Conservative model reduction for finite-volume models

Carlberg, Kevin Thomas; Choi, Youngsoo; Sargsyan, Syuzanna

doi:10.1016/j.jcp.2018.05.019

Conservative model reduction for finite-volume models

Journal Article · Tue Jun 05 00:00:00 EDT 2018 · Journal of Computational Physics

DOI:https://doi.org/10.1016/j.jcp.2018.05.019· OSTI ID:1465805

Carlberg, Kevin Thomas ^[1]; Choi, Youngsoo ^[1]; Sargsyan, Syuzanna ^[1]

Sandia National Lab. (SNL-CA), Livermore, CA (United States)

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.

View Accepted Manuscript (DOE)

Research Organization:: Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States); Sandia National Laboratories (SNL-CA), Livermore, CA (United States)

Sponsoring Organization:: USDOE National Nuclear Security Administration (NNSA)

Grant/Contract Number:: AC04-94AL85000; AC52-07NA27344; NA0003525

OSTI ID:: 1465805

Alternate ID(s):: OSTI ID: 1507486
OSTI ID: 1512042
OSTI ID: 1525753
OSTI ID: 1582871
OSTI ID: 23081850

Report Number(s):: LLNL-JRNL--742522; SAND--2017-13718J; 662974

Journal Information:: Journal of Computational Physics, Journal Name: Journal of Computational Physics Journal Issue: C Vol. 371; ISSN 0021-9991

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

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