An integrated enabling technology interfacing multiple space/time methods/algorithms/domains with model reduction for first-order systems

David Tae, Kumar K. Tamma

Research output: Contribution to journalArticlepeer-review


Purpose: The purpose of this study is to further advance the multiple space/time subdomain framework with model reduction. Existing linear multistep (LMS) methods that are second-order time accurate, and useful for practical applications, have a significant limitation. They do not account for separable controllable numerical dissipation of the primary variables. Furthermore, they have little or no significant choices of altogether different algorithms that can be integrated in a single analysis to mitigate numerical oscillations that may occur. In lieu of such limitations, under the generalized single-step single-solve (GS4) umbrella, several of the deficiencies are circumvented. Design/methodology/approach: The GS4 framework encompasses a wide variety of LMS schemes that are all second-order time accurate and offers controllable numerical dissipation. Unlike existing state-of-art, the present framework permits implicit–implicit and implicit–explicit coupling of algorithms via differential algebraic equations (DAE). As further advancement, this study embeds proper orthogonal decomposition (POD) to further reduce model sizes. This study also uses an iterative convergence check in acquiring sufficient snapshot data to adequately capture the physics to prescribed accuracy requirements. Simple linear/nonlinear transient numerical examples are presented to provide proof of concept. Findings: The present DAE-GS4-POD framework has the flexibility of using different spatial methods and different time integration algorithms in altogether different subdomains in conjunction with the POD to advance and improve the computational efficiency. Originality/value: The novelty of this paper is the addition of reduced order modeling features, how it applies to the previous DAE-GS4 framework and the improvement of the computational efficiency. The proposed framework/tool kit provides all the needed flexibility, robustness and adaptability for engineering computations.

Original languageEnglish (US)
Pages (from-to)2409-2438
Number of pages30
JournalInternational Journal of Numerical Methods for Heat and Fluid Flow
Issue number7
StatePublished - May 19 2023

Bibliographical note

Publisher Copyright:
© 2023, Emerald Publishing Limited.


  • Differential algebraic equations
  • First-order transient systems
  • Generalized single-step single-solve framework
  • Multiple methods
  • Reduced order modeling
  • Time integration


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