Gas kinetic flux solver based finite volume weighted essentially non-oscillatory scheme for inviscid compressible flows

A high-order gas kinetic flux solver(GKFS)is presented for simulating inviscid compressible flows.The weighted essentially non-oscillatory(WENO)scheme on a uniform mesh in the finite volume formulation is combined with the circular function-based GKFS(C-GKFS)to capture more details of the flow fields with fewer grids.Different from most of the current GKFSs,which are constructed based on the Maxwellian distribution function or its equivalent form,the C-GKFS simplifies the Maxwellian distribution function into the circular function,which ensures that the Euler or Navier-Stokes equations can be recovered correctly.This improves the efficiency of the GKFS and reduces its complexity to facilitate the practical application of engineering.Several benchmark cases are simulated,and good agreement can be obtained in comparison with the references,which demonstrates that the high-order C-GKFS can achieve the desired accuracy.

Improved Symmetry Property of High Order Weighted Essentially Non-Oscillatory Finite Difference Schemes for Hyperbolic Conservation Laws

This study aims to investigate the rapid loss of numerical symmetry for problems with symmetrical initial conditions and boundary conditions when solved by the seventh and higher order nonlinear characteristic-wise weighted essentially non-oscillatory(WENO)finite difference schemes.Using the one-dimensional double rarefaction wave problem and the Sedov blast-wave problems,and the twodimensional Rayleigh-Taylor instability(RTI)problem as examples,we illustrate numerically that the sensitive interaction of the round-off error due to the numerical unstable explicit form of the local lower order smoothness indicators in the nonlinear weights definition,which are often given and used in the literature,and the nonlinearity of the WENO scheme are responsible for the rapid growth of asymmetry of an otherwise symmetric problem.An equivalent but compact and numerical stable compact form of the local lower order smoothness indicators is suggested for delaying the onset of and reducing the magnitude of the symmetry error.The benefits of using the compact form of the local lower order smoothness indicators should also be applicable to non-symmetrical strongly non-linear problems in terms of improved numerical stability,reduced rounding errors and increased computational efficiency.

High-order targeted essentially non-oscillatory scheme for two-fluid plasma model

The weakly ionized plasma flows in aerospace are commonly simulated by the single-fluid model,which cannot describe certain nonequilibrium phenomena by finite collisions of particles,decreasing the fidelity of the solution.Based on an alternative formulation of the targeted essentially non-oscillatory(TENO)scheme,a novel high-order numerical scheme is proposed to simulate the two-fluid plasmas problems.The numerical flux is constructed by the TENO interpolation of the solution and its derivatives,instead of being reconstructed from the physical flux.The present scheme is used to solve the two sets of Euler equations coupled with Maxwell's equations.The numerical methods are verified by several classical plasma problems.The results show that compared with the original TENO scheme,the present scheme can suppress the non-physical oscillations and reduce the numerical dissipation.

ESSENTIAL NORMS OF PRODUCTS OF WEIGHTED COMPOSITION OPERATORS AND DIFFERENTIATION OPERATORS BETWEEN BANACH SPACES OF ANALYTIC FUNCTIONS

We obtain several estimates of the essential norms of the products of differen- tiation operators and weighted composition operators between weighted Banach spaces of analytic functions with general weights. As applications, we also give estimates of the es- sential norms of weighted composition operators between weighted Banach space of analytic functions and Bloch-type spaces.

AN UPPER BOUND OF THE ESSENTIAL NORM OF COMPOSITION OPERATORS BETWEEN WEIGHTED BERGMAN SPACES

In this paper, we define the generalized counting functions in the higher dimensional case and give an upper bound of the essential norms of composition operators between the weighted Bergman spaces on the unit ball in terms of these counting functions. The sufficient condition for such operators to be bounded or compact is also given.

Third-order modified coeffcient scheme based on essentially non-oscillatory scheme

A third-order numerical scheme is presented to give approximate solutions to multi-dimensional hyperbolic conservation laws only using modified coefficients of an essentially non-oscillatory （MCENO） scheme without increasing the base points during construction of the scheme. The construction process shows that the modified coefficient approach preserves favourable properties inherent in the original essentially nonoscillatory （ENO） scheme for its essential non-oscillation, total variation bounded （TVB）, etc. The new scheme improves accuracy by one order compared to the original one. The proposed MCENO scheme is applied to simulate two-dimensional Rayleigh-Taylor （RT） instability with densities 1：3 and 1：100, and solve the Lax shock-wave tube numerically. The ratio of CPU time used to implement MCENO, the .third-order ENO and fifth-order weighed ENO （WENO） schemes is 0.62：1：2.19. This indicates that MCENO improves accuracy in smooth regions and has higher accuracy and better efficiency compared to the original ENO scheme.

