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Title: Evaluation of a nonlinear variational multiscale method for fluid transport problems

Abstract

Diverse transport problems, especially those based on fluid flow models, are intrinsically multiscale and nonlinear, characteristics that often lead to intricate dynamics such as the development of instabilities and turbulence. Computational simulations that resolve all scales in these problems are often unfeasible, prompting to coarse-grained simulation strategies in which small-scale features are modeled instead of resolved. Variational Multiscale (VMS) methods, and particularly residual-based Large-Eddy Simulation (LES) approaches, have proven effective and robust for the coarse-grained simulation of complex transport problems. VMS methods avoid the assumption of separable nonlinearity and the reliance on empirical small-scale models by using a variational decomposition of scales together with a residual-based approximation of the small-scales. Evaluation of a nonlinear VMS approach, denoted as VMSn, is presented for the coarse-grained simulation of transient-advective-diffusive-reactive (TADR) transport problems arising from fluid flow models. In contrast to classical VMS approaches that neglect the effect of the small scales on the transport operator, VMSn treats the inter-dependence between large- and small-scales upfront. The treatment of inter-scale coupling involves the solution of a local algebraic nonlinear system describing the evolution of the small-scales. The VMSn approach is complemented with two algebraic approximations of the small-scales: one based on the main diagonalmore » of the transport matrices and another that preserves transport fluxes and is suitable for generic TADR systems. The suitability of the VMSn approach for handling general TADR problems and regimes is evaluated with benchmark incompressible, compressible, and magnetohydrodynamic laminar flow problems, the incompressible Taylor-Green vortex flow, the turbulent free jet, and the two-temperature arc in crossflow. Furthermore, simulation results show that VMSn leads to minor improvements in accuracy with respect to the classical VMS for the laminar flow problems, but to significantly greater accuracy for the turbulent flows and the unsteady plasma flow problems, while using the same cohesive numerical formulation.« less

Authors:
 [1];  [1];  [1]
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  1. Univ. of Massachusetts, Lowell, MA (United States)
Publication Date:
Research Org.:
Univ. of Massachusetts, Lowell, MA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Fusion Energy Sciences (FES)
OSTI Identifier:
1638127
Alternate Identifier(s):
OSTI ID: 1638125
Grant/Contract Number:  
SC0018230
Resource Type:
Accepted Manuscript
Journal Name:
Computers and Fluids
Additional Journal Information:
Journal Volume: 209; Journal Issue: C; Journal ID: ISSN 0045-7930
Publisher:
Elsevier
Country of Publication:
United States
Language:
English
Subject:
70 PLASMA PHYSICS AND FUSION TECHNOLOGY; turbulence intrinsic time scales; incompressible-compressible flow; Taylor-Green vortex; turbulent free jet; arc in crossflow

Citation Formats

Modirkhazeni, S. Mahnaz, Bhigamudre, Vyasaraj G., and Trelles, Juan Pablo. Evaluation of a nonlinear variational multiscale method for fluid transport problems. United States: N. p., 2020. Web. doi:10.1016/j.compfluid.2020.104531.
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Modirkhazeni, S. Mahnaz, Bhigamudre, Vyasaraj G., & Trelles, Juan Pablo. Evaluation of a nonlinear variational multiscale method for fluid transport problems. United States. https://doi.org/10.1016/j.compfluid.2020.104531
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Modirkhazeni, S. Mahnaz, Bhigamudre, Vyasaraj G., and Trelles, Juan Pablo. Tue . "Evaluation of a nonlinear variational multiscale method for fluid transport problems". United States. https://doi.org/10.1016/j.compfluid.2020.104531. https://www.osti.gov/servlets/purl/1638127.
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@article{osti_1638127,
title = {Evaluation of a nonlinear variational multiscale method for fluid transport problems},
author = {Modirkhazeni, S. Mahnaz and Bhigamudre, Vyasaraj G. and Trelles, Juan Pablo},
abstractNote = {Diverse transport problems, especially those based on fluid flow models, are intrinsically multiscale and nonlinear, characteristics that often lead to intricate dynamics such as the development of instabilities and turbulence. Computational simulations that resolve all scales in these problems are often unfeasible, prompting to coarse-grained simulation strategies in which small-scale features are modeled instead of resolved. Variational Multiscale (VMS) methods, and particularly residual-based Large-Eddy Simulation (LES) approaches, have proven effective and robust for the coarse-grained simulation of complex transport problems. VMS methods avoid the assumption of separable nonlinearity and the reliance on empirical small-scale models by using a variational decomposition of scales together with a residual-based approximation of the small-scales. Evaluation of a nonlinear VMS approach, denoted as VMSn, is presented for the coarse-grained simulation of transient-advective-diffusive-reactive (TADR) transport problems arising from fluid flow models. In contrast to classical VMS approaches that neglect the effect of the small scales on the transport operator, VMSn treats the inter-dependence between large- and small-scales upfront. The treatment of inter-scale coupling involves the solution of a local algebraic nonlinear system describing the evolution of the small-scales. The VMSn approach is complemented with two algebraic approximations of the small-scales: one based on the main diagonal of the transport matrices and another that preserves transport fluxes and is suitable for generic TADR systems. The suitability of the VMSn approach for handling general TADR problems and regimes is evaluated with benchmark incompressible, compressible, and magnetohydrodynamic laminar flow problems, the incompressible Taylor-Green vortex flow, the turbulent free jet, and the two-temperature arc in crossflow. Furthermore, simulation results show that VMSn leads to minor improvements in accuracy with respect to the classical VMS for the laminar flow problems, but to significantly greater accuracy for the turbulent flows and the unsteady plasma flow problems, while using the same cohesive numerical formulation.},
doi = {10.1016/j.compfluid.2020.104531},
journal = {Computers and Fluids},
number = C,
volume = 209,
place = {United States},
year = {Tue Jun 09 00:00:00 EDT 2020},
month = {Tue Jun 09 00:00:00 EDT 2020}
}
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