arXiv subjects

Aiguo Xu

Publications and source records attributed to Aiguo Xu.

At least 73 records · Page 4Linked to original sources

arXiv2013

Lattice BGK kinetic model for high speed compressible flows: hydrodynamic and nonequilibrium behaviors

We present a simple and general approach to formulate the lattice BGK model for high speed compressible flows. The main point consists of two parts: an appropriate discrete equilibrium distribution function (DEDF) $\mathbf{f}^{eq}$ and a discrete velocity model with flexible velocity size. The DEDF is obtained by $\mathbf{f}^{eq}=\mathbf{C}^{-1}\mathbf{M}$, where $\mathbf{M}$ is a set of moment of the Maxwellian distribution function, and $\mathbf{C}$ is the matrix connecting the DEDF and the moments. The numerical components of $\mathbf{C}$ are determined by the discrete velocity model. The calculation of $\mathbf{C}^{-1}$ is based on the analytic solution which is a function of the parameter controlling the sizes of discrete velocity. The choosing of discrete velocity model has a high flexibility. The specific heat ratio of the system can be flexible. The approach works for the one-, two- and three-dimensional model constructions. As an example, we compose a new lattice BGK kinetic model which works not only for recovering the Navier-Stokes equations in the continuum limit but also for measuring the departure of system from its thermodynamic equilibrium. Via adjusting the sizes of the discrete velocities the stably simulated Mach number can be significantly increased up to 30 or even higher. The model is verified and validated by well-known benchmark tests. Some macroscopic behaviors of the system due to deviating from thermodynamic equilibrium around the shock wave interfaces are shown.

cond-mat.soft↗

arXiv2013

Two dimensional MRT LB model for compressible and incompressible flows

In the paper we extend the Multiple-Relaxation-Time (MRT) Lattice Boltzmann (LB) model proposed in [Europhys. Lett. \textbf{90}, 54003 (2010)] so that it is suitable also for incompressible flows. To decrease the artificial oscillations, the convection term is discretized by the flux limiter scheme with splitting technique. New model is validated by some well-known benchmark tests, including Riemann problem and Couette flow, and satisfying agreements are obtained between the simulation results and analytical ones. In order to show the merit of LB model over traditional methods, the non-equilibrium characteristics of system are solved. The simulation results are consistent with physical analysis.

cond-mat.soft↗

arXiv2013

Lattice Boltzmann model for combustion and detonation

In this paper we present a lattice Boltzmann model for combustion and detonation. In this model the fluid behavior is described by a finite-difference lattice Boltzmann model by Gan et al. [Physica A, 2008, 387: 1721]. The chemical reaction is described by the Lee-Tarver model [Phys. Fluids, 1980, 23: 2362]. The reaction heat is naturally coupled with the flow behavior. Due to the separation of time scales in the chemical and thermodynamic processes, a key technique for a successful simulation is to use the operator-splitting scheme. The new model is verified and validated by well-known benchmark tests. As a specific application of the new model, we studied the simple steady detonation phenomenon. To show the merit of LB model over the traditional ones, we focus on the reaction zone to study the non-equilibrium effects. It is interesting to find that, at the von Neumann peak, the system is nearly in its thermodynamic equilibrium. At the two sides of the von Neumann peak, the system deviates from its equilibrium in opposite directions. In the front of von Neumann peak, due to the strong compression from the reaction product behind the von Neumann peak, the system experiences a sudden deviation from thermodynamic equilibrium. Behind the von Neumann peak, the release of chemical energy results in thermal expansion of the matter within the reaction zone, which drives the system to deviate the thermodynamic equilibrium in the opposite direction. From the deviation from thermodynamic equilibrium, defined in this paper, one can understand more on the macroscopic effects of the system due to the deviation from its thermodynamic equilibrium.

cond-mat.soft↗

arXiv2012

Cellular automata model for elastic solid material

The Cellular Automaton (CA) modeling and simulation of solid dynamics is a long-standing difficult problem. In this paper we present a new two-dimensional CA model for solid dynamics. In this model the solid body is represented by a set of white and black particles alternatively positioned in the $x$- and $y$- directions. The force acting on each particle is represented by the linear summation of relative displacements of the nearest-neighboring particles. The key technique in this new model is the construction of eight coefficient matrices. Theoretical and numerical analyses show that the present model can be mathematically described by a conservative system. So, it works for elastic material. In the continuum limit the CA model recovers the well-known Navier equations. The coefficient matrices are related to the shear module and Poisson ratio of the material body. Compared with previous CA model for solid body, this model realizes the natural coupling of deformations in the $x$- and $y$- directions. Consequently, the wave phenomena related to the Poisson ratio effects are successfully recovered. This work advances significantly the CA modeling and simulation in the field of computational solid dynamics.

