Lattice Boltzmann study on Kelvin-Helmholtz instability: the roles of velocity and density gradients

Abstract

A two-dimensional lattice Boltzmann model with 19 discrete velocities for compressible Euler equations is proposed (D2V19-LBM). The fifth-order Weighted Essentially Non-Oscillatory (5th-WENO) finite difference scheme is employed to calculate the convection term of the lattice Boltzmann equation. The validity of the model is verified by comparing simulation results of the Sod shock tube with its corresponding analytical solutions. The velocity and density gradient effects on the Kelvin-Helmholtz instability (KHI) are investigated using the proposed model. Sharp density contours are obtained in our simulations. It is found that, the linear growth rate $\gamma$ for the KHI decreases with increasing the width of velocity transition layer $D_v$ but increases with increasing the width of density transition layer $D_{\rho }$. After the initial transient period and before the vortex has been well formed, the linear growth rates, ${\gamma }_v$ and ${\gamma }_{\rho }$, vary with $D_v$ and $D_{\rho }$ approximately in the following way, $\ln {\gamma }_v=a-b{D}_v$ and ${\gamma }_{\rho }=c+e\ln D_{\rho }(D_{\rho }<D_{\rho }^E)$, where $a$, $b$, $c$ and $e$ are fitting parameters and $D_{\rho }^E$ is the effective interaction width of density transition layer. When $D_{\rho }>D_{\rho }^E$ the linear growth rate ${\gamma }_{\rho }$ does not vary significantly any more. One can use the hybrid effects of velocity and density transition layers to stabilize the KHI. Our numerical simulation results are in general agreement with the analytical results [L. F. Wang, \emph{et al.}, Phys. Plasma \textbf{17}, 042103 (2010)].

Accepted for publication in PRE

References in corpus (4)

• Two-Dimensional Lattice Boltzmann Model For Compressible Flows With High Mach Number
• Multiple-Relaxation-Time Lattice Boltzmann Approach to Compressible Flows with Flexible Specific-Heat Ratio and Prandtl Number
• Resonant Kelvin-Helmholtz modes in sheared relativistic flows
• Lattice Boltzmann simulations of phase separation in chemically reactive binary fluids

Cited by in corpus (36)

• Lattice Boltzmann modeling of multiphase flows at large density ratio with an improved pseudopotential model
• Forcing scheme in pseudopotential lattice Boltzmann model for multiphase flows
• Achieving tunable surface tension in the pseudopotential lattice Boltzmann modeling of multiphase flows
• Modeling realistic multiphase flows using a non-orthogonal multiple-relaxation-time lattice Boltzmann method
• Coupling lattice Boltzmann model for simulation of thermal flows on standard lattices
• Three-dimensional cascaded lattice Boltzmann method: improved implementation and consistent forcing scheme
• Discrete Boltzmann trans-scale modeling of high-speed compressible flows
• Nonequilibrium and morphological characterizations of Kelvin-Helmholtz instability in compressible flows
• Polar coordinate lattice Boltzmann modeling of compressible flows
• Lattice Boltzmann model for combustion and detonation
• A multi-component discrete Boltzmann model for nonequilibrium reactive flows
• Discrete Boltzmann modeling of Rayleigh-Taylor instability in two-component compressible flows
• Phase separation in thermal systems: LB study and morphological characterization
• Discrete Boltzmann method for non-equilibrium flows: based on Shakhov model
• Advances in the kinetics of heat and mass transfer in near-continuous complex flows
• High-order quadrature-based lattice Boltzmann models for the flow of ultrarelativistic rarefied gases
• Polar coordinate lattice Boltzmann kinetic modeling of detonation phenomena
• Kelvin-Helmholtz instability of the Dirac fluid of charge carriers on graphene
• Half-range lattice Boltzmann models for the simulation of Couette flow using the Shakhov collision term
• Lattice Boltzmann models based on the vielbein formalism for the simulation of flows in curvilinear geometries
• Two-fluid discrete Boltzmann model for compressible flows: based on Ellipsoidal Statistical Bhatnagar-Gross-Krook
• Knudsen number dependence of 2D single-mode Rayleigh-Taylor fluid instabilities
• Three-dimensional discrete Boltzmann models for compressible flows in and out of equilibrium
• Two-dimensional off-lattice Boltzmann model for van der Waals fluids with variable temperature
• Multicomponent Flow on Curved Surfaces: A Vielbein Lattice Boltzmann Approach
• Comparison between isothermal collision-streaming and finite-difference lattice Boltzmann models
• Thermodynamic nonequilibrium effects in three-dimensional high-speed compressible flows: Multiscale modeling and simulation via the discrete Boltzmann method
• Quadrature-based Lattice Boltzmann model for non-equilibrium dense gas flows
• Cellular automata model for elastic solid material
• Bounded flows of dense gases
• A multiple-relaxation-time lattice Boltzmann model for convection heat transfer in porous media
• Quadrature-based Lattice Boltzmann Model for Relativistic Flows
• Implementation of the force term in half-range lattice Boltzmann models
• Kinetic Simulations of Rayleigh-Taylor Instabilities
• Double-distribution-function discrete Boltzmann model for combustion
• Vielbein Lattice Boltzmann approach for fluid flows on spherical surfaces