A Semi-implicit Numerical Scheme for Reacting Flow

Najm, Habib N.; Wyckoff, P.; Knio, Omar M.

doi:10.1006/jcph.1997.5856

Cited by 199 publications

(185 citation statements)

References 46 publications

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“…(43), is with constant coefficient and can be solved very efficiently. Subsequently, it seems that this approach was used in all the previous studies dealing with low-Mach number flows [1][2][3][4][5][6][7][8]. The approach involving a Poisson equation with variable coefficient as in Subsections 3.1 and 3.2 was preferred in [11][12][13].…”

Section: Scheme With Approximate Poisson Equation: Divsc ρmentioning

confidence: 99%

“…Sandoval (reported in [6]) found that by decreasing the Reynolds number, larger variations in density could be achieved. Larger density ratios seem computable by using a predictor-corrector time-stepping algorithm in which the predictor uses a second-order Adams-Bashforth time integration scheme and the corrector relies on a quasi-Crank-Nicolson integration with the inversion of a pressure Poisson equation at each step [7,8].…”

Section: Introductionmentioning

confidence: 99%

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Conservative High-Order Finite-Difference Schemes for Low-Mach Number Flows

Nicoud¹

2000

Journal of Computational Physics

164

149

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Three finite-difference algorithms are proposed to solve a low-Mach number approximation for the Navier-Stokes equations. These algorithms exhibit fourth-order spatial and second-order temporal accuracy. They are dissipation-free, and thus well suited for DNS and LES of turbulent flows. The key ingredient common to each of the methods presented is a Poisson equation with variable coefficient that is solved for the hydrodynamic pressure. This feature ensures that the velocity field is constrained correctly. It is shown that this approach is needed to avoid violation of the conservation of kinetic energy in the inviscid limit which would otherwise arise through the pressure term in the momentum equation. An existing set of finite-difference formulae for incompressible flow is generalized to handle arbitrary large density fluctuations with no violation of conservation through the non-linear convective terms. An algorithm which conserves mass, momentum, and kinetic energy fully is obtained when an approximate equation of state is used instead of the exact one. Results from a model problem are used to show both spatial and temporal convergence rates and several test cases are presented to illustrate the performance of the algorithms.

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Section: Scheme With Approximate Poisson Equation: Divsc ρmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Conservative High-Order Finite-Difference Schemes for Low-Mach Number Flows

Nicoud¹

2000

Journal of Computational Physics

164

149

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“…[16,17], which provide a detailed discussion of the numerical construction. Brief descriptions of the physical formulation and numerical scheme are provided below.…”

Section: Formulation and Numerical Schemesmentioning

confidence: 99%

“…Under the above assumptions, the governing equations are expressed in non-dimensional form as [16,17] …”

Section: Physical Modelmentioning

confidence: 99%

Effect of stoichiometry and strain rate on transient flame response

Knio

Najm

2000

Proceedings of the Combustion Institute

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“…Several physical phenomena are described by these problems. We mention, for instance, reactive flow processes and combustion theory [13], multi-phase flow in heterogeneous porous media [9], chemical reaction problems, atmospheric circulation problems [11], air pollution [14], etc. To obtain accurate numerical solutions for these problems, it is desirable to use numerical methods with good stability properties and, in addition, that take into account the special structure of the equations.…”

Section: Introducionmentioning

confidence: 99%

A note on B-stability of splitting methods

Araújo¹

2004

Computing and Visualization in Science

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Abstract. An important requirement of numerical methods for the integration of nonlinear stiff initial value problems is B-stability. In many applications it is also convenient to use splitting methods to take advantage of the special structure of the differential operator that defines the model. The purpose of this paper is to provide a necessary and sufficient condition for the B-stability of additive Runge-Kutta methods. We also present a family of B-stable fractional step Runge-Kutta methods.

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A Semi-implicit Numerical Scheme for Reacting Flow

Cited by 199 publications

References 46 publications

Conservative High-Order Finite-Difference Schemes for Low-Mach Number Flows

Conservative High-Order Finite-Difference Schemes for Low-Mach Number Flows

Effect of stoichiometry and strain rate on transient flame response

A note on B-stability of splitting methods

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