The CABARET method for a weakly compressible fluid flows in one- and two-dimensional implementations

Kulikov, Yu. M.; Сон, Э. Е.

doi:10.1088/1742-6596/774/1/012094

Cited by 4 publications

(5 citation statements)

References 3 publications

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“…The small vortexes grew and converged into bigger ones. This behavior is typical to 2D hydrodynamic instabilities [55][56][57]. The animation of figure 7, where merging vortices, can be found in [58].…”

Section: Drift Instabilitiesmentioning

confidence: 66%

2D3V kinetic simulation of Hall effect thruster, including azimuthal waves and diamagnetic effect

Chernyshev

Сон

Gorshkov

2019

J. Phys. D: Appl. Phys.

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Axial-azimuthal (2D3V) full-kinetic PiC+MCC-model was built to simulate dynamics of Hall effect thruster discharge plasma taking into account azimuthal waves and diamagnetic effect. The transition from ignition to the steady-state regime was simulated. Calculation of discharge ignition shows a significant distortion in the shape of the magnetic field caused by high azimuthal-drift current. This effect and intensive ionization lead to the fact that full potential drop localizes in a thin non-magnetized cathode layer. In the steady-state regime, the distortion of the magnetic field is small. Plasma divides into three regions: dense anode plasma where ionization occurs; magnetic layer where ions accelerate and quasineutral cathodeside plasma (plume). The steady-state regime is subject to auto-oscillations at a gas-transit frequency (20 kHz 'breathing modes'). Also, two types of azimuthal instabilities have been observed: gradient drift instability and electron cyclotron instability. All these instabilities lead to collisionless 'anomalous' electron transport across the magnetic field. Kinetic effects also were considered. It was found that the electron distribution function evolves from initial isotropic (Maxwellian) to essentially anisotropic due to electric field heating. Isotropy is partially restored inside anode plasma due to collisions.

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Section: Drift Instabilitiesmentioning

confidence: 66%

2D3V kinetic simulation of Hall effect thruster, including azimuthal waves and diamagnetic effect

Chernyshev

Сон

Gorshkov

2019

J. Phys. D: Appl. Phys.

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“…The CABARET scheme used in this study is implemented in the weak compressibility formulation. The features of this model were described in [55]. In [56] the characteristics of a double layer on a uniform mesh, as well as its stratified [57,58] counterpart were investigated.…”

Section: Cabaret Coveragementioning

confidence: 99%

Double shear layer evolution on the non-uniform computational mesh

Kulikov¹,

Son²

2021

Phys. Scr.

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This paper considers the problem of a thin shear layer evolution at Reynolds number rmRe = 400000 using the novel Compact Accurately Boundary Adjusting high-Resolution Technique (CABARET). The study is focused on the effect of the specific mesh refinement in the high shear rate areas on the flow properties under the influence of the developing instability. The original sequence of computational meshes (2562, 5122, 10242, 20482 cells) is modified using an iterative refinement algorithm based on the hyperbolic tangent. The properties of the solutions obtained are discussed in terms of the initial momentum thickness and the initial vorticity thickness, viscous and dilatational dissipation rates and also integral enstrophy. The growth rate for the most unstable mode depending on the mesh resolution is considered. In conclusion the accuracy of calculated mesh functions is estimated via L 1, L 2, L ∞ norms.

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“…Details of the characteristic decomposition at the extrapolation step (20) are summarised below for the case of orthogonal grid (i,j) that is aligned with coordinates (x,y). The indexing convention is such that point (i+1/2,j+1/2) corresponds to the cell centre and points (i+1,j+1/2), (i,j+1/2) and (i+1/2,j+1), (i+1/2,j) correspond to the cell face centres in the x-and y-directions, respectively.…”

Section: Example Of the Dispersion-improved Cabaret Scheme For 2d Isomentioning

confidence: 99%

“…Grid convergence for the dispersion-improved CABARET schemes without correction (P-DISP-CAB), with the modified relaxed correction (MR-DISP-CAB), and with full correction (F-DISP-CAB) in the linear advection test of a high-frequency wave modulated by a Gaussian. 20 The second initial distribution corresponding to the same linear advection equation is a rectangular pulse appended by a small amplitude high-frequency wave given by…”

Section: D Linear Advectionmentioning

confidence: 99%

“…Starting from the original formulation for one dimensional linear advection equation [6] CABARET was extended to aeroacoustics and turbulent flow modelling [11][12][13], asynchronous time stepping [14,15] and unstructured curvilinear nested grids on GPU [16] for performing computer-under-the-desk simulations of large-size problems within short turn-around solution times. At present, CABARET has found a good use in various applications from geophysical modelling [17,18] to aeroacoustics [12] and from nuclear engineering [19] to weakly compressible flows [20] and linear elasticity problems [21].…”

Section: Introductionmentioning

confidence: 99%

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Flux-corrected dispersion-improved CABARET schemes for linear and nonlinear wave propagation problems

2018

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The new two-time-level dispersion improved CABARET scheme is developed as an upgrade of the original CABARET for improved wave propagation modelling in multiple dimensions and for nonlinear conservation laws including gas dynamics. The new upgrade retains many attractive features of the original CABARET scheme such as shock-capturing and low dissipation. It is simple for implementation in the existing CABARET codes and leads to a greater accuracy for solving linear wave propagation problems. A non-linear version of the dispersion-improved CABARET scheme is introduced to efficiently deal with contact discontinuities and shocks. The properties of the new linear and nonlinear CABARET schemes are analysed for numerical dissipation and dispersion error based on Von Neumann analysis and Pirrozolli's method. Numerical examples for one-dimensional and two-dimensional linear advection, the one-dimensional inviscid Burger's equation, and the isothermal gas dynamics problems in one and two dimensions are presented.

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The CABARET method for a weakly compressible fluid flows in one- and two-dimensional implementations

Cited by 4 publications

References 3 publications

2D3V kinetic simulation of Hall effect thruster, including azimuthal waves and diamagnetic effect

2D3V kinetic simulation of Hall effect thruster, including azimuthal waves and diamagnetic effect

Double shear layer evolution on the non-uniform computational mesh

Flux-corrected dispersion-improved CABARET schemes for linear and nonlinear wave propagation problems

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