arXiv subjects

Chuandong Lin

Publications and source records attributed to Chuandong Lin.

26 records · Page 2Linked to original sources

arXiv2017

Discrete Boltzmann modeling of Rayleigh-Taylor instability in two-component compressible flows

A discrete Boltzmann model (DBM) is proposed to probe the Rayleigh-Taylor instability (RTI) in two-component compressible flows. Each species has a flexible specific heat ratio and is described by one discrete Boltzmann equation (DBE). Independent discrete velocities are adopted for the two DBEs. The collision and force terms in the DBE account for the molecular collision and external force, respectively. Two types of force terms are exploited. In addition to recovering the modified Navier-Stokes equations in the hydrodynamic limit, the DBM has the capability of capturing detailed nonequilibrium effects. Furthermore, we use the DBM to investigate the dynamic process of the RTI. The invariants of tensors for nonequilibrium effects are presented and studied. For low Reynolds numbers, both global nonequilibrium manifestations and the growth rate of the entropy of mixing show three stages (i.e., the reducing, increasing, and then decreasing trends) in the evolution of the RTI. On the other hand, the early reducing tendency is suppressed and even eliminated for high Reynolds numbers. Relevant physical mechanisms are analyzed and discussed.

cond-mat.soft↗

arXiv2017

Modeling incompressible thermal flows using a central-moment-based lattice Boltzmann method

In this paper, a central-moment-based lattice Boltzmann (CLB) method for incompressible thermal flows is proposed. In the method, the incompressible Navier-Stokes equations and the convection-diffusion equation for the temperature field are sloved separately by two different CLB equations. Through the Chapman-Enskog analysis, the macroscopic governing equations for incompressible thermal flows can be reproduced. For the flow field, the tedious implementation for CLB method is simplified by using the shift matrix with a simplified central-moment set, and the consistent forcing scheme is adopted to incorporate forcing effects. Compared with several D2Q5 multiple-relaxation-time (MRT) lattice Boltzmann methods for the temperature equation, the proposed method is shown to be better Galilean invariant through measuring the thermal diffusivities on a moving reference frame. Thus a higher Mach number can be used for convection flows, which decreases the computational load significantly. Numerical simulations for several typical problems confirm the accuracy, efficiency, and stability of the present method. The grid convergence tests indicate that the proposed CLB method for incompressible thermal flows is of second-order accuracy in space.

physics.comp-ph↗

arXiv2016

Kinetic modeling of detonation and effects of negative temperature coefficient

The kinetic modeling and simulation of reactive flows, especially for those with detonation, are further investigated. From the theoretical side, a new set of hydrodynamic equations are deduced, where the viscous stress tensor and heat flux are replaced by two non-equilibrium quantities that have been defined in our previous work. The two non-equilibrium quantities are referred to as NonOrganized Momentum Flux (NOMF) and Non-Organized Energy Flux (NOEF), respectively, here. The numerical results of viscous stress (heat flux) have a good agreement with those of NOMF (NOEF) near equilibrium state. Around sharp interfaces, the values of NOMF (NOEF) deviate reasonably from those of viscous stress (heat flux). Based on this hydrodynamic model, the relations between the two non-equilibrium quantities and entropy productions are established. Based on the discrete Boltzmann model, four kinds of detonation phenomena with different reaction rates, including Negative Temperature Coefficient (NTC) regime, are simulated and investigated. The differences of the four kinds of detonations are studied from three aspects: hydrodynamic quantities, non-equilibrium quantities and entropy productions.

cond-mat.soft↗

arXiv2015

Double-distribution-function discrete Boltzmann model for combustion

A 2-dimensional discrete Boltzmann model for combustion is presented. Mathematically, the model is composed of two coupled discrete Boltzmann equations for two species and a phenomenological equation for chemical reaction process. Physically, the model is equivalent to a reactive Navier-Stokes model supplemented by a coarse-grained model for the thermodynamic nonequilibrium behaviours. This model adopts 16 discrete velocities. It works for both subsonic and supersonic combustion phenomena with flexible specific heat ratio. To discuss the physical accuracy of the coarse-grained model for nonequilibrium behaviours, three other discrete velocity models are used for comparisons. Numerical results are compared with analytical solutions based on both the first-order and second-order truncations of the distribution function. It is confirmed that the physical accuracy increases with the increasing moment relations needed by nonequlibrium manifestations. Furthermore, compared with the single distribution function model, this model can simulate more details of combustion.

