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Title: Conservative model reduction for finite-volume models

Journal Article · · Journal of Computational Physics
 [1];  [2];  [3]
  1. Sandia National Lab. (SNL-CA), Livermore, CA (United States)
  2. Sandia National Lab. (SNL-CA), Livermore, CA (United States); Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
  3. Sandia National Lab. (SNL-CA), Livermore, CA (United States); Univ. of Washington, Seattle, WA (United States); HERE Technologies, Chicago, IL (United States)
+ Show Author Affiliations

Here, this work proposes a method for model reduction of finite-volume models that guarantees the resulting reduced-order model is conservative, thereby preserving the structure intrinsic to finite-volume discretizations. The proposed reduced-order models associate with optimization problems characterized by a minimum-residual objective function and nonlinear equality constraints that explicitly enforce conservation over subdomains. Conservative Galerkin projection arises from formulating this optimization problem at the time-continuous level, while conservative least-squares Petrov–Galerkin (LSPG) projection associates with a time-discrete formulation. We equip these approaches with hyper-reduction techniques in the case of nonlinear flux and source terms, and also provide approaches for handling infeasibility. In addition, we perform analyses that include deriving conditions under which conservative Galerkin and conservative LSPG are equivalent, as well as deriving a posteriori error bounds. Numerical experiments performed on a parameterized quasi-1D Euler equation demonstrate the ability of the proposed method to ensure not only global conservation, but also significantly lower state-space errors than nonconservative reduced-order models such as standard Galerkin and LSPG projection.

Research Organization:
Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States); Sandia National Lab. (SNL-CA), Livermore, CA (United States)
Sponsoring Organization:
USDOE National Nuclear Security Administration (NNSA)
Grant/Contract Number:
AC52-07NA27344; NA-0003525; AC04-94AL85000; 190968
OSTI ID:
1525753
Alternate ID(s):
OSTI ID: 1465805; OSTI ID: 1582871
Report Number(s):
LLNL-JRNL-742522; SAND-2017-13718J; 897398
Journal Information:
Journal of Computational Physics, Vol. 371, Issue C; ISSN 0021-9991
Publisher:
ElsevierCopyright Statement
Country of Publication:
United States
Language:
English
Citation Metrics:
Cited by: 41 works
Citation information provided by
Web of Science

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Cited By (5)

Time Stable Reduced Order Modeling by an Enhanced Reduced Order Basis of the Turbulent and Incompressible 3D Navier–Stokes Equations journal April 2019
Mass conservative reduced order modeling of a free boundary osmotic cell swelling problem journal May 2019
Investigations and Improvement of Robustness of Reduced-Order Models of Reacting Flow journal December 2019
Investigations and Improvement of Robustness of Reduced-Order Models of Reacting Flow conference January 2019
Mass Conservative Reduced Order Modeling of a Free Boundary Osmotic Cell Swelling Problem text January 2018

Figures / Tables (9)

Figure 1(p. 13)figure Figure 1
Figure 2(p. 30)figure Figure 2
Table 1(p. 35)table Table 1
Table 2(p. 35)table Table 2
Figure 3(p. 40)figure Figure 3
Figure 4(p. 41)figure Figure 4
Figure 5(p. 42)figure Figure 5
Figure 6(p. 43)figure Figure 6
Figure 7(p. 44)figure Figure 7

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Related Subjects

97 MATHEMATICS AND COMPUTING
Nonlinear model reduction
Structure preservation
Finite-volume method
Galerkin projection
Least-squares Petrov–Galerkin projection
Conservative schemes
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS