Development of a Parallel Unstructured Multigrid Solver for Laminar Flame Simulations with Detailed Chemistry and Transport

Paxion, Sébastien; Baron, Romain; Gordner, A.; Neuss‐Radu, Maria; Bastian, Peter; Thévenin, Dominique; Wittum, Gabriel

doi:10.1007/978-3-540-44567-8_11

Cited by 2 publications

(2 citation statements)

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“…The energy equation is written in its temperature form, and the spatial gradients of the mixture heat capacity are assumed to be small. The enthalpy transport term due to diffusive fluxes have usually a small influence in the solution, 22,34,35 and is neglected in the energy equation. Under these assumptions, the Navier–Stokes equations, the energy equation (in its temperature form) and the species transport equations are

\begin{align} \frac{\partial \overset{ρ}{true}}{\partial \overset{t}{true}} + \overset{\nabla}{true} \cdot false(\overset{ρ}{true} \overset{boldu}{true} false) & = 0, \end{align}

\begin{align} \frac{\partial \overset{ρ}{true} \overset{boldu}{true}}{\partial \overset{t}{true}} + \overset{\nabla}{true} \cdot false(\overset{ρ}{true} \overset{boldu}{true} \otimes \overset{boldu}{true} false) & = prefix- \overset{\nabla}{true} \overset{p}{true} + \overset{\nabla}{true} \cdot ((), {\overset{μ}{true}}^{} ((), \overset{\nabla}{true} {\overset{boldu}{true}}^{} + {false(\overset{\nabla}{true} {\overset{boldu}{true}}^{} false)}^{T} prefix- \frac{2}{3} false(\overset{\nabla}{true} \cdot {\overset{boldu}{true}}^{} false) bold-italicI)) prefix- \overset{ρ}{true} \overset{boldg}{true}, \end{align}

\begin{align} \frac{\partial \overset{ρ}{true} \overset{T}{true}}{\partial \overset{t}{true}} + \overset{\nabla}{true} \cdot false(\overset{ρ}{true} \overset{boldu}{true} \overset{T}{true} false) & = \frac{1}{...} \end{align}

…”

Section: Governing Equationsmentioning

confidence: 99%

“…This idea was used in several works such as that by Keyes and Smooke 19 for a counter diffusion flame, by Smooke 20 for a Tsuji‐counterflow configuration and in the work by Dobbins et al 21 for an axisymmetric laminar jet diffusion flame with time dependent boundary conditions. In the work of Paxion 22 unstructured multigrid solver for laminar flames with detailed chemistry is presented. A Krylov–Newton method was used for solving several flame configurations.…”

Section: Introduction and State Of The Artmentioning

confidence: 99%

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A fully coupled high‐order discontinuous Galerkin method for diffusion flames in a low‐Mach number framework

Gutiérrez-Jorquera

Kummer

2021

Numerical Methods in Fluids

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We present a fully coupled solver based on the discontinuous Galerkin method for steady‐state diffusion flames using the low‐Mach approximation of the governing equations with a one‐step kinetic model. The nonlinear equation system is solved with a Newton–Dogleg method and initial estimates for flame calculations are obtained from a flame‐sheet model. Details on the spatial discretization and the nonlinear solver are presented. The method is tested with reactive and nonreactive benchmark cases. Convergence studies are presented, and we show that the expected convergence rates are obtained. The solver for the low‐Mach equations is used for calculating a differentially heated cavity configuration, which is validated against benchmark solutions. Additionally, a two‐dimensional counter diffusion flame is calculated, and the results are compared with the self‐similar one dimensional solution of said configuration.

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