A second-order-in-time, explicit approach addressing the redundancy in the low-Mach, variable-density Navier-Stokes equations

Reuter, Bryan W.; Oliver, Todd A.; Moser, Robert D.

doi:10.1016/j.jcp.2024.113216

A second-order-in-time, explicit approach addressing the redundancy in the low-Mach, variable-density Navier-Stokes equations

Journal Article · Tue Jun 25 00:00:00 EDT 2024 · Journal of Computational Physics

DOI:https://doi.org/10.1016/j.jcp.2024.113216· OSTI ID:2430091

^[1]; Oliver, Todd A. ^[2]; Moser, Robert D. ^[2]

Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
Univ. of Texas, Austin, TX (United States)

A novel algorithm for explicit temporal discretization of the variable-density, low-Mach Navier-Stokes equations is presented here in this study. Recognizing there is a redundancy between the mass conservation equation, the equation of state, and the transport equation(s) for the scalar(s) which characterize the thermochemical state, and that it destabilizes explicit methods, we demonstrate how to analytically eliminate the redundancy and propose an iterative scheme to solve the resulting transformed scalar equations. The method obtains second-order accuracy in time regardless of the number of iterations, so one can terminate this subproblem once stability is achieved. Hence, flows with larger density ratios can be simulated while still retaining the efficiency, low cost, and parallelizability of an explicit scheme. The temporal discretization algorithm is used within a pseudospectral direct numerical simulation which extends the method of Kim, Moin, and Moser for incompressible flow to the variable-density, low-Mach setting, where we demonstrate stability for density ratios up to ~25.7.

View Accepted Manuscript (DOE)

Research Organization:: Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States)

Sponsoring Organization:: USDOE National Nuclear Security Administration (NNSA)

Grant/Contract Number:: NA0003525

OSTI ID:: 2430091

Report Number(s):: SAND--2024-10560J

Journal Information:: Journal of Computational Physics, Journal Name: Journal of Computational Physics Journal Issue: 1 Vol. 514; ISSN 0021-9991

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

References (25)

