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 $Ma \sim 5$.Comment: Accepted for publication in EP

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.Comment: 17 pages, 8 figure

Discrete Boltzmann modeling of detonation: based on the Shakhov model

A Discrete Boltzmann Model(DBM) based on the Shakhov model for detonation is proposed. Compared with the DBM based on the Bhatnagar-Gross-Krook (BGK) model, the current model has a flexible Prandtl numbers and consequently can be applied to a much wider range of detonation phenomena. Besides the Hydrodynamic Non-Equilibrium (HNE) behaviors usually investigated by the Navier-Stokes model, the most relevant Thermodynamic Non-Equilibrium (TNE) effects can be probed by the current model. The model is validated by some well-known benchmarks,and some steady and unsteady detonation processes are investigated. As for the von Neumann peak relative to the wave front, it is found that (i) (within the range of numerical experiments) the peak heights of pressure, density and flow velocity increase exponentially with the Prandtl number, the maximum stress increases parabolically with the Prandtl number, and the maximum heat flux decreases exponentially with the Prandtl number; (ii) the peak heights of pressure, density, temperature and flow velocity and the maximum stress within the peak are parabolically increase with the Mach number, the maximum heat flux decreases exponentially with the Mach number

Supplementation of iron alone and combined with vitamins improves haematological status, erythrocyte membrane fluidity and oxidative stress in anaemic pregnant women

Pregnancy is a condition exhibiting increased susceptibility to oxidative stress, and Fe plays a central role in generating harmful oxygen species. The objective of the present study is to investigate the changes in haematological status, oxidative stress and erythrocyte membrane fluidity in anaemic pregnant women after Fe supplementation with and without combined vitamins. The study was a 2 months double-blind, randomised trial. Pregnant women (n 164) were allocated to four groups: group C was the placebo control group; group I was supplemented daily with 60 mg Fe (ferrous sulphate) daily; group IF was supplemented daily with Fe plus 400 µg folic acid; group IM was supplemented daily with Fe plus 2 mg retinol and 1 mg riboflavin, respectively. After the 2-month trial, Hb significantly increased by 15·8, 17·3 and 21·8 g/l, and ferritin by 2·8, 3·6 and 11·0 µg/l, in the I, IF and IM groups compared with placebo. Polarisation (¿) and microviscosity (¿) decreased significantly in other groups compared with placebo, indicating an increase in membrane fluidity. Significant decreases of ¿ and ¿ values compared with group C were 0·033 and 0·959 for group I, 0·037 and 1·074 for group IF and 0·064 and 1·865 for group IM, respectively. In addition, significant increases of glutathione peroxidase activities and decreases of malondialdehyde were shown in all treated groups, as well as increases of plasma retinol and urine riboflavin in group IM. The findings show that supplementation with Fe and particularly in combination with vitamins could improve the haematological status as well as oxidative stress and erythrocyte membrane fluidit

Plasma kinetics: Discrete Boltzmann modelling and Richtmyer-Meshkov instability

A discrete Boltzmann model (DBM) for plasma kinetics is proposed. The constructing of DBM mainly considers two aspects. The first is to build a physical model with sufficient physical functions before simulation. The second is to present schemes for extracting more valuable information from massive data after simulation. For the first aspect, the model is equivalent to a magnetohydrodynamic model plus a coarse-grained model for the most relevant TNE behaviors including the entropy production rate. A number of typical benchmark problems including Orszag-Tang (OT) vortex problem are used to verify the physical functions of DBM. For the second aspect, the DBM use non-conserved kinetic moments of (f-feq) to describe non-equilibrium state and behaviours of complex system. The OT vortex problem and the Richtmyer-Meshkov instability (RMI) are practical applications of the second aspect. For RMI with interface inverse and re-shock process, it is found that, in the case without magnetic field, the non-organized momentum flux shows the most pronounced effects near shock front, while the non-organized energy flux shows the most pronounced behaviors near perturbed interface. The influence of magnetic field on TNE effects shows stages: before the interface inverse, the TNE strength is enhanced by reducing the interface inverse speed; while after the interface inverse, the TNE strength is significantly reduced. Both the global average TNE strength and entropy production rate contributed by non-organized energy flux can be used as physical criteria to identify whether or not the magnetic field is sufficient to prevent the interface inverse.Comment: 20 pages, 15 figure