Hydrodynamic Regimes, Knudsen Layer, Numerical Schemes: Definition of Boundary Fluxes

Besse, Christophe; Borghol, Saja; Goudon, Thierry; Lacroix–Violet, Ingrid; Dudon, Jean-Paul

doi:10.4208/aamm.10-m1041

Cited by 10 publications

(6 citation statements)

References 43 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…It then remains to fix a condition for the momentum flux. To mimic the specular reflection, we reverse the velocity at the boundary, as presented in [4]. 4.2.…”

Section: Boundary Conditionsmentioning

confidence: 99%

A Rescaling Velocity Method for Dissipative Kinetic Equations - Applications to Granular Media

Filbet,

Rey

2012

Preprint

View full text Add to dashboard Cite

We present a new numerical algorithm based on a relative energy scaling for collisional kinetic equations allowing to study numerically their long time behavior, without the usual problems related to the change of scales in velocity variables. It is based on the knowledge of the hydrodynamic limit of the model considered, but is able to compute solutions for either dilute or dense regimes. Several applications are presented for Boltzmann-like equations. This method is particularly efficient for numerical simulations of the granular gases equation with dissipative energy: it allows to study accurately the long time behavior of this equation and is very well suited for the study of clustering phenomena.

show abstract

“…It then remains to fix a condition for the momentum flux. To mimic the specular reflection, we reverse the velocity at the boundary, as presented in [4]. 4.2.…”

Section: Boundary Conditionsmentioning

confidence: 99%

A Rescaling Velocity Method for Dissipative Kinetic Equations - Applications to Granular Media

Filbet,

Rey

2012

Preprint

View full text Add to dashboard Cite

show abstract

“…Since the fluid solver and the kinetic solver are rather standard, the main challenge comes from the computation of the Knudsen layer equation. This approach was then used in some numerical studies, such as [5,13,17,8,9,14], in most of which the layer equation was treated using Marshak condition [21,1].…”

Section: Introductionmentioning

confidence: 99%

A numerical method for coupling the BGK model and Euler equations through the linearized Knudsen layer

Chen

2019

Journal of Computational Physics

View full text Add to dashboard Cite

The Bhatnagar-Gross-Krook (BGK) model, a simplification of the Boltzmann equation, in the absence of boundary effect, converges to the Euler equations when the Knudsen number is small. In practice, however, Knudsen layers emerge at the physical boundary, or at the interfaces between the two regimes. We model the Knudsen layer using a half-space kinetic equation, and apply a half-space numerical solver [19, 20] to quantify the transition between the kinetic to the fluid regime. A full domain numerical solver is developed with a domain-decomposition approach, where we apply the Euler solver and kinetic solver on the appropriate subdomains and connect them via the half-space solver. In the nonlinear case, linearization is performed upon local Maxwellian. Despite the lack of analytical support, the numerical evidence nevertheless demonstrate that the linearization approach is promising.

show abstract

“…However, in zones where these macroscopic models break down, one has to come back to solve the Boltzmann equation. This domain decomposition approach has attracted a great amount of attentions [1][2][3][4][5][6][7][8][9][10]. The main difficulty there is to determine the matching interface conditions between two different domains in which different physical models are used.…”

Section: Introductionmentioning

confidence: 99%

A BGK‐penalization‐based asymptotic‐preserving scheme for the multispecies Boltzmann equation

Jin

2012

Numerical Methods Partial

View full text Add to dashboard Cite

An asymptotic-preserving (AP) scheme is efficient in solving multiscale problems where kinetic and hydrodynamic regimes coexist. In this article, we extend the BGK-penalization-based AP scheme, originally introduced by Filbet and Jin for the single species Boltzmann equation (Filbet and Jin, J Comput Phys 229 (2010) 7625-7648), to its multispecies counterpart. For the multispecies Boltzmann equation, the new difficulties arise due to: (1) the breaking down of the conservation laws for each species and (2) different convergence rates to equilibria for different species in disparate masses systems. To resolve these issues, we find a suitable penalty function-the local Maxwellian that is based on the mean velocity and mean temperature and justify various asymptotic properties of this method. This AP scheme does not contain any nonlinear nonlocal implicit solver, yet it can capture the fluid dynamic limit with time step and mesh size independent of the Knudsen number. Numerical examples demonstrate the correct asymptotic-behavior of the scheme.

show abstract

Hydrodynamic Regimes, Knudsen Layer, Numerical Schemes: Definition of Boundary Fluxes

Cited by 10 publications

References 43 publications

A Rescaling Velocity Method for Dissipative Kinetic Equations - Applications to Granular Media

A Rescaling Velocity Method for Dissipative Kinetic Equations - Applications to Granular Media

A numerical method for coupling the BGK model and Euler equations through the linearized Knudsen layer

A BGK‐penalization‐based asymptotic‐preserving scheme for the multispecies Boltzmann equation

Contact Info

Product

Resources

About