Flux Limiter Lattice Boltzmann for Compressible Flows

In this paper, a new flux limiter scheme with the splitting technique is successfully incorporated into a multiple-relaxation-time lattice Boltzmann （LB） model for shacked compressible flows. The proposed flux limiter scheme is efficient in decreasing the artificial oscillations and numerical diffusion around the interface. Due to the kinetic nature, some interface problems being difficult to handle at the macroscopic level can be modeled more naturally through the LB method. Numerical simulations for the Richtmyer-Meshkov instability show that with the new model the computed interfaces are smoother and more consistent with physical analysis. The growth rates of bubble and spike present a satisfying agreement with the theoretical predictions and other numerical simulations.

Flux Limiter Lattice Boltzmann Scheme Approach to Compressible Flows with Flexible Specific-Heat Ratio and Prandtl Number

We further develop the lattice Boltzmann （LB） model [Physica A 382 （2007） 502] for compressible flows from two aspects. Firstly, we modify the Bhatnagar Gross Krook （BGK） collision term in the LB equation, which makes the model suitable for simulating flows with different Prandtl numbers. Secondly, the flux limiter finite difference （FLFD） scheme is employed to calculate the convection term of the LB equation, which makes the unphysical oscillations at discontinuities be effectively suppressed and the numerical dissipations be significantly diminished. The proposed model is validated by recovering results of some well-known benchmarks, including （i） The thermal Couette flow; （ii） One- and two-dlmenslonal FLiemann problems. Good agreements are obtained between LB results and the exact ones or previously reported solutions. The flexibility, together with the high accuracy of the new model, endows the proposed model considerable potential for tracking some long-standing problems and for investigating nonlinear nonequilibrium complex systems.

Enhancement of the flux for polypropylene hollow fiber membrane in a submerged membrane-bioreactor by surface modification

To improve its limiting flux and antifouling characteristics in a submerged membrane-bioreactor （SMBR） for wastewater treatment, polypropylene hollow fiber microporous membrane （PPHFMM） was surface-modified by the plasma-induced immobilization of poly （N-vinyl-2-pyrrolidone） （PVP） and the plasma treatment with different gases respectively. Attenuated total reflection-Fourier transform infrared spectroscopy （FT-IR/ATR）, X-ray photoelectron spectroscopy （XPS） and field emission scanning electron microscope （FE-SEM） were used to characterize the structural and morphological changes on the membrane surface. Water contact angle was measured by the sessile drop method. It was found that the water contact angle was 128.8, 72.3, 62.7, 74.4, 79.1, 86.3, and 71.3° for the nascent, PVP-immobilized, air, 02, Ar, CO2 and H2O plasma treated PPHFMM, respectively. The SMBR was operated at fixed transmembrane pressure to determine the limiting flux for the PPHFMM before and after surface modification. Results showed that the limiting flux appeared to be 103, 159, 117, 133, 136, 121 and 152 L/（m^2· h） for the nascent, PVP-immobilized, air, O2, At, CO2 and H2O plasma treated PPHFMM, respectively. After continuous operation for about 50 h in the SMBR, the antifouling characteristics were improved to some extent.

Comparison and Modification: TVD Schemes for Scalar Transport on An Unstructured Grid

In most TVD schemes, the r-factors were proposed according to the cell-centered（CC） finite volume method（FVM） framework for the numerical approximation to the convective term. However, it is questionable whether those r-factors would be appropriate and effective for the vertex-centered（VC） FVM. In the paper, we collected five kinds of r-factor formulae and found out that only three of those, respectively by Bruner（1996）, Darwish and Moukalled（2003） and Cassuli and Zanolli（2005） can be formally extended to a context of the VC FVM. Numerical tests indicate that the TVD schemes and r-factors, after being extended and introduced to a context of the VC FVM, maintained their similar characteristics as in a context of the CC FVM. However, when the gradient-based r-factors and the SUPERBEE scheme were applied simultaneously, non-physical oscillations near the sharp step would appear. In the transient case, the oscillations were weaker in a context of the VC FVM than those in a context of the CC FVM, while the effect was reversed in the steady case. To eliminate disadvantages in the gradient-based r-factor formula, a new modification method by limiting values on the virtual node, namely Фu in the paper, was validated by the tests to effectively dissipate spurious oscillations.

