Lattice Boltzmann models based on half-range Gauss–Hermite quadratures

Ambruş, Victor E.; Sofonea, Victor

doi:10.1016/j.jcp.2016.04.010

Cited by 41 publications

(89 citation statements)

References 72 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…These models ensure vanishing errors of the relevant half-space integrals. The Gauss-Laguerre quadratures provides another way to reproduce the Maxwell half-moments exactly [53,54].…”

Section: Finite-volume Formulationmentioning

confidence: 99%

Kinetic multiscale scheme based on the discrete-velocity and lattice-Boltzmann methods

Аристов

Ilyin

Rogozin

2020

Journal of Computational Science

View full text Add to dashboard Cite

A novel hybrid computational method based on the discrete-velocity (DV) approximation including the lattice-Boltzmann (LB) technique is proposed. Numerical schemes for the kinetic equations are used in regions of rarefied flows and LB schemes are employed in continuum flow zones. The schemes are written under the finite-volume (FV) formulation to achieve flexibility of local mesh refinement. The expansion to the Hermite polynomials is used for the coupling of DV and LB solutions. Special attention is paid to the recent high-order and regularized LB models. The linear Couette and Poiseuille flows are analyzed as numerical examples, where a good correspondence with the benchmark solutions is obtained.

show abstract

“…These models ensure vanishing errors of the relevant half-space integrals. The Gauss-Laguerre quadratures provides another way to reproduce the Maxwell half-moments exactly [53,54].…”

Section: Finite-volume Formulationmentioning

confidence: 99%

Kinetic multiscale scheme based on the discrete-velocity and lattice-Boltzmann methods

Аристов

Ilyin

Rogozin

2020

Journal of Computational Science

View full text Add to dashboard Cite

show abstract

“…(2.4) is exact. This is achieved by truncating the expansion of g α (2.2) with respect to the Hermite polynomials at a finite order Q φ /χ − 1 [5,11]:…”

Section: )mentioning

confidence: 99%

Implicit-explicit finite-difference lattice Boltzmann model with varying adiabatic index

Kis¹,

Ambruş²

2020

Tim 19 Physics Conference

Self Cite

View full text Add to dashboard Cite

The perfect fluid limit can be obtained from the Boltzmann equation in the limit of vanishing Knudsen number. By treating the collision term in an implicit manner, the implicit-explicit (IMEX) time stepping scheme allows this limit to be achieved at finite values of the time step. We consider the 9th order monotonicity-preserving (MP-9) scheme to implement the advection, which is treated explicitly in the IMEX approach. We reduce the computational costs using reduced distribution functions, which also permits the adiabatic index to be varied. We validate the capabilities of our model by considering the propagation of shock waves in one-dimensional and two-dimensional setups.

show abstract

“…Recent FDLB studies of the Couette flow showed that accurate solutions of the S-model equation can be obtained by enriching the velocity set [33,88,90,91]. The crucial piece which makes the simulations much more efficient is to take into account the discontinuity in the distribution function, which is induced by the boundary conditions prescribed at the solid walls [104,105].…”

Section: Introductionmentioning

confidence: 99%

“…The crucial piece which makes the simulations much more efficient is to take into account the discontinuity in the distribution function, which is induced by the boundary conditions prescribed at the solid walls [104,105]. For this reason, appropriate half-range quadratures should be employed on the direction perpendicular to the walls [23,36,37,65,[88][89][90][91][92][106][107][108][109][110][111][112][113][114]. In this paper, we will employ the mixed quadrature LB models introduced in Ref.…”

Section: Introductionmentioning

confidence: 99%

“…The discontinuity induced by the diffuse reflection boundary conditions imposed on the walls perpendicular to the x axis warrants the use of the half-range Gauss-Hermite quadrature, which requires Q = N + 1 points on each Cartesian semiaxis to ensure the accurate recovery of the moments of the distribution function f up to N th order. The 2Q quadrature points on the whole axis are twice the number of points required by the full-range Gauss-Hermite quadrature to achieve the same degree of accuracy when considering the full-space moments of f [91]. Thus, it is more convenient to employ the full-range Gauss-Hermite quadratures on the y direction (i.e., the direction parallel to the walls), where no discontinuities in the distribution function arise, resulting in an overall smaller velocity set.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Half-range lattice Boltzmann models for the simulation of Couette flow using the Shakhov collision term

Ambruş

Sofonea

2018

Phys. Rev. E

Self Cite

View full text Add to dashboard Cite

The three-dimensional Couette flow between parallel plates is addressed using mixed lattice Boltzmann models which implement the half-range and the full-range Gauss-Hermite quadratures on the Cartesian axes perpendicular and parallel to the walls, respectively. The ability of our models to simulate rarefied flows are validated through comparison against previously reported results obtained using the linearized Boltzmann-BGK equation for values of the Knudsen number (Kn) up to 100. We find that recovering the non-linear part of the velocity profile (i.e., its deviation from a linear function) at Kn 1 requires high quadrature orders. We then employ the Shakhov model for the collision term to obtain macroscopic profiles for Maxwell molecules using the standard µ ∼ T ω law, as well as for monatomic Helium and Argon gases, modeled through ab-initio potentials, where the viscosity is recovered using the Sutherland model. We validate our implementation by comparison with DSMC results and find excellent match for all macroscopic quantities for Kn 0.1. At Kn 0.1, small deviations can be seen in the profiles of the diagonal components of the pressure tensor, the heat flux parallel to the plates, and the velocity profile, as well as in the values of the velocity gradient at the channel center. We attribute these deviations to the limited applicability of the Shakhov collision model for highly out of equilibrium flows.

show abstract

Lattice Boltzmann models based on half-range Gauss–Hermite quadratures

Cited by 41 publications

References 72 publications

Kinetic multiscale scheme based on the discrete-velocity and lattice-Boltzmann methods

Kinetic multiscale scheme based on the discrete-velocity and lattice-Boltzmann methods

Implicit-explicit finite-difference lattice Boltzmann model with varying adiabatic index

Half-range lattice Boltzmann models for the simulation of Couette flow using the Shakhov collision term

Contact Info

Product

Resources

About