Abstract: A genuinely multidimensional HLL Riemann solver was given. The flux vector of the Euler equations was split into convection and pressure parts based on the TV splitting method. The convection part was evaluated by means of the upwind method similar to the AUSM scheme, and the pressure part was evaluated with a modified HLL scheme. In the modified HLL scheme, the choices of wave speed were based on the pressure system rather than the Euler equations, and the pressure difference was replaced by the density difference in the dissipative term in order to capture the contact accurately. To obtain the genuinely multidimensional property, the numerical fluxes at the midpoint and the 2 corners of the cell interface were evaluated respectively, and the Simpson rule was used to obtain the final numerical flux through the interface. The linear reconstruction based on the SDWLS gradients was implemented for 2nd-order spatial accuracy, and the time derivative was discretized with the 2nd-order Runge-Kutta method. Compared with the traditional 1D HLL scheme, the genuinely multidimensional HLL scheme can effectively capture the contact discontinuity, and use larger time steps. Unlike other schemes which can capture the contact discontinuity accurately such as the HLLC scheme, the genuinely multidimensional HLL scheme eliminates the phenomena of numerical shock instability in 2D cases.
Abstract: An application of the generalized hydrodynamics for soft-matter quasicrystals with 12-fold symmetry—flow past a cylinder, was demonstrated by means of an alternating procedure, and a zeroth-order approximate analytic solution was obtained, in which the classical Oseen solution was used. The flow velocity field and the phonon stress field were approximately determined, and the possible solution of the phason stress field was also discussed. At last a possible modification to dislocation of soft-matter quasicrystals due to the present solution was considered.
Abstract: A regularity criterion for the axisymmetric incompressible NavierStokes system was established.It is proved that, if local axisymmetric smooth solution u satisfies‖ωr‖Lα1((0,T);Lβ1)+‖ωθ/r‖Lα2((0,T);Lβ2))<∞,where 2/α1+3/β1≤1+3/β1,2/α2+3/β2≤2 and β1≥3, β2> 3/2,this strong solution will keep its smoothness up to time T.
Abstract: The droplets’ directional motion characteristics in conical microchannels with different wetting properties and driving mechanisms were studied with the numerical simulation method and the energy-based analytical method to clarify the mechanisms for directional motions of liquid in nature. The effects of the conical angle, the contact angle between the droplet and the microchannel wall as well as the microchannel wetting property on the directional motion characteristics of the droplet in the conical microchannel, were obtained. The energy-based theoretical analysis and the numerical simulation both indicate that, the conical angle and the contact angle substantially influence the motion direction and the driving force of the droplet, but with different effectivenesses. The effectiveness is in holistic consistency in the hydrophilic conical microchannel, but local features emerge in the hydrophobic conical microchannel. The study provides a theoretic base for the research of directional motion mechanisms and microfluidic flow mechanisms in the solid interface.
Abstract: In order to understand the effects of strength anisotropy of bedding shale on the collapse pressures of horizontal wells, the cores of different bedding angles were drilled out of the Longmaxi group, Sichuan Basin, and the macroscopic and microscopic shale characteristics were studied based on the polarizing micrographs and the scanning electron micrographs. Besides, the anisotropic shale strengths were investigated through the uniaxial compressive strength tests. Given the anisotropic physical and mechanical properties of the bedding shale, the practice that the shale was roughly simplified as an isotropic body in the previous borehole stability design made the predicted collapse pressure for maintaining borehole stability incapable of meeting the need for drilling safety. Hence, a calculation model for the stress field around the borehole in anisotropic formation was established. With a transverse isotropic formation model, the effects of the isotropic surface and the elastic parameters’ anisotropic ratios on the well circumferential stresses were analyzed; meanwhile, the Mogi-Coulomb criterion was adopted to estimate the wellbore stability, and the sensitivity analysis was carried out to consider the impacts of different mechanical properties including Young’s modulus and Poisson’s ratio on the collapse pressure. Results show that the formation anisotropy increases the circumferential stress distribution heterogeneity and worsens the wellbore stress situation significantly; the degree of anisotropy affects the collapse pressure a lot. The sensitivity analysis also show that Poisson’s ratio anisotropy does not markedly change the collapse pressure for low anisotropy degrees; however, the effect of the elastic modulus anisotropy is notable. The work is useful for the in-situ wellbore design before drilling.
Abstract: The heat and mass transfer process in microchannels was analyzed with constant heat flux through the wall. In the numerical calculation model, the electric double layer potential, velocity, ion concentration and temperature distribution were characterized with the Poisson-Boltzmann equation, the Navier-Stokes equation, the Nernst-Planck equation and the energy equation, respectively. The effects of different flow parameters on each thermal index in the heat and mass transfer process were investigated by means of the entropy generation, and the influences of important flow parameters on the total entropy generation and the proportion of each thermal effect were discussed in detail. The results reveal that, the increases of the kinetic parameters and the Joule heating coefficient weaken the heat transfer performance, and the influence of the kinetic parameters is more evident. The total entropy of the flow is an increasing function of the kinetic parameters, the mass transfer coefficient and the mass dispersion coefficient.
Abstract: In order to restrain the surplus force caused by position disturbance in the aircraft rudder electrohydraulic load simulator and improve accuracy of the loading system, the mathematical model for each part and the whole system was established. Through the analysis of the mathematical model, the generation mechanism for the surplus force was expounded, and the transfer function for the surplus force was established. A compound control method was proposed which combined PID and feedforward compensation. The numerical simulation and the experimental study were carried out based on the proposed method. The results of simulation and experiment show that, the feedforward PID compound control can effectively restrain the system’s surplus force, so as to improve the loading accuracy of the electrohydraulic load simulation system. At the same time, the experimental results show that the surplus force hits a mutation when the system changes the direction of movement, which points out the direction for further research.
Abstract: The global stability of fractional-order complex-valued neural networks was investigated. For a class of memristor-based fractional-order complex-valued neural networks with time delays, under the concept of the Filippov solution in the sense of Caputo’s fractional derivation, the existence and uniqueness of the equilibrium point were discussed. The comparison principle and the fixed-point theorem were applied to the stability analysis through division of the complex values into the real part and the imaginary part. Some sufficient criteria for the global asymptotic stability of memristor-based fractional-order complex-valued neural networks were derived. Finally, a simulation example shows the effectiveness of the obtained results.
Abstract: Based on the two-velocity Brinkman-extended Darcy flow model, the characteristics of high speed flow in circular and annular ducts occupied by bidisperse porous media were analyzed. The flow fields of the fracture (f) and porous (p) phases were inherently governed by the 4th-order system of coupled differential equations. The original governing equations were simplified to a 2nd-order system of decoupled differential equations with the normal mode reduction method. Furthermore, the analytical solutions of velocity distributions were readily derived for the f- and p-phases. Results from both the circular and the annular ducts show that an increase in the Darcy number leads to a reduction in not only the flow velocities of the two phases but their difference. However, the flow velocities of the two phases exhibit an opposite trend with the increase of the momentum transfer between the two phases, resulting in a decrease in the velocity difference.
Abstract: A predatorprey model was considered, in which both the predators and the preys dispersed among n patches under stochastic perturbations. Based on the method of Lyapunov functions, it was proved that a unique global positive solution existed for any given positive initial value; in turn, the property of ultimate boundedness was obtained. In addition, the sufficient conditions for the extinctions of the preys and even the whole system were given. Finally, the theoretic conclusions were validated by numerical simulations.