A PREDICTING MODEL OF THE LIMITING FLUX FOR THE CHARGED SOLUTE IN ULTRAFILTRATION PROCESS

In the process of ultrafiltration, the occurrence of the limiting flux iselucidated with the formation of a cake(gel) layer on the membrane surface. Before cake formation,the pressure drop on the concentration polarization layer, as well as the permeate flux, increaseswith the applied pressure. The pressure drop on the concentration polarization layer, however, willno longer change with the applied pressure after the formation of the cake layer. The limiting fluxwill be obtained if the hydrodynamic conditions in the filtration channel are not affected by thecake layer. A mathematics model for predicting the limiting flux for the charged solute inultrafiltration is developed. In this model, a repulsive electric force is taken into account inaddition to convection and diffusion when the solute is carrying the same charge as the membranematerial. A procedure to correlate the model with experimental ultrafiltration data is also present.The results show that a model in this paper is developed on a more realistic perception of theultrafiltration system and the predicting data agrees well with experimental data.

Two-dimensional Multiple-Relaxation-Time Lattice Boltzmann model for compressible and incompressible flows

In the paper we extend the Multiple-Relaxation-Time （MRT） Lattice Boltzmann （LB） model pro- posed in [Europhys. Lctt., 2010, 90： 54003] so that it is suitable also for incompressible flows. To decrease tile artificial oscillations, the convection term is discretized by the flux linfiter scheme with splitting technique. A new model is validated by some well-known benchmark tests, including Rie- mann problem and Couette flow, and satisfying agreements are obtained between the sinmlation results and ana.lytical 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 the physical analysis.

Robust Conservative Level SetMethod for 3D Mixed-Element Meshes —Application to LES of Primary Liquid-Sheet Breakup

In this article we detail the methodology developed to construct an efficient interface description technique—the robust conservative level set(RCLS)—to simulate multiphase flows on mixed-element unstructured meshes while conserving mass to machine accuracy.The approach is tailored specifically for industry as the three-dimensional unstructured approach allows for the treatment of very complex geometries.In addition,special care has been taken to optimise the trade-off between accuracy and computational cost while maintaining the robustness of the numerical method.This was achieved by solving the transport equations for the liquid volume fraction using a WENO scheme for polyhedral meshes and by adding a flux-limiter algorithm.The performance of the resulting method has been compared against established multiphase numerical methods and its ability to capture the physics of multiphase flows is demonstrated on a range of relevant test cases.Finally,the RCLS method has been applied to the simulation of the primary breakup of a flat liquid sheet of kerosene in co-flowing high-pressure gas.This quasi-DNS/LES computation was performed at relevant aero-engine conditions on a three-dimensional mixed-element unstructured mesh.The numerical results have been validated qualitatively against theoretical predictions and experimental data.In particular,the expected breakup regime was observed in the simulation results.Finally,the computation reproduced faithfully the breakup length predicted by a correlation based on experimental data.This constitutes a first step towards a quantitative validation.

A High Order Bound Preserving Finite Difference Linear Scheme for Incompressible Flows

We propose a high order finite difference linear scheme combined with ahigh order bound preserving maximum-principle-preserving (MPP) flux limiter tosolve the incompressible flow system. For such problem with highly oscillatory structure but not strong shocks, our approach seems to be less dissipative and much lesscostly than a WENO type scheme, and has high resolution due to a Hermite reconstruction. Spurious numerical oscillations can be controlled by the weak MPP fluxlimiter. Numerical tests are performed for the Vlasov-Poisson system, the 2D guidingcenter model and the incompressible Euler system. The comparison between the linearand WENO type schemes, with and without the MPP flux limiter, will demonstrate thegood performance of our proposed approach.

An updated search of steady TeV γ-ray point sources in northern hemisphere using the Tibet air shower array

Using the data taken from Tibet II High Density （HD） Array （1997 February-1999 September） and Tibet-III array （1999 November--2005 November）, our previous northern sky survey for TeV γ-ray point sources has now been updated by a factor of 2.8 improved statistics. From 0.0° to 60.0° in declination （Dec） range, no new TeV T-ray point sources with sufficiently high significance were identified while the well-known Crab Nebula and Mrk421 remain to be the brightest TeV γ-ray sources within the field of view of the Tibet air shower array. Based on the currently available data and at the 90% confidence level （C.L.）, the flux upper limits for different power law index assumption are re-derived, which are approximately improved by 1.7 times as compared with our previous reported limits.