Numerical simulations of compressible mixing layers with a discontinuous Galerkin method

Discontinuous Galerkin（DG） method is known to have several advantages for flow simulations,in particular,in fiexible accuracy management and adaptability to mesh refinement. In the present work,the DG method is developed for numerical simulations of both temporally and spatially developing mixing layers. For the temporally developing mixing layer,both the instantaneous fiow field and time evolution of momentum thickness agree very well with the previous results. Shocklets are observed at higher convective Mach numbers and the vortex paring manner is changed for high compressibility. For the spatially developing mixing layer,large-scale coherent structures and self-similar behavior for mean profiles are investigated. The instantaneous fiow field for a three-dimensional compressible mixing layer is also reported,which shows the development of largescale coherent structures in the streamwise direction. All numerical results suggest that the DG method is effective in performing accurate numerical simulations for compressible shear fiows.

Early Age Compressive Strength of Pastes by Electrical Resistivity Method and Maturity Method

The compressive strength development of Portland cement pastes was investigated by the electrical resistivity method and the maturity method.The experiments were carried out on the cement pastes with different water-cement ratios at different curing temperatures.The results show that the application of the maturity method has limitation to obtain the strength.It is found that both of the compressive strength and the electrical resistivity follow hyperbolic trend for all the mixes.The hyperbolic equation of each mix is obtained to estimate the ultimate resistivity value which can probably be reached.The relationship between electrical resistivity and compressive strength of the cement pastes is established based on the test results and interpreted by the empirical Archie equation and a strength-porosity equation.The relationship between the electrical resistivity after temperature correction and the compressive strength was linear and independent of curing temperature and water-cement ratio.

A multiple-relaxation-time lattice Boltzmann method for high-speed compressible flows

This paper presents a coupling compressible model of the lattice Boltzmann method. In this model, the multiplerelaxation-time lattice Boltzmann scheme is used for the evolution of density distribution functions, whereas the modified single-relaxation-time （SRT） lattice Boltzmann scheme is applied for the evolution of potential energy distribution functions. The governing equations are discretized with the third-order Monotone Upwind Schemes for scalar conservation laws finite volume scheme. The choice of relaxation coefficients is discussed simply. Through the numerical simulations, it is found that compressible flows with strong shocks can be well simulated by present model. The numerical results agree well with the reference results and are better than that of the SRT version.

Application of the Artificial Compression Method to the Simulation of Two-Dimensional Frontogenesis

The artificial compression method (ACM) that is generally used to capture the contact discontinuity in nonviscous flows is used here in the simulation of quasi-geostrophic ideal frontogenesis in two dimensions. A comparison is made among the result of the ACM, the simulation result of Cullen, and the exact solution of the semi-geostrophic equations. The simulated front in this paper is more prominent than Cullen′s and is much closer to the exact solution.

Compression method based on training dataset of SVM

The method to compress the training dataset of Support Vector Machine （SVM） based on the character of the Support Vector Machine is proposed. First, the distance between the unit in two training datasets, and then the samples that keep away from hyper-plane are discarded in order to compress the training dataset. The time spent in training SVM with the training dataset compressed by the method is shortened obviously. The result of the experiment shows that the algorithm is effective.

A GHOST FLUID BASED FRONT TRACKING METHOD FOR MULTIMEDIUM COMPRESSIBLE FLOWS

Recent years the modify ghost fluid method （MGFM） and the real ghost fluid method （RGFM） based on Riemann problem have been developed for multimedium compressible flows. According to authors, these methods have only been used with the level set technique to track the interface. In this paper, we combine the MCFM and the RGFM respectively with front tracking method, for which the fluid interfaces are explicitly tracked by connected points. The method is tested with some one-dimensional problems, and its applicability is also studied. Furthermore, in order to capture the interface more accurately, especially for strong shock impacting on interface, a shock monitor is proposed to determine the initial states of the Riemann problem. The present method is applied to various one- dimensional problems involving strong shock-interface interaction. An extension of the present method to two dimension is also introduced and preliminary results are given.

An Efficient Projected Gradient Method for Convex Constrained Monotone Equations with Applications in Compressive Sensing

In this paper, a modified Polak-Ribière-Polyak conjugate gradient projection method is proposed for solving large scale nonlinear convex constrained monotone equations based on the projection method of Solodov and Svaiter. The obtained method has low-complexity property and converges globally. Furthermore, this method has also been extended to solve the sparse signal reconstruction in compressive sensing. Numerical experiments illustrate the efficiency of the given method and show that such non-monotone method is suitable for some large scale problems.