A comparative study of high-order variable-property segregated algorithms for unsteady low Mach number flows Knikker, R. International Journal for Numerical Methods in Fluids, Vol. 66, Issue 4 https://doi.org/10.1002/fld.2261	journal	May 2011
A Semi-implicit Numerical Scheme for Reacting Flow Najm, Habib N.; Wyckoff, Peter S.; Knio, Omar M. Journal of Computational Physics, Vol. 143, Issue 2 https://doi.org/10.1006/jcph.1997.5856	journal	July 1998
Conservative High-Order Finite-Difference Schemes for Low-Mach Number Flows Nicoud, F. Journal of Computational Physics, Vol. 158, Issue 1 https://doi.org/10.1006/jcph.1999.6408	journal	February 2000
Accurate Projection Methods for the Incompressible Navier–Stokes Equations Brown, David L.; Cortez, Ricardo; Minion, Michael L. Journal of Computational Physics, Vol. 168, Issue 2 https://doi.org/10.1006/jcph.2001.6715	journal	April 2001
A Semi-implicit Method for Resolution of Acoustic Waves in Low Mach Number Flows Wall, Clifton; Pierce, Charles D.; Moin, Parviz Journal of Computational Physics, Vol. 181, Issue 2 https://doi.org/10.1006/jcph.2002.7141	journal	September 2002
Solutions of Linear Difference Equations with Variable Coefficients Mallik, Ranjan K. Journal of Mathematical Analysis and Applications, Vol. 222, Issue 1 https://doi.org/10.1006/jmaa.1997.5903	journal	June 1998
MASA : a library for verification using manufactured and analytical solutions Malaya, Nicholas; Estacio-Hiroms, Kemelli C.; Stogner, Roy H. Engineering with Computers, Vol. 29, Issue 4 https://doi.org/10.1007/s00366-012-0267-9	journal	June 2012
A Stable Pressure-Correction Scheme for Time-Accurate Non-Premixed Combustion Simulations Rauwoens, Pieter; Vierendeels, Jan; Merci, Bart Flow, Turbulence and Combustion, Vol. 82, Issue 2 https://doi.org/10.1007/s10494-008-9177-8	journal	September 2008
Fourier/Chebyshev methods for the incompressible Navier-Stokes equations in infinite domains Corral, Roque; Jiménez, Javier Journal of Computational Physics, Vol. 121, Issue 2 https://doi.org/10.1016/S0021-9991(95)90085-3	journal	October 1995
Numerical simulation of the three-dimensional Rayleigh–Taylor instability Lee, Hyun Geun; Kim, Junseok Computers & Mathematics with Applications, Vol. 66, Issue 8 https://doi.org/10.1016/j.camwa.2013.08.021	journal	November 2013
An overview of projection methods for incompressible flows Guermond, J. L.; Minev, P.; Shen, Jie Computer Methods in Applied Mechanics and Engineering, Vol. 195, Issue 44-47 https://doi.org/10.1016/j.cma.2005.10.010	journal	September 2006
Pseudo-spectral numerical simulation of miscible fluids with a high density ratio Jang, Y.; de Bruyn Kops, S. M. Computers & Fluids, Vol. 36, Issue 2 https://doi.org/10.1016/j.compfluid.2005.11.003	journal	February 2007
Diffuse interface model for incompressible two-phase flows with large density ratios Ding, Hang; Spelt, Peter D. M.; Shu, Chang Journal of Computational Physics, Vol. 226, Issue 2 https://doi.org/10.1016/j.jcp.2007.06.028	journal	October 2007
A fast pressure-correction method for incompressible two-fluid flows Dodd, Michael S.; Ferrante, Antonino Journal of Computational Physics, Vol. 273 https://doi.org/10.1016/j.jcp.2014.05.024	journal	September 2014
A high-order numerical algorithm for DNS of low-Mach-number reactive flows with detailed chemistry and quasi-spectral accuracy Motheau, E.; Abraham, J. Journal of Computational Physics, Vol. 313 https://doi.org/10.1016/j.jcp.2016.02.059	journal	May 2016
On mass conservation and solvability of the discretized variable-density zero-Mach Navier-Stokes equations Lu, Xiaoyi; Pantano, Carlos Journal of Computational Physics, Vol. 404 https://doi.org/10.1016/j.jcp.2019.109132	journal	March 2020
Turbulence statistics in fully developed channel flow at low Reynolds number Kim, John; Moin, Parviz; Moser, Robert Journal of Fluid Mechanics, Vol. 177 https://doi.org/10.1017/S0022112087000892	journal	April 1987
A numerical study of a variable-density low-speed turbulent mixing layer Almagro, Antonio; García-Villalba, Manuel; Flores, Oscar Journal of Fluid Mechanics, Vol. 830 https://doi.org/10.1017/jfm.2017.583	journal	October 2017
Numerical Simulation of Low Mach Number Reactive Flows Tomboulides, A. G.; Lee, J. C. Y.; Orszag, S. A. Journal of Scientific Computing, Vol. 12, Issue 2, p. 139-167 https://doi.org/10.1023/A:1025669715376	journal	January 1997
On the three-dimensional Rayleigh–Taylor instability He, Xiaoyi; Zhang, Raoyang; Chen, Shiyi Physics of Fluids, Vol. 11, Issue 5 https://doi.org/10.1063/1.869984	journal	May 1999
Direct numerical simulations of incompressible Rayleigh–Taylor instabilities at low and medium Atwood numbers Hamzehloo, Arash; Bartholomew, Paul; Laizet, Sylvain Physics of Fluids, Vol. 33, Issue 5 https://doi.org/10.1063/5.0049867	journal	May 2021
Predicting large-scale pool fire dynamics using an unsteady flamelet- and large-eddy simulation-based model suite Domino, Stefan P.; Hewson, John; Knaus, Robert Physics of Fluids, Vol. 33, Issue 8 https://doi.org/10.1063/5.0060267	journal	August 2021
B-spline Methods in Fluid Dynamics Botella, Olivier; Shariff, Karim International Journal of Computational Fluid Dynamics, Vol. 17, Issue 2 https://doi.org/10.1080/1061856031000104879	journal	March 2003
Analytical Model of Nonlinear, Single-Mode, Classical Rayleigh-Taylor Instability at Arbitrary Atwood Numbers Goncharov, V. N. Physical Review Letters, Vol. 88, Issue 13 https://doi.org/10.1103/PhysRevLett.88.134502	journal	March 2002
DIRECT NUMERICAL SIMULATION: A Tool in Turbulence Research Moin, Parviz; Mahesh, Krishnan Annual Review of Fluid Mechanics, Vol. 30, Issue 1 https://doi.org/10.1146/annurev.fluid.30.1.539	journal	January 1998

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97 MATHEMATICS AND COMPUTING
Iterative methods
Low-Mach-number
Temporal discretization
Variable-density Navier-Stokes

A second-order-in-time, explicit approach addressing the redundancy in the low-Mach, variable-density Navier-Stokes equations

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