An improved method of lines to compute time dependent laminar flame structure

The initial boundary-value problem associated to a semilinear wave equation with time-dependent boundary values was approximated by using the method of lines. Time integration is achieved by means of an explicit time method obtained from an arbitrarily high-order splitting scheme. We propose a technique to incorporate the boundary values that is more accurate than the one obtained in the standard way, which is clearly seen in the numerical experiments. We prove the consistency and convergence, with the same order of the splitting method, of the full discretization carried out with this technique. Although we performed mathematical analysis under the hypothesis that the source term was Lipschitz-continuous, numerical experiments show that this technique works in more general cases.

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The Structure of Laminar Premixed H2-Air Flames at Elevated Pressures

Zeitschrift für Physikalische Chemie ◽

10.1524/zpch.2000.214.4.419 ◽

2000 ◽

Vol 214 (4) ◽

Cited By ~ 5

Author(s):

M. El-Gamal ◽

E. Gutheil ◽

J. Warnatz

Keyword(s):

Laminar Flame ◽

Flame Structure ◽

Ideal Gas ◽

Fortran Program ◽

Laminar Flame Speed ◽

Real Gas ◽

One Dimensional ◽

Rocket Propulsion ◽

Elevated Pressures ◽

Engine Combustion

In high-pressure flames that occur in many practical combustion devices such as industrial furnaces, rocket propulsion and internal engine combustion, the assumption of an ideal gas is not appropriate. The present paper presents a model that includes modifications of the equation of state, transport and thermodynamic properties. The model is implemented into a Fortran program that was developed to simulate numerically one-dimensional planar premixed flames. The influence of the modifications for the real gas behavior on the laminar flame speed and on flame structure is illustrated for stoichiometric H

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A local radial basis function differential quadrature semi-discretisation technique for the simulation of time-dependent reaction-diffusion problems

Engineering Computations ◽

10.1108/ec-05-2020-0291 ◽

2021 ◽

Vol ahead-of-print (ahead-of-print) ◽

Author(s):

Ram Jiwari ◽

Alf Gerisch

Keyword(s):

Meshless Method ◽

Order Of Convergence ◽

Method Of Lines ◽

Reaction Diffusion ◽

Diffusion Models ◽

Second Order ◽

Differential Quadrature ◽

Time Dependent ◽

Content Type ◽

Radial Basis

Purpose This paper aims to develop a meshfree algorithm based on local radial basis functions (RBFs) combined with the differential quadrature (DQ) method to provide numerical approximations of the solutions of time-dependent, nonlinear and spatially one-dimensional reaction-diffusion systems and to capture their evolving patterns. The combination of local RBFs and the DQ method is applied to discretize the system in space; implicit multistep methods are subsequently used to discretize in time. Design/methodology/approach In a method of lines setting, a meshless method for their discretization in space is proposed. This discretization is based on a DQ approach, and RBFs are used as test functions. A local approach is followed where only selected RBFs feature in the computation of a particular DQ weight. Findings The proposed method is applied on four reaction-diffusion models: Huxley’s equation, a linear reaction-diffusion system, the Gray–Scott model and the two-dimensional Brusselator model. The method captured the various patterns of the models similar to available in literature. The method shows second order of convergence in space variables and works reliably and efficiently for the problems. Originality/value The originality lies in the following facts: A meshless method is proposed for reaction-diffusion models based on local RBFs; the proposed scheme is able to capture patterns of the models for big time T; the scheme has second order of convergence in both time and space variables and Nuemann boundary conditions are easy to implement in this scheme.

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Large Eddy Simulation of Premixed Combustion With a Thickened-Flame Approach

Journal of Engineering for Gas Turbines and Power ◽

10.1115/1.3094021 ◽

2009 ◽

Vol 131 (6) ◽

Cited By ~ 11

Author(s):

Ashoke De ◽

Sumanta Acharya

Keyword(s):

Large Eddy Simulation ◽

Laminar Flame ◽

Flame Structure ◽

Reaction Rates ◽

Premixed Combustion ◽

Efficiency Function ◽

Modeling Approach ◽

Eddy Simulation ◽

Reduced Chemistry ◽

Large Eddy

A thickened-flame (TF) modeling approach is combined with a large eddy simulation (LES) methodology to model premixed combustion, and the accuracy of these model predictions is evaluated by comparing with the piloted premixed stoichiometric methane-air flame data of Chen et al. (1996, “The Detailed Flame Structure of Highly Stretched Turbulent Premixed Methane-Air Flames,” Combust. Flame, 107, pp. 233–244) at a Reynolds number Re=24,000. In the TF model, the flame front is artificially thickened to resolve it on the computational LES grid and the reaction rates are specified using reduced chemistry. The response of the thickened-flame to turbulence is taken care of by incorporating an efficiency function in the governing equations. The efficiency function depends on the characteristics of the local turbulence and on the characteristics of the premixed flame such as laminar flame speed and thickness. Three variants of the TF model are examined: the original thickened-flame model, the power-law flame-wrinkling model, and the dynamically modified TF model. Reasonable agreement is found when comparing predictions with the experimental data and with computations reported using a probability distribution function modeling approach. The results of the TF model are in better agreement with data when compared with the predictions of the G-equation approach.

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