Comparative study of the discrete velocity and lattice Boltzmann methods for rarefied gas flows through irregular channels

Wu, Lei; Lindsay, S. W.; Liu, Haihu; Wu, Lei

doi:10.1103/physreve.96.023309

Cited by 45 publications

(40 citation statements)

References 52 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Thus, the spectral Galerkin method becomes inefficient. A similar observation is also presented in [28].…”

Section: One-dimensional Numerical Experimentssupporting

confidence: 87%

Numerical Simulation of Microflows Using Hermite Spectral Methods

Hu¹,

Cai²,

Wang³

2020

SIAM J. Sci. Comput.

View full text Add to dashboard Cite

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.

show abstract

“…Thus, the spectral Galerkin method becomes inefficient. A similar observation is also presented in [28].…”

Section: One-dimensional Numerical Experimentssupporting

confidence: 87%

Numerical Simulation of Microflows Using Hermite Spectral Methods

Hu¹,

Cai²,

Wang³

2020

SIAM J. Sci. Comput.

View full text Add to dashboard Cite

show abstract

“…ρ = M j =1 f x, v j w j with w j being the quadrature weight for the corresponding discretized velocity points v j . The discrete velocities are not necessarily equidistant, especially for low-speed microflows with large Knudsen numbers, where the distribution function varies rapidly around v = 0 due to gas-wall interaction and nonuniform velocity points with refinement in this area is more efficient to capture the variation of f [58]. However, it should be emphasized that the FFT-based convolution could be efficiently employed only when the frequency space is uniformly discretized, though the number of frequency components can be smaller than that of velocity grid points due to the spectral accuracy of the FSM [44].…”

Section: Discretization In the Molecular Velocity Spacementioning

confidence: 99%

Implicit Discontinuous Galerkin Method for the Boltzmann Equation

Wang

Zhang

et al. 2020

J Sci Comput

Self Cite

View full text Add to dashboard Cite

An implicit high-order discontinuous Galerkin (DG) method is developed to find steadystate solution of rarefied gas flow described by the Boltzmann equation with full collision operator. In the physical space, velocity distribution function is approximated by the piecewise polynomials of degree up to 4, while in the velocity space the fast spectral method is incorporated into the DG discretization to evaluate the collision operator. A specific polynomial approximation for the collision operator is proposed to reduce the computational complexity of the fast spectral method by K times, where for two-dimensional problems K is 15 when DG with 4th-order polynomials are used on triangular mesh. Based on the first-order upwind scheme, a sweeping technique is employed to solve the local linear equations resulting from the DG discretization sequentially over spatial elements. This technique can preserve stability of the scheme and requires no nonlinear limiter in solving hypersonic rarefied gas flow when the flow is fully resolved. Moreover, without assembling large sparse linear system, the computational cost in terms of memory and CPU time can be significantly reduced. Five different one/two-dimensional tests including low-speed microscale flows and hypersonic rarefied gas flows are used to verify the proposed approach. Our results show that, DG schemes of different order of approximating polynomial require the same number of iterative steps to obtain the steady-state solution with the same order of accuracy; and the higher order the scheme, fewer spatial elements thus less CPU time is needed. Besides, our method can be faster than the finite difference solver by about one order of magnitude. The produced solutions can be used as benchmark data for assessing the accuracy of other gas kinetic solvers for the Boltzmann equation and gas kinetic models that simplify the Boltzmann collision operator.

show abstract

“…This is further confirmed in Table 1, where the relative L 2 error of MFRs (calculated based on the DUGKS results), the number of iteration steps, and the total CPU time are listed for various rarefaction parameters δ and degrees of approximation polynomials in the HDG method. For each case at δ = 88.62, 20 uniform points were used to discretize the velocity space truncated in the range of [−4, 4] in each direction, while 24 non-uniform points [9] were employed for other cases. It is interesting to note that with the same number of triangles, the number of iterative steps of the CIS reaches a constant value as the degree of polynomials in the HDG discretization increases.…”

Section: Fast Convergence Of the Sis: Poiseuille Flow Between Two Parmentioning

confidence: 99%

A high-order hybridizable discontinuous Galerkin method with fast convergence to steady-state solutions of the gas kinetic equation

Wu¹,

Wang²,

Zhang³

et al. 2019

Journal of Computational Physics

Self Cite

View full text Add to dashboard Cite

The mass flow rate of Poiseuille flow of rarefied gas through long ducts of two-dimensional cross-sections with arbitrary shape are critical in the pore-network modeling of gas transport in porous media. In this paper, for the first time, the high-order hybridizable discontinuous Galerkin (HDG) method is used to find the steady-state solution of the linearized Bhatnagar-Gross-Krook equation on two-dimensional triangular meshes. The velocity distribution function and its traces are approximated in the piecewise polynomial space (of degree up to 4) on the triangular meshes and the mesh skeletons, respectively. By employing a numerical flux that is derived from the first-order upwind scheme and imposing its continuity on the mesh skeletons, global systems for unknown traces are obtained with a few coupled degrees of freedom. To achieve fast convergence to the steady-state solution, a diffusion-type equation for flow velocity that is asymptotic-preserving into the fluid dynamic limit is solved by the HDG simultaneously, on the same meshes. The proposed HDG-synthetic iterative scheme is proved to be accurate and efficient. Specifically, for flows in the near-continuum regime, numerical simulations have shown that, to achieve the same level of accuracy, our scheme could be faster than the conventional iterative scheme by two orders of magnitude, while it is faster than the synthetic iterative scheme based on the finite difference discretization in the spatial space by one order of magnitude. The HDG-synthetic iterative scheme is ready to be extended to simulate rarefied gas mixtures and the Boltzmann collision operator.

show abstract

Comparative study of the discrete velocity and lattice Boltzmann methods for rarefied gas flows through irregular channels

Cited by 45 publications

References 52 publications

Numerical Simulation of Microflows Using Hermite Spectral Methods

Numerical Simulation of Microflows Using Hermite Spectral Methods

Implicit Discontinuous Galerkin Method for the Boltzmann Equation

A high-order hybridizable discontinuous Galerkin method with fast convergence to steady-state solutions of the gas kinetic equation

Contact Info

Product

Resources

About