THREE HIGH-ORDER SPLITTING SCHEMES FOR 3D TRANSPORT EQUATION

Two high-order splitting schemes based on the idea of the operators splitting method are given. The three-dimensional advection-diffusion equation was split into several one-dimensional equations that were solved by these two schemes, only three computational grid points were needed in each direction but the accuracy reaches the spatial fourth-order. The third scheme proposed is based on the classical ADI scheme and the accuracy of the advection term of it can reach the spatial fourth-order. Finally, two typical numerical experiments show that the solutions of these three schemes compare well with that given by the analytical solution when the Peclet number is not bigger than 5.

Calculation of Combustion Products by the New Iteration Method of Non-linear Equations

For a specific combustion problem involving calculations of several species at the equilibrium state, it is simpler to write a general computer program and calculate the combustion concentration. Original work describes, an adaptation of Newton-Raphson method was used for solving the highly nonlinear system of equations describing the formation of equilibrium products in reacting of fuel-additive-air mixtures. This study also shows what possible of the results. In this paper, to be present the efficient numerical algorithms for. solving the combustion problem, to be used nonlinear equations based on the iteration method and high order of the Taylor series. The modified Adomian decomposition method was applied to construct the numerical algorithms. Some numerical illustrations are given to show the efficiency of algorithms. Comparisons of results by the new Matlab routines and previous routines, the result data indicate that the new Matlab routines are reliable, typical deviations from previous results are less than 0.05%.

A High-Order Localized Artificial Diffusivity Scheme for Discontinuity Capturing on 1D Drift-Flux Models for Gas-Liquid Flows

A computational code is developed for the numerical solution of onedimensional transient gas-liquid flows using drift-flux models,in isothermal and also with phase change situations.For these two-phase models,classical upwind schemes such as Roe-and Godunov-type schemes are generally difficult to derive and expensive to use,since there are no treatable analytic expressions for the Jacobian matrix,eigenvalues and eigenvectors of the system of equations.On the other hand,the highorder compact finite difference scheme becomes an attractive alternative on these occasions,as it does not make use of any wave propagation information from the system of equations.The present paper extends the localized artificial diffusivity method for high-order compact finite difference schemes to solve two-phase flows with discontinuities.The numerical method has simple formulation,straightforward implementation,low computational cost and,most importantly,high-accuracy.The numerical methodology proposed is validated by solving several numerical examples given in the literature.The simulations are sixth-order accurate and it is shown that the proposed numerical method provides accurate approximations of shock waves and contact discontinuities.This is an essential property for simulations of realistic mass transport problems relevant to operations in the petroleum industry。

Third Order WENO Scheme on Three Dimensional Tetrahedral Meshes

We extend the weighted essentially non-oscillatory(WENO)schemes on two dimensional triangular meshes developed in[7]to three dimensions,and construct a third order finite volume WENO scheme on three dimensional tetrahedral meshes.We use the Lax-Friedrichs monotone flux as building blocks,third order reconstructions made from combinations of linear polynomials which are constructed on diversified small stencils of a tetrahedral mesh,and non-linear weights using smoothness indicators based on the derivatives of these linear polynomials.Numerical examples are given to demonstrate stability and accuracy of the scheme.

High order DBR GaSb based single longitude mode diode lasers at 2 μm wavelength

The GaSb-based distributed Bragg reflection（DBR） diode laser with 23 rd-order gratings have been fabricated by conventional UV lithography and inductively coupled plasma（ICP） etching. The ICP etching conditions were optimized and the relationship among etching depth, duty ratio and side-mode suppression ratio（SMSR） was studied. The device with a ridge width of 100 μm, gratings period of 13 μm and etching depth of 1.55 μm as well as the duty ratio of 85% was fabricated, its maximum SMSR reached 22.52 dB with uncoated cavity facets under single longitudinal operation mode at room temperature.