nlin.CG↗

arXiv2012

Lattice Boltzmann modeling and simulation of compressible flows

In this mini-review we summarize the progress of Lattice Boltzmann(LB) modeling and simulating compressible flows in our group in recent years. Main contents include (i) Single-Relaxation-Time(SRT) LB model supplemented by additional viscosity, (ii) Multiple-Relaxation-Time(MRT) LB model, and (iii) LB study on hydrodynamic instabilities. The former two belong to improvements of physical modeling and the third belongs to simulation or application. The SRT-LB model supplemented by additional viscosity keeps the original framework of Lattice Bhatnagar-Gross-Krook (LBGK). So, it is easier and more convenient for previous SRT-LB users. The MRT-LB is a completely new framework for physical modeling. It significantly extends the range of LB applications. The cost is longer computational time. The developed SRT-LB and MRT-LB are complementary from the sides of convenience and applicability.

cond-mat.soft↗

arXiv2011

Phase separation in thermal systems: LB study and morphological characterization

We investigate thermal and isothermal symmetric liquid-vapor separations via a FFT-Thermal Lattice Boltzmann (FFT-TLB) model. Structure factor, domain size and Minkowski functionals are employed to characterize the density and velocity fields as well as to understand the configurations and the kinetic processes. Compared with the isothermal phase separation, the freedom in temperature prolongs the Spinodal Decomposition (SD) stage and induces different rheological and morphological behaviors in the thermal system. After the transient procedure, both the thermal and isothermal separations show power-law scalings in domain growth; while the exponent for thermal system is lower than that for isothermal system. With respect to the density of field, the isothermal system presents more likely bicontinuous configurations with narrower interfaces, while the thermal system presents more likely configurations with scattered bubbles. Heat creation, conduction and lower interfacial stresses are main reasons for the differences in thermal system. Different from the case with isothermal phase separation, the release of latent heat causes the changing of local temperature which results in new local mechanical balance. When the Prandtl number becomes smaller, the system approaches thermodynamical equilibrium more quickly. The increasing of mean temperature makes lower the interfacial stress in the following way: $σ=σ_{0}[(T_{c}-T)/(T_{c}-T_{0})]^{3/2}$, where $T_{c}$ is the critical temperature and $σ_{0}$ is the interfacial stress at a reference temperature $T_{0}$, which is the main reason for lower growth exponent in thermal case.

cond-mat.soft↗

arXiv2011

Prandtl number effects in MRT Lattice Boltzmann models for shocked and unshocked compressible fluids

For compressible fluids under shock wave reaction, we have proposed two Multiple-Relaxation-Time (MRT) Lattice Boltzmann (LB) models [F. Chen, et al, EPL \textbf{90} (2010) 54003; Phys. Lett. A \textbf{375} (2011) 2129.]. In this paper, we construct a new MRT Lattice Boltzmann model which is not only for the shocked compressible fluids, but also for the unshocked compressible fluids. To make the model work for unshocked compressible fluids, a key step is to modify the collision operators of energy flux so that the viscous coefficient in momentum equation is consistent with that in energy equation even in the unshocked system. The unnecessity of the modification for systems under strong shock is analyzed. The model is validated by some well-known benchmark tests, including (i) thermal Couette flow, (ii) Riemann problem, (iii) Richtmyer-Meshkov instability. The first system is unshocked and the latter two are shocked. In all the three systems, the Prandtl numbers effects are checked. Satisfying agreements are obtained between new model results and analytical ones or other numerical results.

cond-mat.soft↗

arXiv2011

FFT-LB modeling of thermal liquid-vapor systems

We further develop a thermal LB model for multiphase flows. In the improved model, we propose to use the FFT scheme to calculate both the convection term and external force term. The usage of FFT scheme is detailed and analyzed. By using the FFT algorithm spatiotemporal discretization errors are decreased dramatically and the conservation of total energy is much better preserved. A direct consequence of the improvement is that the unphysical spurious velocities at the interfacial regions can be damped to neglectable scale. Together with the better conservation of total energy, the more accurate flow velocities lead to the more accurate temperature field which determines the dynamical and final states of the system. With the new model, the phase diagram of the liquid-vapor system obtained from simulation is more consistent with that from theoretical calculation. Very sharp interfaces can be achieved. The accuracy of simulation results are also verified by the Laplace law. The FFT scheme can be easily applied to other models for multiphase flows.

