A rescaling velocity method for dissipative kinetic equations. Applications to granular media

Filbet, Francis; Rey, Thomas

doi:10.1016/j.jcp.2013.04.023

Cited by 32 publications

(36 citation statements)

References 46 publications

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“…For granular flows with small values of the restitution coefficient, the temperature decreases drastically from the energy source due to the large dissipation, and thus a large number of discretized velocities is needed. In this case, velocity rescaling may be incorporated to improve the computational efficiency [43].…”

Section: Discussionmentioning

confidence: 99%

Fast spectral solution of the generalized Enskog equation for dense gases

Zhang

Reese

2015

Journal of Computational Physics

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We propose a fast spectral method for solving the generalized Enskog equation for dense gases. For elastic collisions, the method solves the Enskog collision operator with awhere d is the dimension of the velocity space, and M d−1 and N d are the number of solid angle and velocity space discretizations, respectively. For inelastic collisions, the cost is N times higher. The accuracy of this fast spectral method is assessed by comparing our numerical results with analytical solutions of the spatially-homogeneous relaxation of heated granular gases. We also compare our results for force-driven Poiseuille flow and Fourier flow with those from molecular dynamics and Monte Carlo simulations. Although it is phenomenological, the generalized Enskog equation is capable of capturing the flow dynamics of dense granular gases, and the fast spectral method is accurate and efficient. As example applications, Fourier and Couette flows of a dense granular gas are investigated. In addition to the temperature profile, both the density and the high-energy tails in the velocity distribution functions are found to be strongly influenced by the restitution coefficient.

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Section: Discussionmentioning

confidence: 99%

Fast spectral solution of the generalized Enskog equation for dense gases

Zhang

Reese

2015

Journal of Computational Physics

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“…In this paper, we propose a method that has several common features with the method of [27] and [12] but is still very different. The main difference is that each distribution is discretized on its own velocity grid: each grid has its own bounds and step that are evolved in time and space by using the local macroscopic velocity and temperature.…”

Section: Introductionmentioning

confidence: 99%

Local discrete velocity grids for deterministic rarefied flow simulations

Brull

Mieussens

2014

Journal of Computational Physics

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Most of numerical methods for deterministic simulations of rarefied gas flows use the discrete velocity (or discrete ordinate) approximation. In this approach, the kinetic equation is approximated with a global velocity grid. The grid must be large and fine enough to capture all the distribution functions, which is very expensive for high speed flows (like in hypersonic aerodynamics). In this article, we propose to use instead different velocity grids that are local in time and space: these grids dynamically adapt to the width of the distribution functions. The advantages and drawbacks of the method are illustrated in several 1D test cases.

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“…Since the singularity of f is a δ-distribution in velocity, a natural choice of the transformation T ε is a scaling in velocity. Velocity scaling methods have been used in various kinetic systems with singular time asymptotic limits, see, e.g., [1,11,12,21]. The heart of the matter in these methods is to find an appropriate scaling factor ω ε to ensure that the rescaled function g ε is not singular.…”

mentioning

confidence: 99%

An asymptotic preserving scheme for kinetic models with singular limit

Chertock¹,

Tan²,

Yan³

2018

Kinetic &Amp; Related Models

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We propose a new class of asymptotic preserving schemes to solve kinetic equations with mono-kinetic singular limit. The main idea to deal with the singularity is to transform the equations by appropriate scalings in velocity. In particular, we study two biologically related kinetic systems. We derive the scaling factors, and prove that the rescaled solution does not have a singular limit, under appropriate spatial non-oscillatory assumptions, which can be verified numerically by a newly developed asymptotic preserving scheme. We set up a few numerical experiments to demonstrate the accuracy, stability, efficiency and asymptotic preserving property of the schemes.

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A rescaling velocity method for dissipative kinetic equations. Applications to granular media

Cited by 32 publications

References 46 publications

Fast spectral solution of the generalized Enskog equation for dense gases

Fast spectral solution of the generalized Enskog equation for dense gases

Local discrete velocity grids for deterministic rarefied flow simulations

An asymptotic preserving scheme for kinetic models with singular limit

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