cond-mat.soft↗

arXiv2015

Multiple-relaxation-time lattice Boltzmann kinetic model for combustion

To probe both the Hydrodynamic Non-Equilibrium (HNE) and Thermodynamic Non-Equilibrium (TNE) in the combustion process, a two-dimensional Multiple-Relaxation-Time (MRT) version of Lattice Boltzmann Kinetic Model(LBKM) for combustion phenomena is presented. The chemical energy released in the progress of combustion is dynamically coupled into the system by adding a chemical term to the LB kinetic equation. Beside describing the evolutions of the conserved quantities, the density, momentum and energy, which are what the Navier-Stokes model describes, the MRT-LBKM presents also a coarse-grained description on the evolutions of some non-conserved quantities. The current model works for both subsonic and supersonic flows with or without chemical reaction. In this model both the specific-heat ratio and the Prandtl number are flexible, the TNE effects are naturally presented in each simulation step. The model is verified and validated via well-known benchmark tests. As an initial application, various non-equilibrium behaviours, including the complex interplays between various HNEs, between various TNEs and between the HNE and TNE, around the detonation wave in the unsteady and steady one-dimensional detonation processes are preliminarily probed. It is found that the system viscosity (or heat conductivity) decreases the local TNE, but increase the global TNE around the detonation wave, that even locally, the system viscosity (or heat conductivity) results in two kinds of competing trends, to increase and to decrease the TNE effects. The physical reason is that the viscosity (or heat conductivity) takes part in both the thermodynamic and hydrodynamic responses.

cond-mat.soft↗

arXiv2014

Polar coordinate lattice Boltzmann kinetic modeling of detonation phenomena

A novel polar coordinate lattice Boltzmann kinetic model for detonation phenomena is presented and applied to investigate typical implosion and explosion processes. In this model, the change of discrete distribution function due to local chemical reaction is dynamically coupled into in the modified lattice Boltzmann equation, which could recovery the Navier-Stokes equations, including contribution of chemical reaction, via the Chapman-Enskog expansion. For the numerical investigations, the main focuses are the nonequilibrium behaviors in these processes. The system at the disc center is always in its thermodynamic equilibrium. The internal kinetic energies in different degrees freedoms around the detonation front do not coincide due to the fluid viscosity. They show the maximum difference at the inflexion point where the pressure has the largest spatial derivative. The dependence of the reaction rate on the pressure, influences of the shock strength and reaction rate on the departure amplitude of the system from its local thermodynamic equilibrium are probed.

cond-mat.soft↗

arXiv2014

Discrete Boltzmann model of compressible flows with spherical or cylindrical symmetry

To study simultaneously the hydrodynamic and thermodynamic behaviors in compressible flow systems with spherical or cylindrical symmetry, we present a theoretical framework for constructing Discrete Boltzmann Model(DBM) with spherical or cylindrical symmetry in spherical or cylindrical coordinates. To this aim, a key technique is to use \emph{local} Cartesian coordinates to describe the particle velocity in the kinetic model. Thus, the geometric effects, like the divergence and convergence, are described as a \textquotedblleft force term\textquotedblright . Even though the hydrodynamic models are one- or two-dimensional, the DBM needs a Discrete Velocity Model(DVM) with 3 dimensions. We use a DVM with 26 velocities to formulate the DBM which recovers the Navier-Stokes equations with spherical or cylindrical symmetry in the hydrodynamic limit. For the system with \emph{global} cylindrical symmetry, we formulated also a DBM based on a DVM with 2 dimensions and 16 velocities. In terms of the nonconserved moments, we define two sets of measures for the deviations of the system from its thermodynamic equilibrium state. The extension of current model to the multiple-relaxation-time version is straightforward.

cond-mat.stat-mech↗

arXiv2014

Polar coordinate lattice Boltzmann modeling of compressible flows

We present a polar coordinate lattice Boltzmann kinetic model for compressible flows. A method to recover the continuum distribution function from the discrete distribution function is indicated. Within the model, a hybrid scheme being similar to, but different from, the operator splitting is proposed. The temporal evolution is calculated analytically, and the convection term is solved via a modifiedWarming-Beam (MWB) scheme.Within theMWB scheme a suitable switch function is introduced. The current model works not only for subsonic flows but also for supersonic flows. It is validated and verified via the following well-known benchmark tests: (i) the rotational flow, (ii) the stable shock tube problem, (iii) the Richtmyer-Meshkov (RM) instability, and (iv) the Kelvin-Helmholtz instability. As an original application, we studied the nonequilibrium characteristics of the system around three kinds of interfaces, the shock wave, the rarefaction wave, and the material interface, for two specific cases. In one of the two cases, the material interface is initially perturbed, and consequently the RMinstability occurs. It is found that themacroscopic effects due to deviating from thermodynamic equilibrium around thematerial interface differ significantly from those around the mechanical interfaces. The initial perturbation at the material interface enhances the coupling of molecular motions in different degrees of freedom. The amplitude of deviation from thermodynamic equilibrium around the shock wave is much higher than those around the rarefaction wave and material interface. By comparing each component of the high-order moments and its value in equilibrium, we can draw qualitatively the main behavior of the actual distribution function.

cond-mat.soft↗