cond-mat.soft↗

arXiv2011

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

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 $γ$ for the KHI decreases with increasing the width of velocity transition layer ${D_{v}}$ but increases with increasing the width of density transition layer ${D_ρ}$. After the initial transient period and before the vortex has been well formed, the linear growth rates, $γ_v$ and $γ_ρ$, vary with ${D_{v}}$ and ${D_ρ}$ approximately in the following way, $\lnγ_{v}=a-bD_{v}$ and $γ_ρ=c+e\ln D_ρ ({D_ρ}<{D_ρ^{E}})$, where $a$, $b$, $c$ and $e$ are fitting parameters and ${D_ρ^{E}}$ is the effective interaction width of density transition layer. When ${D_ρ}>{D_ρ^{E}}$ the linear growth rate $γ_ρ$ 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)].

cond-mat.soft↗

arXiv2010

Three-Dimensional Lattice Boltzmann Model for High-Speed Compressible Flows

A highly efficient three-dimensional (3D) Lattice Boltzmann (LB) model for high speed compressible flows is proposed. This model is developed from the original one by Kataoka and Tsutahara[Phys. Rev. E 69, 056702 (2004)]. The convection term is discretized by the Non-oscillatory, containing No free parameters and Dissipative (NND) scheme, which effectively damps oscillations at discontinuities. To be more consistent with the kinetic theory of viscosity and to further improve the numerical stability, an additional dissipation term is introduced. Model parameters are chosen in such a way that the von Neumann stability criterion is satisfied. The new model is validated by well-known benchmarks, (i) Riemann problems, including the problem with Lax shock tube and a newly designed shock tube problem with high Mach number; (ii) reaction of shock wave on droplet or bubble. Good agreements are obtained between LB results and exact ones or previously reported solutions. The model is capable of simulating flows from subsonic to supersonic and capturing jumps resulted from shock waves.

cond-mat.stat-mech↗

arXiv2010

Multiple-Relaxation-Time Lattice Boltzmann Approach to Compressible Flows with Flexible Specific-Heat Ratio and Prandtl Number

A new multiple-relaxation-time lattice Boltzmann scheme for compressible flows with arbitrary specific heat ratio and Prandtl number is presented. In the new scheme, which is based on a two-dimensional 16-discrete-velocity model, the moment space and the corresponding transformation matrix are constructed according to the seven-moment relations associated with the local equilibrium distribution function. In the continuum limit, the model recovers the compressible Navier-Stokes equations with flexible specific-heat ratio and Prandtl number. Numerical experiments show that compressible flows with strong shocks can be simulated by the present model up to Mach numbers $Ma \sim 5$.

cond-mat.soft↗

arXiv2010

Shock Wave Response of Porous Materials: From Plasticity to Elasticity

Shock wave reaction results in various characteristic regimes in porous material. The geometrical and topological properties of these regimes are highly concerned in practical applications. Via the morphological analysis to characteristic regimes with high temperature, we investigate the thermodynamics of shocked porous materials whose mechanical properties cover a wide range from hyperplasticity to elasticity. It is found that, under fixed shock strength, the total fractional area $A$ of the high-temperature regimes with $T \geq T_{th}$ and its saturation value first increase, then decrease with the increasing of the initial yield $σ_{Y0}$, where $T_{th}$ is a given threshold value of temperature $T$. In the shock-loading procedure, the fractional area $A(t)$ may show the same behavior if $T_{th}$ and $σ_{Y0}$ are chosen appropriately. Under the same $A(t)$ behavior, $T_{th}$ first increases then decreases with $σ_{Y0}$. At the maximum point $σ_{Y0M}$, the shock wave contributes the maximum plastic work. Around $σ_{Y0M}$, two materials with different mechanical properties may share the same $A(t)$ behavior even for the same $T_{th}$. The characteristic regimes in the material with the larger $σ_{Y0}$ are more dispersed.

cond-mat.mtrl-sci↗

arXiv2010

Multiple-relaxation-time lattice Boltzmann model for compressible fluids

We present an energy-conserving multiple-relaxation-time finite difference lattice Boltzmann model for compressible flows. This model is based on a 16-discrete-velocity model. The collision step is first calculated in the moment space and then mapped back to the velocity space. The moment space and corresponding transformation matrix are constructed according to the group representation theory. Equilibria of the nonconserved moments are chosen according to the need of recovering compressible Navier-Stokes equations through the Chapman-Enskog expansion. Numerical experiments showed that compressible flows with strong shocks can be well simulated by the present model. The used benchmark tests include (i) shock tubes, such as the Sod, Lax, Sjogreen, Colella explosion wave and collision of two strong shocks, (ii) regular and Mach shock reflections, and (iii) shock wave reaction on cylindrical bubble problems. The new model works for both low and high speeds compressible flows. It contains more physical information and has better numerical stability and accuracy than its single-relaxation-time version.

