arXiv subjects

Aiguo Xu

Publications and source records attributed to Aiguo Xu.

87 records · Page 5Linked to original sources

arXiv2008

Two-Dimensional Lattice Boltzmann Model For Compressible Flows With High Mach Number

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 Watari and Tsutahara [Phys Rev E \textbf{67},036306(2003)], (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.

cond-mat.soft↗

arXiv2007

Generalized Interpolation Material Point Approach to High Melting Explosive with Cavities Under Shock

Criterion for contacting is critically important for the Generalized Interpolation Material Point(GIMP) method. We present an improved criterion by adding a switching function. With the method dynamical response of high melting explosive(HMX) with cavities under shock is investigated. The physical model used in the present work is an elastic-to-plastic and thermal-dynamical model with Mie-Grüneissen equation of state. We mainly concern the influence of various parameters, including the impacting velocity $v$, cavity size $R$, etc, to the dynamical and thermodynamical behaviors of the material. For the colliding of two bodies with a cavity in each, a secondary impacting is observed. Correspondingly, the separation distance $D$ of the two bodies has a maximum value $D_{\max}$ in between the initial and second impacts. When the initial impacting velocity $v$ is not large enough, the cavity collapses in a nearly symmetric fashion, the maximum separation distance $D_{\max}$ increases with $v$. When the initial shock wave is strong enough to collapse the cavity asymmetrically along the shock direction, the variation of $D_{\max}$ with $v$ does not show monotonic behavior. Our numerical results show clear indication that the existence of cavities in explosive helps the creation of ``hot spots''.

cond-mat.mtrl-sci↗

arXiv2007

Three-dimensional multi-mesh material point method for solving collision problems

Contact algorithm between different bodies plays an important role in solving collision problems. Usually it is not easy to be treated very well. Several ones for material point method were proposed by Bardenhangen, Brackbill, and Sulsky\cite{Bardenhagen2000,Bardenhagen2001}, Hu and Chen\cite{Hu_Chen2003}. An improved one for three-dimensional material point method is presented in this paper. The improved algorithm emphasizes the energy conservation of the system and faithfully recovers opposite acting forces between contacting bodies. Contrasted to the one by Bardenhagen, both the normal and tangential contacting forces are more appropriately applied to the contacting bodies via the contacting nodes of the background mesh; Contrasted to the one by Hu and Chen, not only the tangential velocities but also the normal ones are handled separately in respective individual mesh. This treatment ensures not only the contact/sliding/separation procedure but also the friction between contacting bodies are recovered. The presented contact algorithm is validated via numerical experiments including rolling simulation, impact of elastic spheres, impact of a Taylor bar and impact of plastic spheres. The numerical results show that the multi-mesh material point method with the improved contact algorithm is more suitable for solving collision problems.

physics.comp-ph↗

arXiv2007

Material-Point Simulation to Cavity Collapse Under Shock

The collapse of cavities under shock is a key problem in various fields ranging from erosion of material, ignition of explosive, to sonoluminescence, etc. We study such processes using the material-point-method developed recently in the field of solid physics. The main points of the research include the relations between symmetry of collapsing and the strength of shock, other coexisting interfaces, as well as hydrodynamic and thermal-dynamic behaviors ignored by the pure fluid models. In the case with strong shock, we study the procedure of jet creation in the cavity; in the case with weak shock, we found that the cavity can not be collapsed completely by the shock and the cavity may collapse in a nearly isotropic way. The history of collapsing significantly influences the distribution of "hot spots" in the shocked material. The change in symmetry of collapsing is investigated. Since we use the Mie-Gr% üneisen equation of state and the effects of strain rate are not taken into account, the behavior is the same if one magnifies the spatial and temporal scales in the same way.

cond-mat.mtrl-sci↗

arXiv2007

Lattice Boltzmann Approach to High-Speed Compressible Flows

We present an improved lattice Boltzmann model for high-speed compressible flows. The model is composed of a discrete-velocity model by Kataoka and Tsutahara [Phys. Rev. E \textbf{69}, 056702 (2004)] and an appropriate finite-difference scheme combined with an additional dissipation term. With the dissipation term parameters in the model can be flexibly chosen so that the von Neumann stability condition is satisfied. The influence of the various model parameters on the numerical stability is analyzed and some reference values of parameter are suggested. The new scheme works for both subsonic and supersonic flows with a Mach number up to 30 (or higher), which is validated by well-known benchmark tests. Simulations on Riemann problems with very high ratios ($1000:1$) of pressure and density also show good accuracy and stability. Successful recovering of regular and double Mach shock reflections shows the potential application of the lattice Boltzmann model to fluid systems where non-equilibrium processes are intrinsic. The new scheme for stability can be easily extended to other lattice Boltzmann models.

