Untitled

Seta, Takeshi; Takahashi, Ryutaro

doi:10.1023/a:1014599729717

Cited by 29 publications

(15 citation statements)

References 19 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The smaller the hydrodynamic velocity, the less this part of contribution. Other discussions on the origin of spurious velocities and possible remedies are referred to [9,17,18,33,34,35,36,37,38].…”

Section: Finite-difference Schemes Spurious Viscosities and Diffumentioning

confidence: 99%

Finite-difference lattice-Boltzmann methods for binary fluids

2005

Phys. Rev. E

View full text Add to dashboard Cite

We investigate two-fluid BGK kinetic methods for binary fluids. The developed theory works for asymmetric as well as symmetric systems. For symmetric systems it recovers Sirovich's theory and is summarized in models A and B. For asymmetric systems it contributes models C, D and E which are especially useful when the total masses and/or local temperatures of the two components are greatly different. The kinetic models are discretized based on an octagonal discrete velocity model. The discrete-velocity kinetic models and the continuous ones are required to describe the same hydrodynamic equations. The combination of a discrete-velocity kinetic model and an appropriate finite-difference scheme composes a finite-difference lattice Boltzmann method. The validity of the formulated methods is verified by investigating (i) uniform relaxation processes, (ii) isothermal Couette flow, and (iii) diffusion behavior.

show abstract

Section: Finite-difference Schemes Spurious Viscosities and Diffumentioning

confidence: 99%

Finite-difference lattice-Boltzmann methods for binary fluids

2005

Phys. Rev. E

View full text Add to dashboard Cite

show abstract

“…We analyze the numerical stability of the FDLBM by means of von Neumann stability analysis [21,22]. In theanalysis solution of finitedifference equation is written as the familiar Fourier series, and the numerical stability isevaluated by the magnitude of eigenvalues of an amplification matrix.…”

Section: ⅲ Von Neumann Stability Analysismentioning

confidence: 99%

“…In theanalysis solution of finitedifference equation is written as the familiar Fourier series, and the numerical stability isevaluated by the magnitude of eigenvalues of an amplification matrix. The small perturbation 1fki is defined as: 公式18-20 Several researchers have analyzed the stability of the incompressible LB models [21,26,27], it is found that there is nota single wave number being always the most unstable. For the 2D DVM by WT, Gi j is a matrix with 33×33 elements.Moreover, every element is related to the macroscopical variables (density, temperature, velocities), discrete velocitiesand other constants, so it is difficult to analyze with explicit expressions.…”

Section: ⅲ Von Neumann Stability Analysismentioning

confidence: 99%

“…But similar to previous LB models, the numerical stability problemremains one of the few blocks for its practical simulation to high Mach number flows. The stability problem of LBhas been addressed and attempted for some years [13][14][15][16][17][18][19][20][21][22][23]. Among them, the entropic LB method [16,17] tries tomake the scheme to follow the Htheorem; The FIX-UP method [16,18] is based on the standard BGK scheme, usesa third-order equilibrium distribution function and a selfadapting updating parameter to avoid negativeness of themass distribution function.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

The Design and Application of English Online Learning System Based on Bs

Xuana¹,

He²,

Sun³

et al. 2017

Acta inform. Malays.

View full text Add to dashboard Cite

In this paper we present an improved lattice Boltzmann model for compressible Navier-Stokes system with high Mach number.The model is composed of three components: (i) the discrete-velocity-model by M. Watari and M. Tsutahara [Phys. Rev. E 67(2003) 036306], (ii) a modified Lax-Wendroff finite difference scheme where reasonable dissipation and dispersion are naturallyincluded, (iii) artificial viscosity. The improved model is convenient to compromise the high accuracy and stability. The includeddispersion term can effectively reduce the numerical oscillation at discontinuity. The added artificial viscosity helps the schemeto satisfy the von Neumann stability condition. Shock tubes and shock reflections are used to validate the new scheme. In ournumerical tests the Mach numbers are successfully increased up to 20 or higher. The flexibility of the new model makes it suitablefor tracking shock waves with high accuracy and for investigating nonlinear nonequilibrium complex systems.

show abstract

“…But similar to previous LB models, the numerical stability problem remains one of the few blocks for its practical simulation to high Mach number flows. The stability problem of LB has been addressed and attempted for some years [13][14][15][16][17][18][19][20][21][22][23]. Among them, the entropic LB method [16,17] tries to make the scheme to follow the H -theorem; The FIX-UP method [16,18] is based on the standard BGK scheme, uses a third-order equilibrium distribution function and a self-adapting updating parameter to avoid negativeness of the mass distribution function.…”

Section: Introductionmentioning

confidence: 99%

Two-dimensional lattice Boltzmann model for compressible flows with high Mach number

Gan

Zhang

et al. 2008

Physica A: Statistical Mechanics and its Applications

View full text Add to dashboard Cite

In this paper we present an improved lattice Boltzmann model for compressible Navier-Stokes system with high Mach number. The model is composed of three components: (i) the discrete-velocity-model by M. Watari and M. Tsutahara [Phys. Rev. E 67 (2003) 036306], (ii) a modified Lax-Wendroff finite difference scheme where reasonable dissipation and dispersion are naturally included, (iii) artificial viscosity. The improved model is convenient to compromise the high accuracy and stability. The included dispersion term can effectively reduce the numerical oscillation at discontinuity. The added artificial viscosity helps the scheme to satisfy the von Neumann stability condition. Shock tubes and shock reflections are used to validate the new scheme. In our numerical tests the Mach numbers are successfully increased up to 20 or higher. The flexibility of the new model makes it suitable for tracking shock waves with high accuracy and for investigating nonlinear nonequilibrium complex systems.

show abstract

Untitled

Cited by 29 publications

References 19 publications

Finite-difference lattice-Boltzmann methods for binary fluids

Finite-difference lattice-Boltzmann methods for binary fluids

The Design and Application of English Online Learning System Based on Bs

Two-dimensional lattice Boltzmann model for compressible flows with high Mach number

Contact Info

Product

Resources

About