cond-mat.stat-mech↗

arXiv2010

Control spiral wave dynamics using feedback signals from line detectors

We numerically study trajectories of spiral-wave-cores in excitable systems modulated proportionally to the integral of the activity on the straight line, several or dozens of equi-spaced measuring points on the straight line, the double-line and the contour-line. We show the single-line feedback results in the drift of core center along a straight line being parallel to the detector. An interesting finding is that the drift location in $y$ is a piecewise linear-increasing function of both the feedback line location and time delay. Similar trajectory occurs when replacing the feedback line with several or dozens of equi-spaced measuring points on the straight line. This allows to move the spiral core to the desired location along a chosen direction by measuring several or dozens of points. Under the double-line feedback, the shape of the tip trajectory representing the competition between the first and second feedback lines is determined by the distance of two lines. Various drift attractors in spiral wave controlled by square-shaped contour-line feedback are also investigated. A brief explanation is presented.

cond-mat.stat-mech↗

arXiv2010

Cluster Identification and Characterization of Physical Fields

The description of complex configuration is a difficult issue. We present a powerful technique for cluster identification and characterization. The scheme is designed to treat with and analyze the experimental and/or simulation data from various methods. Main steps are as follows. We first divide the space using face or volume elements from discrete points. Then, combine the elements with the same and/or similar properties to construct clusters with special physical characterizations. In the algorithm, we adopt administrative structure of hierarchy-tree for spatial bodies such as points, lines, faces, blocks, and clusters. Two fast search algorithms with the complexity are realized. The establishing of the hierarchy-tree and the fast searching of spatial bodies are general, which are independent of spatial dimensions. Therefore, it is easy to extend the skill to other fields. As a verification and validation, we treated with and analyzed some two-dimensional and three-dimensional random data.

cond-mat.stat-mech↗

arXiv2009

Simulating liquid-vapor phase separation under shear with lattice Boltzmann method

We study liquid-vapor phase separation under shear via the Shan-Chen lattice Boltzmann model. Besides the rheological characteristics, we analyze the Kelvin-Helmholtz(K-H) instability resulting from the tangential velocity difference of the fluids on two sides of the interface. We discuss also the growth behavior of droplets. The domains being close to the walls are lamellar-ordered, where the hydrodynamic effects dominate. The patterns in the bulk of the system are nearly isotropic, where the domain growth results mainly from the diffusion mechanism. Both the interfacial tension and the K-H instability make the liquid-bands near the walls tend to rupture. When the shear rate increases, the inequivalence of evaporation in the upstream and coagulation in the downstream of the flow as well as the role of surface tension makes the droplets elongate obliquely. Stronger convection makes easier the transferring of material particles so that droplets become larger.

cond-mat.soft↗

arXiv2009

Morphological characterization of shocked porous material

Morphological measures are introduced to probe the complex procedure of shock wave reaction on porous material. They characterize the geometry and topology of the pixelized map of a state variable like the temperature. Relevance of them to thermodynamical properties of material is revealed and various experimental conditions are simulated. Numerical results indicate that, the shock wave reaction results in a complicated sequence of compressions and rarefactions in porous material. The increasing rate of the total fractional white area $A$ roughly gives the velocity $D$ of a compressive-wave-series. When a velocity $D$ is mentioned, the corresponding threshold contour-level of the state variable, like the temperature, should also be stated. When the threshold contour-level increases, $D$ becomes smaller. The area $A$ increases parabolically with time $t$ during the initial period. The $A(t)$ curve goes back to be linear in the following three cases: (i) when the porosity $δ$ approaches 1, (ii) when the initial shock becomes stronger, (iii) when the contour-level approaches the minimum value of the state variable. The area with high-temperature may continue to increase even after the early compressive-waves have arrived at the downstream free surface and some rarefactive-waves have come back into the target body. In the case of energetic material ... (see the full text)

cond-mat.mtrl-sci↗

arXiv2009

Simulation study of shock reaction on porous material

Direct modeling of porous materials under shock is a complex issue. We investigate such a system via the newly developed material-point method. The effects of shock strength and porosity size are the main concerns. For the same porosity, the effects of mean-void-size are checked. It is found that, local turbulence mixing and volume dissipation are two important mechanisms for transformation of kinetic energy to heat. When the porosity is very small, the shocked portion may arrive at a dynamical steady state; the voids in the downstream portion reflect back rarefactive waves and result in slight oscillations of mean density and pressure; for the same value of porosity, a larger mean-void-size makes a higher mean temperature. When the porosity becomes large, hydrodynamic quantities vary with time during the whole shock-loading procedure: after the initial stage, the mean density and pressure decrease, but the temperature increases with a higher rate. The distributions of local density, pressure, temperature and particle-velocity are generally non-Gaussian and vary with time. The changing rates depend on the porosity value, mean-void-size and shock strength. The stronger the loaded shock, the stronger the porosity effects. This work provides a supplement to experiments for the very quick procedures and reveals more fundamental mechanisms in energy and momentum transportation.

cond-mat.mtrl-sci↗