cond-mat.soft↗

arXiv2005

Morphologies and flow patterns in quenching of lamellar systems with shear

We study the behavior of a fluid quenched from the disordered into the lamellar phase under the action of a shear flow. The dynamics of the system is described by Navier-Stokes and convection-diffusion equations with pressure tensor and chemical potential derived by the Brazovskii free-energy. Our simulations are based on a mixed numerical method with Lattice Boltzmann equation and finite difference scheme for Navier-Stokes and order parameter equations, respectively. We focus on cases where banded flows are observed with two different slopes for the component of velocity in the direction of the applied flow. Close to the walls the system reaches a lamellar order with very few defects and the slope of the horizontal velocity is higher than the imposed shear rate. In the middle of the system the local shear rate is lower than the imposed one and the system looks as a mixture of tilted lamellae, droplets and small elongated domains. We refer to this as to a region with a Shear Induced Structures (SIS) configuration. The local behavior of the stress shows that the system with the coexisting lamellar and SIS regions is in mechanical equilibrium. This phenomenon occurs, at fixed viscosity, for shear rates under a certain threshold; when the imposed shear rate is sufficiently large, lamellar order develops in the whole system. Effects of different viscosities have been also considered: The SIS region is observed only at low enough viscosity. We compare the above scenario with the usual one of shear banding. In particular, we do not find evidence for a plateau of the stress at varying imposed shear rates in the region with banded flow. We interpret our results as due to a tendency of the lamellar system to oppose to the presence of the applied flow.

cond-mat.soft↗

arXiv2005

Finite-Difference Lattice Boltzmann Methods for binary fluids

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.

cond-mat.soft↗

arXiv2005

Response of Autonomic Nervous System to Body Positions: Fourier and Wavelet Analysis

Two mathematical methods, the Fourier and wavelet transforms, were used to study the short term cardiovascular control system. Time series, picked from electrocardiogram and arterial blood pressure lasting 6 minutes, were analyzed in supine position (SUP), during the first (HD1), and the second parts (HD2) of $90^{\circ}$ head down tilt and during recovery (REC). The wavelet transform was performed using the Haar function of period $T=2^j$ ($% j=1$,2,$... $,6) to obtain wavelet coefficients. Power spectra components were analyzed within three bands, VLF (0.003-0.04), LF (0.04-0.15) and HF (0.15-0.4) with the frequency unit cycle/interval. Wavelet transform demonstrated a higher discrimination among all analyzed periods than the Fourier transform. For the Fourier analysis, the LF of R-R intervals and VLF of systolic blood pressure show more evident difference for different body positions. For the wavelet analysis, the systolic blood pressures show much more evident difference than the R-R intervals. This study suggests a difference in the response of the vessels and the heart to different body positions. The partial dissociation between VLF and LF results is a physiologically relevant finding of this work.

physics.bio-ph↗

arXiv2005

Scaling and hydrodynamic effects in lamellar ordering

We study the kinetics of domain growth of fluid mixtures quenched from a disordered to a lamellar phase. At low viscosities, in two dimensions, when hydrodynamic modes become important, dynamical scaling is verified in the form $C(\vec k, t) \sim L^α f[(k-k_M)L]$ where $C$ is the structure factor with maximum at $k_M$ and $L$ is a typical length changing from power law to logarithmic growth at late times. The presence of extended defects can explain the behavior of $L$. Three-dimensional simulations confirm that diffuse grain boundaries inhibit complete ordering of lamellae. Applied shear flow alleviates frustration and gives power-law growth at all times.

cond-mat.soft↗

arXiv2005

Two-dimensional finite-difference lattice Boltzmann method for the complete Navier-Stokes equations of binary fluids

