A hybrid adaptive lowMach number/compressible method: Euler equations
Abstract
© 2018 Elsevier Inc. Flows in which the primary features of interest do not rely on highfrequency acoustic effects, but in which longwavelength acoustics play a nontrivial role, present a computational challenge. Integrating the entire domain with lowMachnumber methods would remove all acoustic wave propagation, while integrating the entire domain with the fully compressible equations can in some cases be prohibitively expensive due to the CFL time step constraint. For example, simulation of thermoacoustic instabilities might require fine resolution of the fluid/chemistry interaction but not require fine resolution of acoustic effects, yet one does not want to neglect the longwavelength wave propagation and its interaction with the larger domain. The present paper introduces a new multilevel hybrid algorithm to address these types of phenomena. In this new approach, the fully compressible Euler equations are solved on the entire domain, potentially with local refinement, while their lowMachnumber counterparts are solved on subregions of the domain with higher spatial resolution. The finest of the compressible levels communicates inhomogeneous divergence constraints to the coarsest of the lowMachnumber levels, allowing the lowMachnumber levels to retain the longwavelength acoustics. The performance of the hybrid method is shown for a series of test cases, including resultsmore »
 Authors:

 Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
 Publication Date:
 Research Org.:
 Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). National Energy Research Scientific Computing Center (NERSC); Univ. of California, Oakland, CA (United States)
 Sponsoring Org.:
 USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)
 OSTI Identifier:
 1543561
 Alternate Identifier(s):
 OSTI ID: 1602830; OSTI ID: 1693635
 Grant/Contract Number:
 AC0205CH11231; AC02005CH11231
 Resource Type:
 Accepted Manuscript
 Journal Name:
 Journal of Computational Physics
 Additional Journal Information:
 Journal Volume: 372; Journal Issue: C; Journal ID: ISSN 00219991
 Publisher:
 Elsevier
 Country of Publication:
 United States
 Language:
 English
 Subject:
 97 MATHEMATICS AND COMPUTING; Computer Science; Physics; Hybrid methods; LowMachnumber flows; Compressible flows; Projection methods; Adaptive mesh refinement; Acoustics
Citation Formats
Motheau, Emmanuel, Duarte, Max, Almgren, Ann, and Bell, John B. A hybrid adaptive lowMach number/compressible method: Euler equations. United States: N. p., 2018.
Web. https://doi.org/10.1016/j.jcp.2018.01.036.
Motheau, Emmanuel, Duarte, Max, Almgren, Ann, & Bell, John B. A hybrid adaptive lowMach number/compressible method: Euler equations. United States. https://doi.org/10.1016/j.jcp.2018.01.036
Motheau, Emmanuel, Duarte, Max, Almgren, Ann, and Bell, John B. Wed .
"A hybrid adaptive lowMach number/compressible method: Euler equations". United States. https://doi.org/10.1016/j.jcp.2018.01.036. https://www.osti.gov/servlets/purl/1543561.
@article{osti_1543561,
title = {A hybrid adaptive lowMach number/compressible method: Euler equations},
author = {Motheau, Emmanuel and Duarte, Max and Almgren, Ann and Bell, John B.},
abstractNote = {© 2018 Elsevier Inc. Flows in which the primary features of interest do not rely on highfrequency acoustic effects, but in which longwavelength acoustics play a nontrivial role, present a computational challenge. Integrating the entire domain with lowMachnumber methods would remove all acoustic wave propagation, while integrating the entire domain with the fully compressible equations can in some cases be prohibitively expensive due to the CFL time step constraint. For example, simulation of thermoacoustic instabilities might require fine resolution of the fluid/chemistry interaction but not require fine resolution of acoustic effects, yet one does not want to neglect the longwavelength wave propagation and its interaction with the larger domain. The present paper introduces a new multilevel hybrid algorithm to address these types of phenomena. In this new approach, the fully compressible Euler equations are solved on the entire domain, potentially with local refinement, while their lowMachnumber counterparts are solved on subregions of the domain with higher spatial resolution. The finest of the compressible levels communicates inhomogeneous divergence constraints to the coarsest of the lowMachnumber levels, allowing the lowMachnumber levels to retain the longwavelength acoustics. The performance of the hybrid method is shown for a series of test cases, including results from a simulation of the aeroacoustic propagation generated from a Kelvin–Helmholtz instability in lowMachnumber mixing layers. It is demonstrated that compared to a purely compressible approach, the hybrid method allows timesteps two orders of magnitude larger at the finest level, leading to an overall reduction of the computational time by a factor of 8.},
doi = {10.1016/j.jcp.2018.01.036},
journal = {Journal of Computational Physics},
number = C,
volume = 372,
place = {United States},
year = {2018},
month = {1}
}
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