Linear Combination of Derivative Weighted Composition Operators

The relation between composition operators on the Dirichlet spaces in the open unit disk and derivative weighted composition operators on the Bergman spaces in the open unit disk is investigated firstly,and for a combination of several derivative weighted composition operators which acts on classic Bergman space,the lower bound of its essential norm is estimated in terms of the boundary data of the symbols of d-composition operators.Some similar results about composition operators on the Dirichlet space are also presented.A necessary condition is given to determine the compactness of the combination of several derivative weighted composition operators on Bergman spaces.

Effect of High Digestible Essential Amino Acids on Weight Gains and Carcass Compositions of Laying Hens

The objective of this study was to evaluate the effect of high digestible essential amino acids （DEAA） on weight gains and carcass compositions of laying hens. Three hundred and sixty lsa Brown hens in five replications per treatment （12 birds/replicate） were used. Six experimental diets which contained of treatment 1 （negative control） as the conventional layer diet are recommended by NRC （1994） while another dietary treatments; treatments 2 （positive control）, 3, 4, 5 and 6 were formulated to meet 100%, 110%, 120%, 130% and 140% of Standard Ileal Digestible Lysine Levels （SIDLL） without crude protein minimum, while methionine （Met）, threonine （Thre） and tryptophan （Tryp） as related by Ideal Protein Concept （IPC） which suggested by NRC （1994） and INRA （2004）. However, metabolizable energy （ME）, calcium and available phosphorus （Avai P） levels of all experimental diets were meet requirement as recommended by NRC （1994）. The experiment was assigned in CRD and laying hens fed dietary treatments from 28 to 44 weeks of age and cage was the experimental unit （3 hens/cage）. The result shown that percentages of thigh （TP）, feet （FP）, drumstick （DP）, heart （HP）, liver （LP） and gizzard （GP） were not affected by dietary treatment. However, weight gains （WG） and percentage of dressed weight （DWP）, eviscerate weight （EWP） and breast （BP） were increased （P 〈 0.05） and abdominal fat was reduced （P 〈 0.05） when birds fad diets containing 130% of SIDLL as compared with control group and another dietary treatments, when increasing the DEAA levels upper to 130% of SIDLL. The result indicated that diets formulated without crude protein minimum and increased DEAA resulted in increasing the efficiency of converting metabolizable energy （ME） to net energy （NE） for increasing weight gain and improved meat products while fat deposition in carcass composition was reduced.

APPLICATION OF WEIGHTED NONOSCILLATORY AND NON-FREE-PARAMETER DISSIPATION DIFFERENCE SCHEME IN CALCULATING THE FLOW OF VIBRATING FLAT CASCADE

A dual-time method is introduced to calculate the unsteady flow in a certain vibrating flat cascade. An implicit lower-upper symmetric-gauss-seidel scheme（LU-SGS） is applied for time stepping in pseudo time domains, and the convection items are discretized with the spatial three-order weighted non-oscillatory and non-free-parameter dissipation difference （WNND） scheme. The turbulence model adopts q-co low-Reynolds-number model. The frequency specmuns of lift coefficients and the unsteady pressure-difference coefficients at different spanwise heights as well as the entropy contours at blade tips on different vibrating instants, are obtained. By the analysis of frequency specmuns of lift coefficients at three spanwise heights, it is considered that there exist obvious non-linear perturbations in the flow induced by the vibrating, and the perturbation frequencies are higher than the basic frequency. The entropy contours at blade tips at different times display an intensively unsteady attribute of the flow under large amplitudes.

Sparse-Grid Implementation of Fixed-Point Fast Sweeping WENO Schemes for Eikonal Equations

Fixed-point fast sweeping methods are a class of explicit iterative methods developed in the literature to efficiently solve steady-state solutions of hyperbolic partial differential equations(PDEs).As other types of fast sweeping schemes,fixed-point fast sweeping methods use the Gauss-Seidel iterations and alternating sweeping strategy to cover characteristics of hyperbolic PDEs in a certain direction simultaneously in each sweeping order.The resulting iterative schemes have a fast convergence rate to steady-state solutions.Moreover,an advantage of fixed-point fast sweeping methods over other types of fast sweeping methods is that they are explicit and do not involve the inverse operation of any nonlinear local system.Hence,they are robust and flexible,and have been combined with high-order accurate weighted essentially non-oscillatory(WENO)schemes to solve various hyperbolic PDEs in the literature.For multidimensional nonlinear problems,high-order fixed-point fast sweeping WENO methods still require quite a large amount of computational costs.In this technical note,we apply sparse-grid techniques,an effective approximation tool for multidimensional problems,to fixed-point fast sweeping WENO methods for reducing their computational costs.Here,we focus on fixed-point fast sweeping WENO schemes with third-order accuracy(Zhang et al.2006[41]),for solving Eikonal equations,an important class of static Hamilton-Jacobi(H-J)equations.Numerical experiments on solving multidimensional Eikonal equations and a more general static H-J equation are performed to show that the sparse-grid computations of the fixed-point fast sweeping WENO schemes achieve large savings of CPU times on refined meshes,and at the same time maintain comparable accuracy and resolution with those on corresponding regular single grids.

