Adaptive Time-Space Algorithms for the Simulation of Multi-scale Reaction Waves

Duarte, Max; Massot, Marc; Descombes, Stéphane; Dumont, Thierry

doi:10.1007/978-3-642-20671-9_40

Cited by 3 publications

(2 citation statements)

References 13 publications

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“…The second scheme, denoted scheme B, is based on the formulation of the nonconservative product described in Equation (4.9), where the timestep is also limited by the same Fourier stability condition. The third scheme, denoted scheme C, is based on the formulation of the nonconservative product defined in Equation (4.9), using an operator splitting approach based on a second-order Strang formalism in order to separate the convection and diffusion operators [32,13,9,12]. The idea is to not be limited by the small timesteps ∆t F imposed by the Fourier stability condition, due to the electron thermal diffusivity.…”

Section: Specific Treatment Of the Nonconservative Productmentioning

confidence: 99%

Numerical Treatment of the Nonconservative Product in a Multiscale Fluid Model for Plasmas in Thermal Nonequilibrium: Application to Solar Physics

Wargnier¹,

Faure²,

Graille³

et al. 2020

SIAM J. Sci. Comput.

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This contribution deals with the modeling of collisional multicomponent magnetized plasmas in thermal and chemical nonequilibrium aiming at simulating and predicting magnetic reconnections in the chromosphere of the sun. We focus on the numerical simulation of a simplified fluid model in order to properly investigate the influence on shock solutions of a nonconservative product present in the electron energy equation. Then, we derive jump conditions based on travelling wave solutions and propose an original numerical treatment in order to avoid non-physical shocks for the solution, that remains valid in the case of coarse-resolution simulations. A key element for the numerical scheme proposed is the presence of diffusion in the electron variables, consistent with the physically-sound scaling used in the model developed by Graille et al. following a multiscale Chapman-Enskog expansion method [M3AS, 19 (2009) 527-599]. The numerical strategy is eventually assessed in the framework of a solar physics test case. The computational method is able to capture the travelling wave solutions in both the highly-and coarsely-resolved cases.

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Section: Specific Treatment Of the Nonconservative Productmentioning

confidence: 99%

Numerical Treatment of the Nonconservative Product in a Multiscale Fluid Model for Plasmas in Thermal Nonequilibrium: Application to Solar Physics

Wargnier¹,

Faure²,

Graille³

et al. 2020

SIAM J. Sci. Comput.

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“…The model under consideration is borrowed from a configuration investigated by Laverdant & Candel in [80]. Some of these results were previously announced in [81], in a more general context without any detailed analysis.…”

Section: Propagation Of Premixed Flamesmentioning

confidence: 99%

Time–space adaptive numerical methods for the simulation of combustion fronts

Duarte¹,

Descombes²,

Tenaud³

et al. 2013

Combustion and Flame

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To cite this version:Max Duarte, Stéphane Descombes, Christian Tenaud, Sébastien Candel, Marc Massot. Time-space adaptive numerical methods for the simulation of combustion fronts. Combustion and Flame, Elsevier, 2013, 160 (6) AbstractThis paper presents a new computational strategy for the simulation of combustion fronts based on adaptive time operator splitting and spatial multiresolution. High-order and dedicated onestep solvers compose the splitting scheme for the reaction, diffusion, and convection subproblems, to independently cope with their inherent numerical difficulties and to properly solve the corresponding temporal scales. Adaptive and thus highly compressed spatial representations for localized fronts originating from multiresolution analysis result in important reductions of memory usage, and hence numerical simulations with sufficiently fine spatial resolution can be performed with standard computational resources. The computational efficiency is further enhanced by splitting time steps established beyond standard stability constraints associated to mesh size or stiff source time scales. The splitting time steps are chosen according to a dynamic splitting technique relying on solid mathematical foundations, which ensures error control of the time integration and successfully discriminates time-varying multi-scale physics. For a given semidiscretized problem, the solution scheme provides dynamic accuracy estimates that reflect the quality of numerical results in terms of numerical errors of integration and compressed spatial representations, for general multi-dimensional problems modeled by stiff PDEs. The strategy is efficiently applied to simulate the propagation of laminar premixed flames interacting with vortex structures, as well as various configurations of self-ignition processes of diffusion flames in similar vortical hydrodynamics fields. A detailed study of the error control is provided and show the potential of the approach. It yields large gains in CPU time, while consistently describing a broad spectrum of space and time scales as well as different physical scenarios.

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A new numerical strategy with space-time adaptivity and error control for multi-scale streamer discharge simulations

Duarte

Bonaventura

Massot

et al. 2012

Journal of Computational Physics

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Support of Ecole Centrale Paris is gratefully acknowledged for several month stay of Z. Bonaventura at Laboratory EM2C as visiting Professor. Authors express special thanks to Christian Tenaud (LIMSI-CNRS) for providing the basis of the multiresolution kernel of MR CHORUS, code developed for compressible Navier-Stokes equations (Déclaration d'Invention DI 03760-01). Accepted for publication.International audienceThis paper presents a new resolution strategy for multi-scale streamer discharge simulations based on a second order time adaptive integration and space adaptive multiresolution. A classical fluid model is used to describe plasma discharges, considering drift-diffusion equations and the computation of electric field. The proposed numerical method provides a time-space accuracy control of the solution, and thus, an effective accurate resolution independent of the fastest physical time scale. An important improvement of the computational efficiency is achieved whenever the required time steps go beyond standard stability constraints associated with mesh size or source time scales for the resolution of the drift-diffusion equations, whereas the stability constraint related to the dielectric relaxation time scale is respected but with a second order precision. Numerical illustrations show that the strategy can be efficiently applied to simulate the propagation of highly nonlinear ionizing waves as streamer discharges, as well as highly multi-scale nanosecond repetitively pulsed discharges, describing consistently a broad spectrum of space and time scales as well as different physical scenarios for consecutive discharge/post-discharge phases, out of reach of standard non-adaptive methods

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Adaptive Time-Space Algorithms for the Simulation of Multi-scale Reaction Waves

Cited by 3 publications

References 13 publications

Numerical Treatment of the Nonconservative Product in a Multiscale Fluid Model for Plasmas in Thermal Nonequilibrium: Application to Solar Physics

Numerical Treatment of the Nonconservative Product in a Multiscale Fluid Model for Plasmas in Thermal Nonequilibrium: Application to Solar Physics

Time–space adaptive numerical methods for the simulation of combustion fronts

A new numerical strategy with space-time adaptivity and error control for multi-scale streamer discharge simulations

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