Implicit-Explicit Finite-Difference Lattice Boltzmann Method for Compressible Flows

Wang, Yueshe; He, Ya‐Ling; Zhao, Tianshou; Tang, G.H.; Tao, Wen‐Quan

doi:10.1142/s0129183107011868

Cited by 70 publications

(56 citation statements)

References 42 publications

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“…For the implementation of the advection term, we use a 5th order WENO scheme [21]. It was shown that the WENO scheme is suitable when simulating flows with discontinuities or strong gradients, in effect suppressing spurious oscillations and reducing numerical viscosity [20].…”

Section: Numerical Resultsmentioning

confidence: 99%

Quadrature-based lattice Boltzmann model for relativistic flows

Blaga¹,

Ambruş²

2017

AIP Conference Proceedings

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Abstract. A quadrature-based finite-difference lattice Boltzmann model is developed that is suitable for simulating relativistic flows of massless particles. We briefly review the relativistc Boltzmann equation and present our model. The quadrature is constructed such that the stress-energy tensor is obtained as a second order moment of the distribution function. The results obtained with our model are presented for a particular instance of the Riemann problem (the Sod shock tube). We show that the model is able to accurately capture the behavior across the whole domain of relaxation times, from the hydrodynamic to the ballistic regime. The property of the model of being extendable to arbitrarily high orders is shown to be paramount for the recovery of the analytical result in the ballistic regime.

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Section: Numerical Resultsmentioning

confidence: 99%

Quadrature-based lattice Boltzmann model for relativistic flows

Blaga¹,

Ambruş²

2017

AIP Conference Proceedings

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“…Of course, in reality there is no fluid or flow that is absolutely incompressible (i.e., with infinite acoustic velocity). Recent works have shown that it is possible to define lattices able to overcome this limitation (see, for instance, [8], where the authors lay the theoretical foundation of the lattice Boltzmann model for the simulation of flows with shock waves and contact discontinuities, also [9], where one can find a powerful scheme the computational convergence rate of which can be improved compared to classical previous ones, while proving to be efficient for Taylor vortex flow, Couette flow, Riemann problem).…”

Section: Introductionmentioning

confidence: 99%

Structural stability of Lattice Boltzmann schemes

David

Sagaut

2016

Physica A: Statistical Mechanics and its Applications

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The goal of this work is to determine classes of traveling solitary wave solutions for Lattice Boltzmann schemes by means of an hyperbolic ansatz. It is shown that spurious solitary waves can occur in finite-difference solutions of nonlinear wave equation.The occurence of such a spurious solitary wave, which exhibits a very long life time, results in a non-vanishing numerical error for arbitrary time in unbounded numerical domain. Such a behavior is referred here to have a structural instability of the scheme, since the space of solutions spanned by the numerical scheme encompasses types of solutions (solitary waves in the present case) that are not solutions of the original continuous equations. This paper extends our previous work about classical schemes to Lattice Boltzmann schemes (

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“…Since the LBM can be regarded as a discrete velocity method for the Boltzmann equation with the BGK approximation, it is not surprising that there is a trend in the LBM world to use the finite-difference method [16,17,23,[25][26][27][28][29][30][31][32][33][34], the finite-volume method [24,[35][36][37][38] and the finite-element method [39] to improve the computational efficiency and accuracy. In the finite-difference LBM (FDLBM), the streaming-collision procedure in the standard LBM is replaced by the combination of finitedifference schemes for the convection term in the Boltzmann equation and step advancements in time.…”

Section: Introductionmentioning

confidence: 99%

Implicit–explicit finite‐difference lattice Boltzmann method with viscid compressible model for gas oscillating patterns in a resonator

Wang

Huang

et al. 2008

Numerical Methods in Fluids

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SUMMARYDifficulties for the conventional computational fluid dynamics and the standard lattice Boltzmann method (LBM) to study the gas oscillating patterns in a resonator have been discussed. In light of the recent progresses in the LBM world, we are now able to deal with the compressibility and non-linear shock wave effects in the resonator. A lattice Boltzmann model for viscid compressible flows is introduced firstly. Then, the Boltzmann equation with the Bhatnagar-Gross-Krook approximation is solved by the finite-difference method with a third-order implicit-explicit (IMEX) Runge-Kutta scheme for time discretization, and a fifth-order weighted essentially non-oscillatory (WENO) scheme for space discretization. Numerical results obtained in this study agree quantitatively with both experimental data available and those using conventional numerical methods. Moreover, with the IMEX finite-difference LBM (FDLBM), the computational convergence rate can be significantly improved compared with the previous FDLBM and standard LBM. This study can also be applied for simulating some more complex phenomena in a thermoacoustics engine.

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Implicit-Explicit Finite-Difference Lattice Boltzmann Method for Compressible Flows

Cited by 70 publications

References 42 publications

Quadrature-based lattice Boltzmann model for relativistic flows

Quadrature-based lattice Boltzmann model for relativistic flows

Structural stability of Lattice Boltzmann schemes

Implicit–explicit finite‐difference lattice Boltzmann method with viscid compressible model for gas oscillating patterns in a resonator

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