Regularization and the particles-on-demand method for the solution of the discrete Boltzmann equation

Zipunova, Elizaveta Vyacheslavovna; Perepelkina, Anastasia; Zakirov, Andrey; Khilkov, Sergey A.

doi:10.1016/j.jocs.2021.101376

Cited by 14 publications

(15 citation statements)

References 55 publications

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“…In [66] and [69], it was experimentally found that some simulations conserve mass exactly, and in [66] the reason was shown for 1D simulations. There, PoMPonD was outlined as a suggestion, but the predictor-corrector procedure was still used, even though it was observed to converge to the same value that was predicted explicitly.…”

Section: Validity Conditionsmentioning

confidence: 92%

“…We expect that more symmetries may be found, and that the optimal parameters may not necessarily satisfy the conditions in Table 2. The conditions, however, are not satisfied with the minimal schemes found in [69] for RegPonD simulations. With RegPonD, athermal problems can be simulated with minimal cubatures of the 5-th order, such as D2Q7 and D2Q13.…”

Section: Validity Conditionsmentioning

confidence: 95%

“…Obtaining the explicit gauge transfer expression even for the smallest 3D velocity sets is a difficult task, and the matrix inversion at each lattice node at each time step is a costly operation. To tackle this issue, an alternative way of gauge transfer has been introduced in the RegPonD method [69,70].…”

Section: Introductionmentioning

confidence: 99%

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Prediction of Moments in the Particles on Demand Method for LBM

Zipunova¹,

Perepelkina²,

null³

et al. 2023

CICP

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PonD is a method to extend LBM calculations to arbitrary ranges of Mach number and temperature. The current work was motivated by the issue of mass, momentum and energy conservation in the PonD method for LBM. The collision guarantees their conservation, thus, the study involves all aspects of the streaming step: both coordinate and velocity space discretizations, gauge transfer method, resolution of the scheme implicitness. After obtaining the expressions for the change of moments in the system in a time update of the scheme, it was found that the scheme can be formulated as explicit in some cases. Thus, we found the sufficient conditions to make Pond/RegPonD computations explicit and mass, momentum, and energy conserving. The scheme was implemented in the explicit form, and validated for several test cases.

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Section: Validity Conditionsmentioning

confidence: 92%

Section: Validity Conditionsmentioning

confidence: 95%

See 1 more Smart Citation

Prediction of Moments in the Particles on Demand Method for LBM

Zipunova¹,

Perepelkina²,

null³

et al. 2023

CICP

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show abstract

“…Below, the transformation proposed in [40] is supplemented by a regularization procedure [41,46]. Specifically, the transformed populations f λ i are sought as a third-order Grad's projection,…”

Section: Regularized Reference Frame Transformationmentioning

confidence: 99%

“…First, the reference frame transformation is supplemented with a regularization procedure based on Grad's projection. In the framework of PonD, regularization was recently suggested in [41], with the purpose of reducing the computational cost. Here we show that a carefully tailored moment system, serving as a basis for the transformation, enables PonD to simulate flows with strong discontinuities.…”

Section: Introductionmentioning

confidence: 99%

Particles on Demand for flows with strong discontinuities

Kallikounis,

Dorschner,

Karlin

2022

Preprint

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Particles on Demand formulation of kinetic theory [B. Dorschner, F. Bösch and I. V. Karlin, Phys. Rev. Lett. 121, 130602 (2018)] is used to simulate a variety of compressible flows with strong discontinuities in density, pressure and velocity. Two modifications are applied to the original formulation of the Particles on Demand method. First, a regularization by Grad's projection of particles populations is combined with the reference frame transformations in order to enhance stability and accuracy. Second, a finite-volume scheme is implemented which allows tight control of mass, momentum and energy conservation. The proposed model is validated with an array of challenging one-and two-dimensional benchmarks of compressible flows, including hypersonic and near-vacuum situations, Richtmyer-Meshkov instability, double Mach reflection and astrophysical jet. Excellent performance of the modified Particles on Demand method is demonstrated beyond the limitations of other lattice Boltzmann-like approaches to compressible flows.

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High speed flows with particles on demand: Boundary conditions

Bhadauria,

Karlin

2024

Computers & Fluids

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Regularization and the particles-on-demand method for the solution of the discrete Boltzmann equation

Cited by 14 publications

References 55 publications

Prediction of Moments in the Particles on Demand Method for LBM

Prediction of Moments in the Particles on Demand Method for LBM

Particles on Demand for flows with strong discontinuities

High speed flows with particles on demand: Boundary conditions

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