Lagrangian Reduced Order Modeling Using Finite Time Lyapunov Exponents
| Autor: | Changhong Mou, Xuping Xie, Shane D. Ross, Traian Iliescu, Peter J. Nolan |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Quasi-geostrophic equations
ComputingMethodologies_SIMULATIONANDMODELING Computer science Closure (topology) MathematicsofComputing_NUMERICALANALYSIS 010103 numerical & computational mathematics Lyapunov exponent Computer Science::Human-Computer Interaction lcsh:Thermodynamics 01 natural sciences Computer Science::Digital Libraries Projection (linear algebra) 010305 fluids & plasmas quasi-geostrophic equations finite time Lyapunov exponent symbols.namesake Lagrangian inner product lcsh:QC310.15-319 0103 physical sciences Stream function Applied mathematics 0101 mathematics Lagrangian reduced order model ComputingMethodologies_COMPUTERGRAPHICS lcsh:QC120-168.85 Fluid Flow and Transfer Processes Hardware_MEMORYSTRUCTURES Basis (linear algebra) Mechanical Engineering Eulerian path Condensed Matter Physics Nonlinear system symbols Computer Science::Programming Languages lcsh:Descriptive and experimental mechanics Hardware_CONTROLSTRUCTURESANDMICROPROGRAMMING |
| Zdroj: | Fluids, Vol 5, Iss 189, p 189 (2020) Fluids Volume 5 Issue 4 |
| ISSN: | 2311-5521 |
| Popis: | There are two main strategies for improving the projection-based reduced order model (ROM) accuracy&mdash (i) improving the ROM, that is, adding new terms to the standard ROM and (ii) improving the ROM basis, that is, constructing ROM bases that yield more accurate ROMs. In this paper, we use the latter. We propose two new Lagrangian inner products that we use together with Eulerian and Lagrangian data to construct two new Lagrangian ROMs, which we denote &alpha ROM and &lambda ROM. We show that both Lagrangian ROMs are more accurate than the standard Eulerian ROMs, that is, ROMs that use standard Eulerian inner product and data to construct the ROM basis. Specifically, for the quasi-geostrophic equations, we show that the new Lagrangian ROMs are more accurate than the standard Eulerian ROMs in approximating not only Lagrangian fields (e.g., the finite time Lyapunov exponent (FTLE)), but also Eulerian fields (e.g., the streamfunction). In particular, the &alpha ROM can be orders of magnitude more accurate than the standard Eulerian ROMs. We emphasize that the new Lagrangian ROMs do not employ any closure modeling to model the effect of discarded modes (which is standard procedure for low-dimensional ROMs of complex nonlinear systems). Thus, the dramatic increase in the new Lagrangian ROMs&rsquo accuracy is entirely due to the novel Lagrangian inner products used to build the Lagrangian ROM basis. |
| Databáze: | OpenAIRE |
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