Richardson, Brian Ross (2008-05). A reduced-order model based on proper orthogonal decomposition for non-isothermal two-phase flows. Master's Thesis. Thesis uri icon

abstract

  • This thesis presents a study of reduced-order models based on proper orthogonal decomposition applied to non-isothermal transport phenomena in ?uidized beds. A numerical ?ow solver called Multiphase Flow with Interphase eXchanges (MFIX) was used to generate a database of solution snapshots for proper orthogonal decomposi- tion (POD). Using POD, time independent basis functions were extracted from the data and the governing equations of the numerical solver were projected onto the basis functions to generate reduced-order models. A reduced-order model was constructed that simulates multi-phase isothermal and non-isothermal ?ow. In the reduced-order models (ROMs) the large number of partial di(R)erential equations were replaced by a much smaller number of ordinary di(R)erential equations. These reduced-order models were applied to two reference cases, a time extrapolation case and a time-dependent period boundary condition case. Three additional acceleration techniques were devel- oped to further improve computational e?ciency of the POD based ROM: 1) Database splitting, 2) Freezing the matrix of the linear system and 3) Time step adjustment. Detailed numerical analysis of both the full-order model, MFIX and the POD-based ROM, including estimating the number of operations and the CPU time per iteration, was performed as part of this study. The results of this investigation show that the reduced-order models are capable of producing qualitatively accurate results with less than 5% error with a two-order of magnitude reduction of computational costs.
  • This thesis presents a study of reduced-order models based on proper orthogonal
    decomposition applied to non-isothermal transport phenomena in ?uidized beds. A
    numerical ?ow solver called Multiphase Flow with Interphase eXchanges (MFIX) was
    used to generate a database of solution snapshots for proper orthogonal decomposi-
    tion (POD). Using POD, time independent basis functions were extracted from the
    data and the governing equations of the numerical solver were projected onto the basis
    functions to generate reduced-order models. A reduced-order model was constructed
    that simulates multi-phase isothermal and non-isothermal ?ow. In the reduced-order
    models (ROMs) the large number of partial di(R)erential equations were replaced by a
    much smaller number of ordinary di(R)erential equations. These reduced-order models
    were applied to two reference cases, a time extrapolation case and a time-dependent
    period boundary condition case. Three additional acceleration techniques were devel-
    oped to further improve computational e?ciency of the POD based ROM: 1) Database
    splitting, 2) Freezing the matrix of the linear system and 3) Time step adjustment.
    Detailed numerical analysis of both the full-order model, MFIX and the POD-based
    ROM, including estimating the number of operations and the CPU time per iteration,
    was performed as part of this study. The results of this investigation show that the
    reduced-order models are capable of producing qualitatively accurate results with less than 5% error with a two-order of magnitude reduction of computational costs.

publication date

  • May 2008