TY - JOUR

T1 - Semi-implicit iterative methods for low Mach number turbulent reacting flows

T2 - Operator splitting versus approximate factorization

AU - MacArt, Jonathan F.

AU - Mueller, Michael Edward

N1 - Funding Information:
The authors gratefully acknowledge valuable support in the form of computational time on the TIGRESS high performance computer center at Princeton University, which is jointly supported by the Princeton Institute for Computational Science and Engineering ( PICSciE ) and the Princeton University Office of Information Technology's Research Computing Department .
Publisher Copyright:
© 2016 Elsevier Inc.
Copyright:
Copyright 2019 Elsevier B.V., All rights reserved.

PY - 2016/12/1

Y1 - 2016/12/1

N2 - Two formally second-order accurate, semi-implicit, iterative methods for the solution of scalar transport–reaction equations are developed for Direct Numerical Simulation (DNS) of low Mach number turbulent reacting flows. The first is a monolithic scheme based on a linearly implicit midpoint method utilizing an approximately factorized exact Jacobian of the transport and reaction operators. The second is an operator splitting scheme based on the Strang splitting approach. The accuracy properties of these schemes, as well as their stability, cost, and the effect of chemical mechanism size on relative performance, are assessed in two one-dimensional test configurations comprising an unsteady premixed flame and an unsteady nonpremixed ignition, which have substantially different Damköhler numbers and relative stiffness of transport to chemistry. All schemes demonstrate their formal order of accuracy in the fully-coupled convergence tests. Compared to a (non-)factorized scheme with a diagonal approximation to the chemical Jacobian, the monolithic, factorized scheme using the exact chemical Jacobian is shown to be both more stable and more economical. This is due to an improved convergence rate of the iterative procedure, and the difference between the two schemes in convergence rate grows as the time step increases. The stability properties of the Strang splitting scheme are demonstrated to outpace those of Lie splitting and monolithic schemes in simulations at high Damköhler number; however, in this regime, the monolithic scheme using the approximately factorized exact Jacobian is found to be the most economical at practical CFL numbers. The performance of the schemes is further evaluated in a simulation of a three-dimensional, spatially evolving, turbulent nonpremixed planar jet flame.

AB - Two formally second-order accurate, semi-implicit, iterative methods for the solution of scalar transport–reaction equations are developed for Direct Numerical Simulation (DNS) of low Mach number turbulent reacting flows. The first is a monolithic scheme based on a linearly implicit midpoint method utilizing an approximately factorized exact Jacobian of the transport and reaction operators. The second is an operator splitting scheme based on the Strang splitting approach. The accuracy properties of these schemes, as well as their stability, cost, and the effect of chemical mechanism size on relative performance, are assessed in two one-dimensional test configurations comprising an unsteady premixed flame and an unsteady nonpremixed ignition, which have substantially different Damköhler numbers and relative stiffness of transport to chemistry. All schemes demonstrate their formal order of accuracy in the fully-coupled convergence tests. Compared to a (non-)factorized scheme with a diagonal approximation to the chemical Jacobian, the monolithic, factorized scheme using the exact chemical Jacobian is shown to be both more stable and more economical. This is due to an improved convergence rate of the iterative procedure, and the difference between the two schemes in convergence rate grows as the time step increases. The stability properties of the Strang splitting scheme are demonstrated to outpace those of Lie splitting and monolithic schemes in simulations at high Damköhler number; however, in this regime, the monolithic scheme using the approximately factorized exact Jacobian is found to be the most economical at practical CFL numbers. The performance of the schemes is further evaluated in a simulation of a three-dimensional, spatially evolving, turbulent nonpremixed planar jet flame.

KW - Chemical Jacobian

KW - Direct numerical simulation

KW - Operator splitting

KW - Strang splitting

KW - Turbulent reacting flows

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U2 - 10.1016/j.jcp.2016.09.016

DO - 10.1016/j.jcp.2016.09.016

M3 - Article

AN - SCOPUS:84988422394

VL - 326

SP - 569

EP - 595

JO - Journal of Computational Physics

JF - Journal of Computational Physics

SN - 0021-9991

ER -