Approximation of the linearized Boltzmann collision operator for hard-sphere and inverse-power-law models

Cai, Zhenning; Torrilhon, Manuel

doi:10.1016/j.jcp.2015.04.031

Cited by 21 publications

(30 citation statements)

References 29 publications

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“…about the Maxwellian M coincides with the approximation of the linearized collision operator proposed in [8].…”

Section: Coefficients Formulasupporting

confidence: 76%

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Approximation of the Boltzmann collision operator based on hermite spectral method

Wang¹,

Cai

2019

Journal of Computational Physics

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Based on the Hermite expansion of the distribution function, we introduce a Galerkin spectral method for the spatially homogeneous Boltzmann equation with the realistic inversepower-law models. A practical algorithm is proposed to evaluate the coefficients in the spectral method with high accuracy, and these coefficients are also used to construct new computationally affordable collision models. Numerical experiments show that our method captures the low-order moments very efficiently.

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“…about the Maxwellian M coincides with the approximation of the linearized collision operator proposed in [8].…”

Section: Coefficients Formulasupporting

confidence: 76%

“…Additionally, it has also been shown in [8] that such a choice of ν M agrees with the choice of ν in the Shakhov model (3.28). By taking the same…”

Section: Coefficients Formulamentioning

confidence: 61%

Approximation of the Boltzmann collision operator based on hermite spectral method

Wang¹,

Cai

2019

Journal of Computational Physics

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“…We refer the readers to [8] for more details. By now, we have obtained the ordinary differential equations to approximate the homogeneous Boltzmann equation (1.2) under the framework of Burnett polynomials.…”

Section: Framework Of the Burnett Spectral Methodsmentioning

confidence: 99%

“…Other methods include the fast discrete velocity method [21] and the discontinuous Galerkin method [1]. Another type of spectral method based on global orthogonal polynomials is also being studied recently [8,13,25]. In this paper, we follow the work [8,13] and adopt the spectral method based on Burnett polynomials [6], which has been applied to the linearized Boltzmann equation [8,9], and shows great potential to achieve higher numerical efficiency.…”

Section: Introductionmentioning

confidence: 99%

Burnett spectral method for the spatially homogeneous Boltzmann equation

2020

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We develop a spectral method for the spatially homogeneous Boltzmann equation using Burnett polynomials in the basis functions. Using the sparsity of the coefficients in the expansion of the collision term, the computational cost is reduced by one order of magnitude for general collision kernels and by two orders of magnitude for Maxwell molecules. The proposed method can couple seamlessly with the BGK-type modelling techniques to make future applications affordable. The implementation of the algorithm is discussed in detail, including a numerical scheme to compute all the coefficients accurately, and the design of the data structure to achieve high cache hit ratio. Numerical examples are provided to demonstrate the accuracy and efficiency of our method.

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“…Before closing this section, we would like to mention that the choice of the constant ν M0 in (3.18) and (3.19) should probably be determined by further numerical studies. Currently, we adopt the choice in [9,29] and set ν M0 to be the spectral radius of the operatorL M0 : F M0 (0, 1) → F M0 (0, 1), whose definition is…”

Section: Bmentioning

confidence: 99%

Numerical Simulation of Microflows Using Hermite Spectral Methods

Hu¹,

Cai²,

Wang³

2020

SIAM J. Sci. Comput.

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We propose a Hermite spectral method for the spatially inhomogeneous Boltzmann equation. For the inverse-power-law model, we generalize a class of approximate quadratic collision operators defined in the normalized and dimensionless setting to operators for arbitrary distribution functions. An efficient algorithm with a fast transform is introduced to discretize the new collision operators. The method is tested for one-and two-dimensional benchmark microflow problems.

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Approximation of the linearized Boltzmann collision operator for hard-sphere and inverse-power-law models

Cited by 21 publications

References 29 publications

Approximation of the Boltzmann collision operator based on hermite spectral method

Approximation of the Boltzmann collision operator based on hermite spectral method

Burnett spectral method for the spatially homogeneous Boltzmann equation

Numerical Simulation of Microflows Using Hermite Spectral Methods

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