The semi-Lagrangian method on curvilinear grids

Hamiaz, Adnane; Mehrenberger, Michel; Sellama, Hocine; Sonnendrücker, Éric

doi:10.1515/caim-2016-0024

Cited by 5 publications

(22 citation statements)

References 35 publications

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“…We refer to [24] for the derivation of the equations and only put here the results. We denote by Ω ∈ R 2 the physical domain where the equations are set.…”

Section: Curvilinear Frameworkmentioning

confidence: 99%

“…Previous Poisson solvers using FFT (for polar or cartesian mesh) are no more valid in this context. Alternative possible strategies are to interface the code with other existing softwares (like Mudpack, used in [24]). Note that these difficulties were not present in the context of semi-Lagrangian simulations on simple grids.…”

Section: Introductionmentioning

confidence: 99%

“…Note that a further study about semi-Lagrangian schemes on curvilinear geometry is performed in [24], written after the first submission of this work. We focus here on the Poisson solver and on the ability of the same code to perform simulations on different geometries, such points being not discussed in [24].…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…We focus here on the Poisson solver and on the ability of the same code to perform simulations on different geometries, such points being not discussed in [24]. We refer to [24] for more references on semi-Lagrangian schemes, motivations, context description and other validations of the code that is used for the simulations. We mention also the work on the SELHEX project [27], which is an alternative strategy allowing to avoid geometrical singularity of the Jacobian, as it is the case for example using polar mesh.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Guiding center simulations on curvilinear grids

Hamiaz¹,

Mehrenberger²,

Back³

et al. 2016

ESAIM: Proc.

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Abstract. Semi-Lagrangian guiding center simulations are performed on sinusoidal perturbations of cartesian grids, and on deformed polar grid with different boundary conditions. Key ingredients are: the use of a B-spline finite element solver for the Poisson equation and the classical backward semiLagrangian method (BSL) for the advection. We are able to reproduce standard Kelvin-Helmholtz and diocotron instability tests on such grids. When the perturbation leads to a strong distorted mesh, we observe that the solution differs if one takes standard numerical parameters that are used in the cartesian reference case. We can recover good results together with correct mass conservation, by diminishing the time step.Résumé. Des simulations semi-lagrangiennes du modèle centre-guide sont effectuées sur des perturbations sinusoïdales de maillages cartésiens et sur des maillages polaires déformés. Les ingrédients clés sont: l'utilisation d'un solveuréléments finis splines pour l'équation de Poisson et la méthode semi-Lagrangienne en arrière classique (BSL) pour l'advection. Nous pouvons reproduire des tests standards d'instabilité de Kelvin-Helmholtz et diocotron sur ces grilles. Lorsque la déformation du maillage est forte, on observe que la solution diffère, si on prend les paramètres numériques standards qui sont utilisés dans le cas cartésien de référence. On peut retrouver néanmoins les bons résultats et une conservation de masse correcte, en diminuant le pas de temps.

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“…We refer to [24] for the derivation of the equations and only put here the results. We denote by Ω ∈ R 2 the physical domain where the equations are set.…”

Section: Curvilinear Frameworkmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Guiding center simulations on curvilinear grids

Hamiaz¹,

Mehrenberger²,

Back³

et al. 2016

ESAIM: Proc.

Self Cite

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A semi-Lagrangian transport method for kinetic problems with application to dense-to-dilute polydisperse reacting spray flows

Doisneau

Arienti

Oefelein

2017

Journal of Computational Physics

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For sprays, as described by a kinetic disperse phase model strongly coupled to the Navier-Stokes equations, the resolution strategy is constrained by accuracy objectives, robustness needs, and the computing architecture. In order to leverage the good properties of the Eulerian formalism, we introduce a deterministic particle-based numerical method to solve transport in physical space, which is simple to adapt to the many types of closures and moment systems. The method is inspired by the semi-Lagrangian schemes, developed for Gas Dynamics. We show how semi-Lagrangian formulations are relevant for a disperse phase far from equilibrium and where the particle-particle coupling barely influences the transport; i.e., when particle pressure is negligible. The particle behavior is indeed close to free streaming. The new method uses the assumption of parcel transport and avoids to compute fluxes and their limiters, which makes it robust. It is a deterministic resolution method so that it does not require efforts on statistical convergence, noise control, or post-processing. All couplings are done among data under the form of Eulerian fields, which allows one to use efficient algorithms and to anticipate the computational load. This makes the method both accurate and efficient in the context of parallel computing. After a complete verification of the new transport method on various academic test cases, we demonstrate the overall strategy's ability to solve a strongly-coupled liquid jet with fine spatial resolution and we apply it to the case of high-fidelity Large Eddy Simulation of a dense spray flow. A fuel spray is simulated after atomization at Diesel engine combustion chamber conditions. The large, parallel, strongly coupled computation proves the efficiency of the method for dense, polydisperse, reacting spray flows.

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Highly accurate monotonicity-preserving Semi-Lagrangian scheme for Vlasov-Poisson simulations

Yang

Mehrenberger

2021

Journal of Computational Physics

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In this paper, we study a highly accurate monotonicity-preserving (MP) Semi-Lagrangian scheme for Vlasov-Poisson simulations. The classical Semi-Lagrangian scheme is known to be highly accurate and free from CFL condition, but it does not satisfy local maximum principle. To remedy this drawback, using the conservative form of the Semi-Lagrangian scheme, we recast existing MP schemes for the numerical flux in a common framework, and then substitute the local extremum by some "better" guess, in order to avoid as much as possible loss of accuracy and clipping near extrema, while keeping the monotonicity on monotone portions. With the limiter, on the one hand, the scheme keeps the good properties of the unlimited scheme: it is conservative, free from CFL condition and highly accurate. On the other hand, for locally monotonic data, the monotonicity of the solution is preserved. Numerical tests are made on free transport equation and Vlasov-Poisson system illustrating that the limited scheme is more diffusive compared to cubic splines but has better L 1 conservation, which is primarily an advantage for problems with sharp gradients.

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The semi-Lagrangian method on curvilinear grids

Cited by 5 publications

References 35 publications

Guiding center simulations on curvilinear grids

Guiding center simulations on curvilinear grids

A semi-Lagrangian transport method for kinetic problems with application to dense-to-dilute polydisperse reacting spray flows

Highly accurate monotonicity-preserving Semi-Lagrangian scheme for Vlasov-Poisson simulations

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