A Runge Kutta Discontinuous Galerkin approach to solve reactive flows on conforming hybrid grids: the parabolic and source operators

Billet, G.; Ryan, Juliette; Borrel, M.

doi:10.1016/j.compfluid.2014.01.031

Cited by 7 publications

(13 citation statements)

References 21 publications

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“…and λ (1) y = λ (2) y = −1/4, λ (3) y = λ (4) y = 1/4. For k = 1, one can use the same formulas with w…”

Section: Data Prolongation and Data Projectionmentioning

confidence: 99%

“…The proper understanding of the detonation waves propagation plays an important role in protecting human lives and avoiding property damages. To study detonation phenomena, various numerical methods have been employed, including second order Godunov scheme [1,27], extended space-time CE/SE method [35], unsplit scheme [23], non-MUSCL-type TVD scheme [31], classical weighted essentially non-oscillatory (WENO) scheme [11,32], optimal WENO-Z scheme [14,15], hybrid central-WENO scheme [13], Runge-Kutta discontinuous Galerkin (RKDG) method [3,33,34] and adaptive finite volume methods [17] .…”

Section: Introductionmentioning

confidence: 99%

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An $h$-Adaptive RKDG Method for Two-Dimensional Detonation Wave Simulations

Gao¹

2019

EAJAM

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An h-adaptive Runge-Kutta discontinuous Galerkin (RKDG) method with a positivity-preserving technique to simulate classical two-dimensional detonation waves is developed. The KXRCF troubled-cell indicator is used to detect the troubled cells with possible discontinuities or high gradients. At each time-level, an adaptive mesh is generated by refining troubled cells and coarsening others. In order to avoid the situations where detonation front moves too fast and there are not enough cells to describe detonation front before it leaves, a recursive multi-level mesh refinement technique is designed. The numerical results show that for smooth solutions, this h-adaptive method does not degrade the optimal convergence order of the nonadaptive method and outperforms it in terms of computational storage for shocked flows.

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“…and λ (1) y = λ (2) y = −1/4, λ (3) y = λ (4) y = 1/4. For k = 1, one can use the same formulas with w…”

Section: Data Prolongation and Data Projectionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

An $h$-Adaptive RKDG Method for Two-Dimensional Detonation Wave Simulations

Gao¹

2019

EAJAM

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“…Almost twenty years later, Cockburn and Shu applied the DG approach to conservation laws and more specifically to the Navier-Stokes equations (NSE) [4][5][6]. Since then, it has been widely employed to perform LES simulations of multiple problems such as turbulent jets [7], laminar to turbulent transition [8] or shock waves [9] and combustion applications [10][11][12]. However, as the scheme order increases, the computational cost of the DG approach soars fastly.…”

Section: Introductionmentioning

confidence: 99%

“…Then, γ is non-constant and without any treatments, a pressure jump can appear through any contact discontinuity (such as the one initialized in Figure 1) and this jump will create spurious oscillations of all physical quantities according to Abgrall et al [48]. The same authors have proposed a special treatment named as the Double Flux method which has been successfully applied in reactive DG computations [10][11][12]. Adapting this treatment to the SD formalism is out of the scope of this paper but will be the purpose of future work.…”

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confidence: 99%

Extension of the Spectral Difference method to combustion

Marchal¹,

Deniau²,

Boussuge³

et al. 2021

Preprint

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A Spectral Difference (SD) algorithm on tensor-product elements which solves the reacting compressible Navier-Stokes equations (NSE) is presented. The classical SD algorithm is shown to be unstable when a multispecies gas where thermodynamic properties depend on temperature and species mass fractions is considered. In that case, a modification of the classical algorithm was successfully employed making it stable. It uses the fact that it is better for the multispecies case to compute primitive variables from conservative variables at solution points and then extrapolate them at flux points rather than extrapolating conservative variables at flux points and reconstruct primitive variables on these points. Characteristic, wall and symmetry boundary conditions for reactive flows in the SD framework are also introduced. They all use the polynomial form of the variables and of the fluxes to impose the correct boundary condition at a boundary flux point. Validation test cases on one-dimensional and two-dimensional laminar flames have been performed using both global chemistry and Analytically Reduced Chemistry (ARC). Results show excellent agreement with the reference combustion code AVBP validating the implementation of this SD method on laminar combustion.

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“…The DG approach marries the ability to allow discontinuities in a natural way with its great accuracy granted even on general meshes, both important properties to compute the wrinkled flame fronts encountered in turbulent combustion, and indeed reactive DG codes have recently appeared (see e.g. [5,6]). …”

Section: Introductionmentioning

confidence: 99%

Discontinuous Galerkin Computation of Gaseous Mixture Coaxial Jets

Franchina¹,

Savini²,

Bassi³

2016

Proceedings of the VII European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS Congress 2016)

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Abstract. A novel approach based upon Discontinuous Galerkin (DG) discretization, applied to the divergence form of the multicomponent Navier-Stokes equations, is here presented and used to compute non reactive turbulent axisymmetric gaseous jets. The original key feature is the use of L 2 -projection form of the (perfect gas) equation of state. This choice mitigates problems typically encountered by the front-capturing schemes in computing multicomponent flow fields, i.e. spurious oscillations across material and contact surfaces where the mixture composition is changing. The solver makes also use of a shock-capturing technique based on artificial dissipation selectively added into the equations and tuned in connection with the magnitude of inviscid residuals of the equations and on suitable coefficients accounting for the variation of the unknown variables within and across grid elements. A simple limiting procedure is introduced in order to avoid the occurrence of unphysical gas properties due to negative and/or greater that one mass fractions values within the domain. The DG code based on the proposed novel technique for multicomponent flow computation is here employed to study the mixing mode and the preferential diffusion mechanism of a mixture jet of helium and carbon dioxide in a surrounding flow of air, both in laminar and turbulent flow regimes. Mass diffusion is modelled by means of Fick's first law and use is made of constant Prandtl and Schmidt numbers in Wilcox's (2008) k − ω model. Third-order accurate results are presented, discussed and compared with the available experimental data. They confirm the possible existence in coaxial jets of different periodic flow structures, greatly affecting mixing rates, and different species diffusive mass fluxes. The relative importance of both phenomena depends on the flow regime and its characteristics. The tests carried out give at the same time indications about the accuracy of the proposed method and its effectiveness in computing complex unsteady flow fields.

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A Runge Kutta Discontinuous Galerkin approach to solve reactive flows on conforming hybrid grids: the parabolic and source operators

Cited by 7 publications

References 21 publications

An $h$-Adaptive RKDG Method for Two-Dimensional Detonation Wave Simulations

An $h$-Adaptive RKDG Method for Two-Dimensional Detonation Wave Simulations

Extension of the Spectral Difference method to combustion

Discontinuous Galerkin Computation of Gaseous Mixture Coaxial Jets

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