A POD-based solver for the advection-diffusion equation

Elia Merzari, W. David Pointer, Paul Fischer

Research output: Chapter in Book/Report/Conference proceedingConference contribution

7 Scopus citations

Abstract

We present a methodology based on proper orthogonal decomposition (POD). We have implemented the POD-based solver in the large eddy simulation code Nek5000 and used it to solve the advection-diffusion equation for temperature in cases where buoyancy is not present. POD allows for the identification of the most energetic modes of turbulence when applied to a sufficient set of snapshots generated through Nek5000. The Navier-Stokes equations are then reduced to a set of ordinary differential equations by Galerkin projection. The flow field is reconstructed and used to advect the temperature on longer time scales and potentially coarser grids. The methodology is validated and tested on two problems: two-dimensional flow past a cylinder and three-dimensional flow in T-junctions. For the latter case, the benchmark chosen corresponds to the experiments of Hirota et al., who performed particle image velocimetry on the flow in a counterflow T-junction. In both test problems the dynamics of the reduced-order model reproduce well the history of the projected modes when a sufficient number of equations are considered. The dynamics of flow evolution and the interaction of different modes are also studied in detail for the T-junction.

Original languageEnglish (US)
Title of host publicationASME-JSME-KSME 2011 Joint Fluids Engineering Conference, AJK 2011
Pages1139-1147
Number of pages9
EditionPARTS A, B, C, D
DOIs
StatePublished - Dec 1 2011
EventASME-JSME-KSME 2011 Joint Fluids Engineering Conference, AJK 2011 - Hamamatsu, Japan
Duration: Jul 24 2011Jul 29 2011

Publication series

NameASME-JSME-KSME 2011 Joint Fluids Engineering Conference, AJK 2011
NumberPARTS A, B, C, D
Volume1

Other

OtherASME-JSME-KSME 2011 Joint Fluids Engineering Conference, AJK 2011
CountryJapan
CityHamamatsu
Period7/24/117/29/11

All Science Journal Classification (ASJC) codes

  • Fluid Flow and Transfer Processes

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    Merzari, E., Pointer, W. D., & Fischer, P. (2011). A POD-based solver for the advection-diffusion equation. In ASME-JSME-KSME 2011 Joint Fluids Engineering Conference, AJK 2011 (PARTS A, B, C, D ed., pp. 1139-1147). (ASME-JSME-KSME 2011 Joint Fluids Engineering Conference, AJK 2011; Vol. 1, No. PARTS A, B, C, D). https://doi.org/10.1115/AJK2011-01022