Based on Sirovich's two-fluid kinetic theory and a dodecagonal discrete velocity model, a two-dimensional 61-velocity finite-difference lattice Boltzmann method for the complete Navier-Stokes equations of binary fluids is formulated. Previous constraints, in most existing lattice Boltzmann methods, on the studied systems, like isothermal and nearly incompressible, are released within the present method. This method is designed to simulate compressible and thermal binary fluid mixtures. The validity of the proposed method is verified by investigating (i) the Couette flow and (ii) the uniform relaxation process of the two components.

cond-mat.stat-mech↗

arXiv2003

Phase separation of incompressible binary fluids with Lattice Boltzmann Methods

We introduce new versions of lattice Boltzmann methods (LBM) for incompressible binary mixtures where fluctuations of total density are inhibited. As a test for the improved algorithms we consider the problem of phase separation of two-dimensional binary mixtures quenched from a disordered state into the coexistence region. We find that the stability properties of LBM are greatly improved. The control of density fluctuations and the possibility of running longer simulations allow a more precise evaluation of the growth exponent.

cond-mat.soft↗

arXiv2003

Scattering of signal in vertical granular chain with impurities

We investigate the scattering process of impulse from impurities in vertical granular chain system under gravity. Most of the studies are focused on the case of light impurities. The reflection rates follow power laws with the impuity depth. There is a valley in the curve of reflection rate versus the initial perturbation strength and the curve is not symmetric. Some results on the scattering process from heavy impurities are also presented. There is a transition region in the initial velocity space. Through this region the exponent for leading peak changes smoothly from its saturant value in small $ v_i$ side to its saturant value in large $v_i$ side; the exponent for signal speed changes smoothly from its saturant value in small $v_i$ side to its saturant value in large $v_i$ side. Both the peak of the exponent for reflection rate and the valley for the reflection rate versus $v_i$ also locate within this transition region.

cond-mat.soft↗

arXiv2003

Lattice Boltzmann Study of Velocity Behaviour in Binary Mixtures Under Shear

We apply lattice Boltzmann methods to study the relaxation of the velocity profile in binary fluids under shear during spinodal decomposition. In simple fluids, when a shear flow is applied on the boundaries of the system, the time required to obtain a triangular profile is inversely proportional to the viscosity and proportional to the square of the size of the system. We find that the same behaviour also occurs for binary mixtures, for any component ratio in the mixture and independently from the time when shear flow is switched on during phase separation.

physics.flu-dyn↗

arXiv2003

Dc-Driven Diatomic Frenkel-Kontorova Model

We investigate the resonance steps, spatiotemporal dynamics, and dynamical phase diagrams of the dc-driven diatomic Frenkel-Kontorova model. The complete resonance velocity spectrum is given. The diatomic effects result in each resonant state being characterized by two integer pairs, $(k_1,k_2)$ and $(k_1,k_2^{\prime})$. In the high-velocity region the linear response of the average velocity, $v$, of the chain to the driving force $F$ is often punctuated by subharmonic resonances $(k_1>k_2)$. There are two kinds of nonlinear response regions in the high-velocity region. A new physical interpretation of the mean-field treatment is presented.

cond-mat.mtrl-sci↗

arXiv2002

Phase separating binary fluids under oscillatory shear

We apply lattice Boltzmann methods to study the segregation of binary fluid mixtures under oscillatory shear flow in two dimensions. The algorithm allows to simulate systems whose dynamics is described by the Navier-Stokes and the convection-diffusion equations. The interplay between several time scales produces a rich and complex phenomenology. We investigate the effects of different oscillation frequencies and viscosities on the morphology of the phase separating domains. We find that at high frequencies the evolution is almost isotropic with growth exponents 2/3 and 1/3 in the inertial (low viscosity) and diffusive (high viscosity) regimes, respectively. When the period of the applied shear flow becomes of the same order of the relaxation time $T_R$ of the shear velocity profile, anisotropic effects are clearly observable. In correspondence with non-linear patterns for the velocity profiles, we find configurations where lamellar order close to the walls coexists with isotropic domains in the middle of the system. For particular values of frequency and viscosity it can also happen that the convective effects induced by the oscillations cause an interruption or a slowing of the segregation process, as found in some experiments. Finally, at very low frequencies, the morphology of domains is characterized by lamellar order everywhere in the system resembling what happens in the case with steady shear.

cond-mat.soft↗