HIGH ORDER WEIGHTED ESSENTIALLY NON-OSCILLATION SCHEMES FOR ONE-DIMENSIONAL DETONATION WAVE SIMULATIONS

In this paper, three versions of WENO schemes WENO-JS, WENO-M and WENO-Z are used for one-dimensional detonation wave simulations with fifth order characteristic based spatial flux reconstruction. Numerical schemes for solving the system of hyperbolic conversation laws using the ZND analytical solution as initial condition are presented. Numerical simulations of one-dimensional detonation wave for both stable and unstable cases are performed. In the stable case with overdrive factor f = 1.8, the temporal histories of peak pressure of the detonation front computed by WENO-JS and WENO-Z reach the theoretical steady state. In comparison, the temporal history of peak pressure computed by the WENO-M scheme fails to reach and oscillates around the theoretical steady state. In the unstable cases with overdrive factors f = 1.6 and f = 1.3, the results of all WENO schemes agree well with each other as the resolution, defined as the number of grid points per half-length of reaction zone, increases. Furthermore, for overdrive factor f = 1.6, the grid convergence study demonstrates that the high order WENO schemes converge faster than other existing lower order schemes such as unsplit scheme, Roe＇s solver with minmod limiter and Roe＇s solver with superbee limiter in reaching the predicted peak pressure. For overdrive factor f = 1.3, the temporal history of peak pressure shows an increasingly chaotic behavior even at high resolution. In the case of overdrive factor f = 1.1, in accordance with theoretical studies, an explosion occurs and different WENO schemes leading to this explosion appear at slightly different times.

Interface flux reconstruction method based on optimized weight essentially non-oscillatory scheme

Aimed at the computational aeroacoustics multi-scale problem of complex configurations discretized with multi-size mesh, the flux reconstruction method based on modified Weight Essentially Non-Oscillatory（WENO） scheme is proposed at the interfaces of multi-block grids.With the idea of Dispersion-Relation-Preserving（DRP） scheme, different weight coefficients are obtained by optimization, so that it is in WENO schemes with various characteristics of dispersion and dissipation. On the basis, hybrid flux vector splitting method is utilized to intelligently judge the amplitude of the gap between grid interfaces. After the simulation and analysis of 1D convection equation with different initial conditions, modified WENO scheme is proved to be able to independently distinguish the gap amplitude and generate corresponding dissipation according to the grid resolution. Using the idea of flux reconstruction at grid interfaces, modified WENO scheme with increasing dissipation is applied at grid points, while DRP scheme with low dispersion and dissipation is applied at the inner part of grids. Moreover, Gauss impulse spread and periodic point sound source flow among three cylinders with multi-scale grids are carried out. The results show that the flux reconstruction method at grid interfaces is capable of dealing with Computational Aero Acoustics（CAA） multi-scale problems.

A simple and robust method for essential boundary condition treatments in mesh-less methods

To improve the treatment efficiency of essential boundary condition in mesh-less methods, a simple and robust method is proposed in this paper. Rising weight of nodes in the construction of trail function, specified for essential boundary condition, can make the trail function pass through these nodes. And then, the trail function can satisfy the essential boundary condition previously by setting diagonal element to 1 or multiplying diagonal element by a big number in FEM. The MLS method is adopted to validate this method, and it is proved that this method is eostless and robust in most of mesh-less methods.

High-Order Bound-Preserving Finite Difference Methods for Multispecies and Multireaction Detonations

In this paper,we apply high-order finite difference(FD)schemes for multispecies and multireaction detonations(MMD).In MMD,the density and pressure are positive and the mass fraction of the ith species in the chemical reaction,say zi,is between 0 and 1,withΣz_(i)=1.Due to the lack of maximum-principle,most of the previous bound-preserving technique cannot be applied directly.To preserve those bounds,we will use the positivity-preserving technique to all the zi'is and enforceΣz_(i)=1 by constructing conservative schemes,thanks to conservative time integrations and consistent numerical fluxes in the system.Moreover,detonation is an extreme singular mode of flame propagation in premixed gas,and the model contains a significant stiff source.It is well known that for hyperbolic equations with stiff source,the transition points in the numerical approximations near the shocks may trigger spurious shock speed,leading to wrong shock position.Intuitively,the high-order weighted essentially non-oscillatory(WENO)scheme,which can suppress oscillations near the discontinuities,would be a good choice for spatial discretization.However,with the nonlinear weights,the numerical fluxes are no longer“consistent”,leading to nonconservative numerical schemes and the bound-preserving technique does not work.Numerical experiments demonstrate that,without further numerical techniques such as subcell resolutions,the conservative FD method with linear weights can yield better numerical approximations than the nonconservative WENO scheme.

