TY - JOUR
T1 - A time-relaxation reduced order model for the turbulent channel flow
AU - Tsai, Ping Hsuan
AU - Fischer, Paul
AU - Iliescu, Traian
N1 - The research used resources at the Oak Ridge Leadership Computing Facility at Oak Ridge National Laboratory, which is supported by the Office of Science of the U.S. Department of Energy under Contract DE-AC05-00OR22725, at the Argonne Leadership Computing Facility, under Contract DE-AC02-06CH11357, and at the Delta advanced computing, which is supported by the National Science Foundation (award OAC 2005572) and the State of Illinois.
P.T. and P.F. acknowledge support through he DOE Office of Nuclear Energy under the Nuclear Energy University Program (Projs. No. DE_NE0008780 and DE_NE0009396). T.I. acknowledges support through National Science Foundation grants DMS-2012253 and CDS&E-MSS-1953113.
The research used resources at the Oak Ridge Leadership Computing Facility at Oak Ridge National Laboratory, which is supported by the Office of Science of the U.S. Department of Energy under Contract DE-AC05-00OR22725, at the Argonne Leadership Computing Facility, under Contract DE-AC02-06CH11357, and at the Delta advanced computing, which is supported by the National Science Foundation (award OAC 2005572) and the State of Illinois. P.T. and P.F. acknowledge support through he DOE Office of Nuclear Energy under the Nuclear Energy University Program (Projs. No. DE_NE0008780 and DE_NE0009396). T.I. acknowledges support through National Science Foundation grants DMS-2012253 and CDS&E-MSS-1953113. We thank the reviewers for their comments and suggestions, which significantly improved the quality and clarity of the manuscript.
PY - 2025/1/15
Y1 - 2025/1/15
N2 - Regularized reduced order models (Reg-ROMs) are stabilization strategies that leverage spatial filtering to alleviate the spurious numerical oscillations generally displayed by the classical Galerkin ROM (G-ROM) in under-resolved numerical simulations of turbulent flows. In this paper, we propose a new Reg-ROM, the time-relaxation ROM (TR-ROM), which filters the marginally resolved scales. We compare the new TR-ROM with the two other Reg-ROMs in current use, i.e., the Leray ROM (L-ROM) and the evolve-filter-relax ROM (EFR-ROM) and one eddy viscosity model, the mixing-length model, in the numerical simulation of the turbulent channel flow at Reτ=180 and Reτ=395 in both the reproduction and the predictive regimes. For each Reg-ROM, we investigate two different filters: (i) the differential filter (DF), and (ii) the higher-order algebraic filter (HOAF). In our numerical investigation, we monitor the Reg-ROM performance with respect to the ROM dimension, N, and the filter order. We also perform sensitivity studies of the three Reg-ROMs with respect to the time interval, relaxation parameter, and filter radius. The numerical results yield the following conclusions: (i) All three Reg-ROMs are significantly more accurate than the G-ROM. (ii) All three Reg-ROMs are more accurate than the ROM projection in terms of Reynolds stresses. (iii) With the optimal parameter values, the new TR-ROM yields more accurate results than the L-ROM and the EFR-ROM in all tests. (iv) The new TR-ROM is more accurate than the mixing-length ROM. (v) For most N values, DF yields the most accurate results for all three Reg-ROMs. (vi) The optimal parameters trained in the reproduction regime are also optimal for the predictive regime for most N values, demonstrating the Reg-ROM predictive capabilities. (vii) All three Reg-ROMs are sensitive to the filter order and the filter radius, and the EFR-ROM and the TR-ROM are sensitive to the relaxation parameter. (viii) The optimal range for the filter radius and the effect of relaxation parameter are similar for the two Reτ values.
AB - Regularized reduced order models (Reg-ROMs) are stabilization strategies that leverage spatial filtering to alleviate the spurious numerical oscillations generally displayed by the classical Galerkin ROM (G-ROM) in under-resolved numerical simulations of turbulent flows. In this paper, we propose a new Reg-ROM, the time-relaxation ROM (TR-ROM), which filters the marginally resolved scales. We compare the new TR-ROM with the two other Reg-ROMs in current use, i.e., the Leray ROM (L-ROM) and the evolve-filter-relax ROM (EFR-ROM) and one eddy viscosity model, the mixing-length model, in the numerical simulation of the turbulent channel flow at Reτ=180 and Reτ=395 in both the reproduction and the predictive regimes. For each Reg-ROM, we investigate two different filters: (i) the differential filter (DF), and (ii) the higher-order algebraic filter (HOAF). In our numerical investigation, we monitor the Reg-ROM performance with respect to the ROM dimension, N, and the filter order. We also perform sensitivity studies of the three Reg-ROMs with respect to the time interval, relaxation parameter, and filter radius. The numerical results yield the following conclusions: (i) All three Reg-ROMs are significantly more accurate than the G-ROM. (ii) All three Reg-ROMs are more accurate than the ROM projection in terms of Reynolds stresses. (iii) With the optimal parameter values, the new TR-ROM yields more accurate results than the L-ROM and the EFR-ROM in all tests. (iv) The new TR-ROM is more accurate than the mixing-length ROM. (v) For most N values, DF yields the most accurate results for all three Reg-ROMs. (vi) The optimal parameters trained in the reproduction regime are also optimal for the predictive regime for most N values, demonstrating the Reg-ROM predictive capabilities. (vii) All three Reg-ROMs are sensitive to the filter order and the filter radius, and the EFR-ROM and the TR-ROM are sensitive to the relaxation parameter. (viii) The optimal range for the filter radius and the effect of relaxation parameter are similar for the two Reτ values.
KW - Reduced order model
KW - Regularized model
KW - Spatial filter
KW - Time relaxation
KW - Turbulent channel flow
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U2 - 10.1016/j.jcp.2024.113563
DO - 10.1016/j.jcp.2024.113563
M3 - Article
AN - SCOPUS:85208479408
SN - 0021-9991
VL - 521
JO - Journal of Computational Physics
JF - Journal of Computational Physics
M1 - 113563
ER -