Stabilization of thermal lattice Boltzmann models

McNamara, Guy R.; Garcia, Alejandro L.; Alder, B. J.

doi:10.1007/bf02179986

Cited by 194 publications

(97 citation statements)

References 19 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The number of hydrodynamic variables increases in these thermal lattice Boltzmann equations to include an independent heat flux vector, but the total number of variables usually increases even more to ensure isotropy. There is therefore additional scope for instabilities associated with the nonhydrodynamic modes to limit the accessible range of Reynold numbers, which may explain why thermal lattice Boltzmann equations have generally proved less successful than their isothermal predecessors [27].…”

Section: Resultsmentioning

confidence: 99%

“…These lattice eigenvectors define a basis in which ∆tΩ and (1 + 1 2 ∆tΩ) −1 are both diagonal, so the matrix C ij in (25) becomes simply ∆t/(τ λ + 1 2 ∆t) multiplying each eigenvector λ as in (27). For instance, a collision operator that changes only the relaxation time τ N for the ghost variable N may be implemented as…”

Section: Numerical Implementationmentioning

confidence: 99%

“…Lallemand and Luo [25] used a non-hydrodynamic relaxation time τ g slightly larger that ∆t/2, while Higuera et al [24] and Succi [32] recommended choosing τ g = ∆t/2, for which γ = 0 in (3), to maximally damp the non-hydrodynamic variables. The latter is equivalent to McNamara et al's [27] approach of setting the non-hydrodynamic modes to zero at each lattice point after each timestep.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Incompressible limits of lattice Boltzmann equations using multiple relaxation times

Dellar¹

2003

Journal of Computational Physics

159

150

View full text Add to dashboard Cite

Lattice Boltzmann equations using multiple relaxation times are intended to be more stable than those using a single relaxation time. The additional relaxation times may be adjusted to suppress non-hydrodynamic modes that do not appear directly in the continuum equations, but may contribute to instabilities on the grid scale. If these relaxation times are fixed in lattice units, as in previous work, solutions computed on a given lattice are found to diverge in the incompressible (small Mach number) limit. This non-existence of an incompressible limit is analysed for an inclined one dimensional jet. An incompressible limit does exist if the nonhydrodynamic relaxation times are not fixed, but scaled by the Mach number in the same way as the hydrodynamic relaxation time that determines the viscosity.

show abstract

Section: Resultsmentioning

confidence: 99%

Section: Numerical Implementationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Incompressible limits of lattice Boltzmann equations using multiple relaxation times

Dellar¹

2003

Journal of Computational Physics

159

150

View full text Add to dashboard Cite

show abstract

“…Instead we treat the temperature as an intrinsic and dynamical part of the distribution function. One way to stabilize thermal LB is by diminishing the time step [14][15][16][17][18]. This so-called fractional step method requires interpolations to advance the streaming operator in time and compromises the exact advection property of the LB method.…”

Section: Introductionmentioning

confidence: 99%

“…An example of a modified equation method is increasing the number of discrete velocities beyond the requirement for correct hydrodynamics, which increases the computational expenses [6,[19][20][21][22][23][24]. Thermal LB has also been stabilized by reducing the velocity set below this requirement [14,25]. The resulting inconsistencies in the hydrodynamics can be remedied by subtracting the finite difference discretizations of the corresponding error terms [25].…”

Section: Introductionmentioning

confidence: 99%

Stabilizing the thermal lattice Boltzmann method by spatial filtering

Gillissen

2016

Phys. Rev. E

View full text Add to dashboard Cite

We propose to stabilize the thermal lattice Boltzmann method by filtering the second-and third-order moments of the collision operator. By means of the Chapman-Enskog expansion, we show that the additional numerical diffusivity diminishes in the low-wavnumber limit. To demonstrate the enhanced stability, we consider a threedimensional thermal lattice Boltzmann system involving 33 discrete velocities. Filtering extends the linear stability of this thermal lattice Boltzmann method to 10-fold smaller transport coefficients. We further demonstrate that the filtering does not compromise the accuracy of the hydrodynamics by comparing simulation results to reference solutions for a number of standardized test cases, including natural convection in two dimensions.

show abstract

A multi‐energy‐level lattice Boltzmann model for the compressible Navier–Stokes equations

Yan

Zhang

Liu

et al. 2007

Numerical Methods in Fluids

View full text Add to dashboard Cite

SUMMARYIn this paper, we propose a new lattice Boltzmann model for the compressible Navier-Stokes equations. The new model is based on a three-energy-level and three-speed lattice Boltzmann equation by using a method of higher moments of the equilibrium distribution functions. As the 25-bit model, we obtained the equilibrium distribution functions and the compressible Navier-Stokes equations with the second accuracy of the truncation errors. The numerical examples show that the model can be used to simulate the shock waves, contact discontinuities and supersonic flows around circular cylinder. The numerical results are compared with those obtained by traditional method.

show abstract

Stabilization of thermal lattice Boltzmann models

Cited by 194 publications

References 19 publications

Incompressible limits of lattice Boltzmann equations using multiple relaxation times

Incompressible limits of lattice Boltzmann equations using multiple relaxation times

Stabilizing the thermal lattice Boltzmann method by spatial filtering

A multi‐energy‐level lattice Boltzmann model for the compressible Navier–Stokes equations

Contact Info

Product

Resources

About