Comparison of Fifth-OrderWENO Scheme and Finite Volume WENO-Gas-Kinetic Scheme for Inviscid and Viscous Flow Simulation

The development of high-order schemes has been mostly concentrated on the limiters and high-order reconstruction techniques.In this paper,the effect of the flux functions on the performance of high-order schemes will be studied.Based on the same WENO reconstruction,two schemes with different flux functions,i.e.,the fifthorderWENO method and the WENO-Gas-kinetic scheme(WENO-GKS),will be compared.The fifth-order finite difference WENO-SW scheme is a characteristic variable reconstruction based method which uses the Steger-Warming flux splitting for inviscid terms,the sixth-order central difference for viscous terms,and three stages Runge-Kutta time stepping for the time integration.On the other hand,the finite volume WENO-GKS is a conservative variable reconstruction based method with the same WENO reconstruction.But,it evaluates a time dependent gas distribution function along a cell interface,and updates the flow variables inside each control volume by integrating the flux function along the boundary of the control volume in both space and time.In order to validate the robustness and accuracy of the schemes,both methods are tested under a wide range of flow conditions:vortex propagation,Mach 3 step problem,and the cavity flow at Reynolds number 3200.Our study shows that both WENO-SW and WENO-GKS yield quantitatively similar results and agree with each other very well provided a sufficient grid resolution is used.With the reduction of mesh points,the WENO-GKS behaves to have less numerical dissipation and present more accurate solutions than those from the WENO-SW in all test cases.For the Navier-Stokes equations,since theWENO-GKS couples inviscid and viscous terms in a single flux evaluation,and the WENO-SW uses an operator splitting technique,it appears that theWENO-SWismore sensitive to theWENO reconstruction and boundary treatment.In terms of efficiency,the finite volume WENO-GKS is about 4 times slower than the finite differenceWENO-SW in two dimensional simulations.The current study clearly shows that besides high-order reconstruction,an accurate gas evolution model or flux function in a high-order scheme is also important in the capturing of physical solutions.In a physical flow,the transport,stress deformation,heat conduction,and viscous heating are all coupled in a single gas evolution process.Therefore,it is preferred to develop such a scheme with multi-dimensionality,and unified treatment of inviscid and dissipative terms.A high-order scheme does prefer a high-order gas evolution model.Even with the rapid advances of high-order reconstruction techniques,the first-order dynamics of the Riemann solution becomes the bottleneck for the further development of high-order schemes.In order to avoid the weakness of the low order flux function,the development of high-order schemes relies heavily on the weak solution of the original governing equations for the update of additional degree of freedom,such as the non-conservative gradients of flow variables,which cannot be physically valid in discontinuous regions.

High-Order Bit Independence Criterion Test for the S-boxes

A new security test for the substitution boxes （S-boxes） high-order bit independence criterion （HOBIC） test, is presented. Different from the previous security tests for S-boxes, the HOBIC test can be used to measure the strength of an S-box against attacks that keep some of its input bits constant. Test results over the S-boxes of Data Encryption Standard （DES） and Advanced Encryption Standard （AES） are given and some possible applications of the HOBIC test are analyzed. Meanwhile, the source code for a basic version of the HOBIC test is also provided, the implement process of which shows that it is very fast and efficient for practical applications .

Wave Propagation Across Acoustic/Biot’s Media:A Finite-Difference Method

Numerical methods are developed to simulate the wave propagation in heterogeneous 2D fluid/poroelastic media.Wave propagation is described by the usual acoustics equations(in the fluid medium)and by the low-frequency Biot’s equations(in the porous medium).Interface conditions are introduced to model various hydraulic contacts between the two media:open pores,sealed pores,and imperfect pores.Well-posedness of the initial-boundary value problem is proven.Cartesian grid numerical methods previously developed in porous heterogeneous media are adapted to the present context:a fourth-order ADER scheme with Strang splitting for timemarching;a space-time mesh-refinement to capture the slow compressional wave predicted by Biot’s theory;and an immersed interface method to discretize the interface conditions and to introduce a subcell resolution.Numerical experiments and comparisons with exact solutions are proposed for the three types of interface conditions,demonstrating the accuracy of the approach.