (JfNK) method with a generalized minimum residual iterative linear solver. This strategy is tested on a coupled nonlinear diffusion system forced by a truncated Gaussian noise at the boundary. Enforcement of path-wise continuity of the state variable and its flux, as opposed to continuity in the mean, at interfaces between subdomains enables the DD algorithm to correctly propagate boundary fluctuations throughout the computational domain. Reliance on a single Newton iteration (explicit coupling), rather than on the fully converged JfNK (implicit) coupling, may increase the solution error by an order of magnitude. Increase in communication frequency between the DD components reduces the explicit coupling's error, but makes it less efficient than the implicit coupling at comparable error levels for all noise strengths considered. Finally, the DD algorithm with the implicit JfNK couplingmore » resolves temporally-correlated fluctuations of the boundary noise when the correlation time of the latter exceeds some multiple of an appropriately defined characteristic diffusion time.« less

Authors:
;
Publication Date:
OSTI Identifier:
22622251
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Computational Physics; Journal Volume: 330; Other Information: Copyright (c) 2016 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ALGORITHMS; COMPARATIVE EVALUATIONS; COMPUTERIZED SIMULATION; CORRELATIONS; COUPLING; DECOMPOSITION; DIFFUSION; ENFORCEMENT; ERRORS; FLUCTUATIONS; HYDROGEN; INTERFACES; ITERATIVE METHODS; MATHEMATICAL SOLUTIONS; NOISE; NONLINEAR PROBLEMS; RANDOMNESS; STOCHASTIC PROCESSES

Citation Formats

Taverniers, Søren, and Tartakovsky, Daniel M., E-mail: dmt@ucsd.edu. A tightly-coupled domain-decomposition approach for highly nonlinear stochastic multiphysics systems. United States: N. p., 2017. Web. doi:10.1016/J.JCP.2016.10.052.
Taverniers, Søren, & Tartakovsky, Daniel M., E-mail: dmt@ucsd.edu. A tightly-coupled domain-decomposition approach for highly nonlinear stochastic multiphysics systems. United States. doi:10.1016/J.JCP.2016.10.052.
Taverniers, Søren, and Tartakovsky, Daniel M., E-mail: dmt@ucsd.edu. Wed . "A tightly-coupled domain-decomposition approach for highly nonlinear stochastic multiphysics systems". United States. doi:10.1016/J.JCP.2016.10.052.
@article{osti_22622251,
title = {A tightly-coupled domain-decomposition approach for highly nonlinear stochastic multiphysics systems},
author = {Taverniers, Søren and Tartakovsky, Daniel M., E-mail: dmt@ucsd.edu},
abstractNote = {Multiphysics simulations often involve nonlinear components that are driven by internally generated or externally imposed random fluctuations. When used with a domain-decomposition (DD) algorithm, such components have to be coupled in a way that both accurately propagates the noise between the subdomains and lends itself to a stable and cost-effective temporal integration. We develop a conservative DD approach in which tight coupling is obtained by using a Jacobian-free Newton–Krylov (JfNK) method with a generalized minimum residual iterative linear solver. This strategy is tested on a coupled nonlinear diffusion system forced by a truncated Gaussian noise at the boundary. Enforcement of path-wise continuity of the state variable and its flux, as opposed to continuity in the mean, at interfaces between subdomains enables the DD algorithm to correctly propagate boundary fluctuations throughout the computational domain. Reliance on a single Newton iteration (explicit coupling), rather than on the fully converged JfNK (implicit) coupling, may increase the solution error by an order of magnitude. Increase in communication frequency between the DD components reduces the explicit coupling's error, but makes it less efficient than the implicit coupling at comparable error levels for all noise strengths considered. Finally, the DD algorithm with the implicit JfNK coupling resolves temporally-correlated fluctuations of the boundary noise when the correlation time of the latter exceeds some multiple of an appropriately defined characteristic diffusion time.},
doi = {10.1016/J.JCP.2016.10.052},
journal = {Journal of Computational Physics},
number = ,
volume = 330,
place = {United States},
year = {Wed Feb 01 00:00:00 EST 2017},
month = {Wed Feb 01 00:00:00 EST 2017}
}
  • Multiphysics problems often involve components whose macroscopic dynamics is driven by microscopic random fluctuations. The fidelity of simulations of such systems depends on their ability to propagate these random fluctuations throughout a computational domain, including subdomains represented by deterministic solvers. When the constituent processes take place in nonoverlapping subdomains, system behavior can be modeled via a domain-decomposition approach that couples separate components at the interfaces between these subdomains. Its coupling algorithm has to maintain a stable and efficient numerical time integration even at high noise strength. We propose a conservative domain-decomposition algorithm in which tight coupling is achieved by employingmore » either Picard's or Newton's iterative method. Coupled diffusion equations, one of which has a Gaussian white-noise source term, provide a computational testbed for analysis of these two coupling strategies. Fully-converged (“implicit”) coupling with Newton's method typically outperforms its Picard counterpart, especially at high noise levels. This is because the number of Newton iterations scales linearly with the amplitude of the Gaussian noise, while the number of Picard iterations can scale superlinearly. At large time intervals between two subsequent inter-solver communications, the solution error for single-iteration (“explicit”) Picard's coupling can be several orders of magnitude higher than that for implicit coupling. Increasing the explicit coupling's communication frequency reduces this difference, but the resulting increase in computational cost can make it less efficient than implicit coupling at similar levels of solution error, depending on the communication frequency of the latter and the noise strength. This trend carries over into higher dimensions, although at high noise strength explicit coupling may be the only computationally viable option.« less
  • We have developed a tightly coupled multiphysics simulation tool for the pebble-bed reactor (PBR) concept, a type of Very High-Temperature gas-cooled Reactor (VHTR). The simulation tool, PRONGHORN, takes advantages of the Multiphysics Object-Oriented Simulation Environment library, and is capable of solving multidimensional thermal-fluid and neutronics problems implicitly with a Newton-based approach. Expensive Jacobian matrix formation is alleviated via the Jacobian-free Newton-Krylov method, and physics-based preconditioning is applied to minimize Krylov iterations. Motivation for the work is provided via analysis and numerical experiments on simpler multiphysics reactor models. We then provide detail of the physical models and numerical methods in PRONGHORN.more » Finally, PRONGHORN's algorithmic capability is demonstrated on a number of PBR test cases.« less
  • Data transfer from one distinct mesh to another may be necessary in any number of applications, including prolongation operations supporting multigrid solution methods, spatial adaptation, remeshing, and arbitrary Lagrangian-Eulerian (ALE) and multiphysics simulation. This data transfer process is also referred to as remapping, rezoning and interpolation. Intermesh data transfer has the potential to introduce error into a simulation; the magnitude and importance of which depends on the transfer scenario and the algorithm used to perform the transfer. For a transient analysis, data transfer may occur many times during a simulation, with possible error accumulation at each transfer. The present studymore » develops selected scenarios that illustrate data transfer error and how it might impact an analysis. This study examines remapping error by using static analytical functions to compare various remapping schemes. It also investigates the significance and nature of data transfer error for a simple multiphysics system involving a transient coupled system of partial differential equations. It concludes that remapping error can be significant both for static functions and for coupled multiphysics systems. Aggregate error is shown to be a function of remapping scheme, mesh coarseness, nature of the remapped function and mesh disparity. In cases of extreme mesh disparity, this study shows that remapping can lead to excessive error and even to solution instability. Further, this work motivates that remapping error should be included in the estimation of numerical error, if data transfer is employed in a numerical simulation.« less