Birth Weight in Relation to Maternal Blood Levels of Selected Elements in Slovenian Populations： A Cross-sectional Study

The objective of the present study was to evaluate the relation between maternal blood levels of selected toxic and potentially toxic elements （manganese （Mn）, copper （Cu）, zinc （Zn）, arsenic （As）, selenium （Se）, cadmium （Cd）, lead （Pb） and mercury （Hg）） and birth weight of their new-borns in a Slovenian population, taking into account maternal socio-demographic characteristics and dietary habits. 535 women from 12 regions of Slovenia were recruited at delivery. Maternal blood was collected at 1.5 months after birth. Associations between birth weight and a） predictors obtained through the questionnaires and b） levels of selected elements were tested using bivariate tests and multiple linear regression. Multiple regression models revealed maternal age as an additional predictor for birth weight and confirmed pre-pregnancy body mass, estimated gestational age and gender of the baby as the main predictors for birth weight. Mn in maternal blood was significantly and positively associated with birth weight. The positive association observed between birth weight and Mn in maternal blood could be explained by the essentiality of Mn in foetal development as an important cofactor in enzymereactions in bone formation and in metabolic regulation for amino acid, lipid, protein and carbohydrate levels.

Efficient Sparse-Grid Implementation of a Fifth-Order Multi-resolution WENO Scheme for Hyperbolic Equations

High-order accurate weighted essentially non-oscillatory(WENO)schemes are a class of broadly applied numerical methods for solving hyperbolic partial differential equations(PDEs).Due to highly nonlinear property of the WENO algorithm,large amount of computational costs are required for solving multidimensional problems.In our previous work(Lu et al.in Pure Appl Math Q 14:57–86,2018;Zhu and Zhang in J Sci Comput 87:44,2021),sparse-grid techniques were applied to the classical finite difference WENO schemes in solving multidimensional hyperbolic equations,and it was shown that significant CPU times were saved,while both accuracy and stability of the classical WENO schemes were maintained for computations on sparse grids.In this technical note,we apply the approach to recently developed finite difference multi-resolution WENO scheme specifically the fifth-order scheme,which has very interesting properties such as its simplicity in linear weights’construction over a classical WENO scheme.Numerical experiments on solving high dimensional hyperbolic equations including Vlasov based kinetic problems are performed to demonstrate that the sparse-grid computations achieve large savings of CPU times,and at the same time preserve comparable accuracy and resolution with those on corresponding regular single grids.

草果精油微胶囊的制备工艺优化及性质研究

草果精油易挥发、不稳定的特点限制其应用范围。为了有效提高草果精油利用率,本文对草果精油微胶囊的制备工艺进行优化并对其性质进行探究。以草果精油、乳化剂为芯材,辛烯基琥珀酸酐淀粉钠(Octenyl Succinic Anhydride Starch,OSA淀粉)、麦芽糊精、胶体为壁材,采用喷雾干燥法制备草果精油微胶囊。通过单因素和正交实验优化其制备工艺,并研究了草果精油微胶囊的物理性质、形貌特征、热稳定性。结果表明:最佳工艺配方为草果精油30%(w/w)、单,双甘油脂肪酸酯1%(w/w)、N-CREAMER 46型号OSA淀粉15%(w/w)、阿拉伯胶0.2%(w/w),喷雾干燥制备的草果精油微胶囊包埋率81.07%±3.20%,负载率64.43%±5.32%,水分含量3.40%±0.08%,复水后平均粒径(226.37±3.06)nm,微胶囊产品呈干燥粉末状,复水溶解迅速,包埋效果较好。经过同步热重差热分析,包埋后的草果精油的热稳定性得到了明显提高,扫描电镜观察草果精油微胶囊颗粒分布均匀。本研究可为喷雾干燥法制备草果精油微胶囊的工业生产提供一定技术参考。

The Essential Spectrum and Banach Reducibility of Operator Weighted Shifts

For an operator weighted shift S,the essential spectrum σ_e(S) and the indices associated with holes in σ_e(S) are described.Moreover,Banach reducibility of S is investigated and a condition for S~* to be a Cowen-Douglas operator is characterized.

Essential Norms of Composition Operators between Weighted Bergman Spaces of the Unit Disc

In this paper, we express the essential norms of composition operators between weighted Bergman spaces of the unit disc in terms of the generalized Nevanlinna counting function.