Simulation and Analysis of Ring Compression Using RP/RVP Meshless Method

To avoid mesh distortion and iterative remeshing in mesh-based numerical analysis,a meshless approach based on element free Galerkin (EFG) method is applied to the metal forming analysis of ring compression. Discrete equations are formulated upon the moving least-squares (MLS) approximation and modified Markov variational principles for rigid-plastic/ rigid-viscoplastic (RP/RVP) material models. The penalty function is used for the incompressible condition without volumetric locking. Based on the axisymmetric mechanical model,ring tests with different friction coefficients are studied. The deformed nodal configurations and shaded contours of equivalent strains are shown by developed meshless post processor. The comparison of meshless and finite element (FE) results validates the feasibility and accuracy for meshless method to simulate metal forming process.

Clinical observation of Hot Compress and Mounting Medicine Method

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ERROR ESTIMATION OF SPECTRAL-DIFFERENCE METHOD FOR COMPRESSIBLE FLUID FLOW IN THREE-DIMENSIONAL SPACE

This paper is devoted to a combined Fourier spectral-finite difference method for solving 3-dimensional, semi-periodic compressible fluid flow problem. The error estimation, as well as the convergence rate, is presented.

Mixed Method for Compressible Miscible Displacement with Dispersion in Porous Media

Compressible miscible displacement of one fluid by another in porous media is modelled by a nonlinear parabolic system. A finite element procedure is introduced to approximate the concentration of one fluid and the pressure of the mixture. The concentration is treated by a Galerkin method while the pressure is treated by a parabolic mixed finite element method. The effect of dispersion, which is neglected in [1], is considered. Optimal order estimates in L2 are derived for the errors in the approximate solutions.

Variational iteration method for solving compressible Euler equations

This paper applies the variational iteration method to obtain approximate analytic solutions of compressible Euler equations in gas dynamics. This method is based on the use of Lagrange multiplier for identification of optimal values of parameters in a functional. Using this method, a rapid convergent sequence is produced which converges to the exact solutions of the problem. Numerical results and comparison with other two numerical solutions verify that this method is very convenient and efficient.

An RKDG finite element method for the one-dimensional inviscid compressible gas dynamics equations in a Lagrangian coordinate

In this paper,Runge-Kutta Discontinuous Galerkin（RKDG） finite element method is presented to solve the onedimensional inviscid compressible gas dynamic equations in a Lagrangian coordinate.The equations are discretized by the DG method in space and the temporal discretization is accomplished by the total variation diminishing Runge-Kutta method.A limiter based on the characteristic field decomposition is applied to maintain stability and non-oscillatory property of the RKDG method.For multi-medium fluid simulation,the two cells adjacent to the interface are treated differently from other cells.At first,a linear Riemann solver is applied to calculate the numerical ？ux at the interface.Numerical examples show that there is some oscillation in the vicinity of the interface.Then a nonlinear Riemann solver based on the characteristic formulation of the equation and the discontinuity relations is adopted to calculate the numerical ？ux at the interface,which suppresses the oscillation successfully.Several single-medium and multi-medium fluid examples are given to demonstrate the reliability and efficiency of the algorithm.

Application of the Hierarchical Functions Expansion Method for the Solution of the Two Dimensional Navier-Stokes Equations for Compressible Fluids in High Velocity

This work presents a new application for the Hierarchical Function Expansion Method for the solution of the Navier-Stokes equations for compressible fluids in two dimensions and in high velocity. This method is based on the finite elements method using the Petrov-Galerkin formulation, know as SUPG (Streamline Upwind Petrov-Galerkin), applied with the expansion of the variables into hierarchical functions. To test and validate the numerical method proposed as well as the computational program developed simulations are performed for some cases whose theoretical solutions are known. These cases are the following: continuity test, stability and convergence test, temperature step problem, and several oblique shocks. The objective of the last cases is basically to verify the capture of the shock wave by the method developed. The results obtained in the simulations with the proposed method were good both qualitatively and quantitatively when compared with the theoretical solutions. This allows concluding that the objectives of this work are reached.

Application of the Combined Method for Evaluating the Compressive Strength of Concrete on Site

Ultrasonic pulse velocity (UPV) and rebound hammer (RH) tests are often used for assessing the quality of concrete and estimation of its compressive strength. Several parameters influence this property of concrete as the type and size of aggregates, cement content, the implementation of concrete, etc. To account for these factors, both of the two tests are combined and their measurements are calibrated with the results of mechanical tests on cylindrical specimens cast on site and on cores taken from the existing structure in work progress at the new-city Massinissa El-Khroub Constantine in Algeria. In this study;the two tests cited above have been used to determine the concrete quality by applying regression analysis models between compressive strength of in situ concrete on existing structure and the nondestructive tests values, the combined method is used, equations are derived using statistical analysis (simple and multiple regression) to estimate compressive strength of concrete on site and the reliability of the technique for prediction of the strength is discussed for this case study.

NUMERICAL SIMULATION ON COMPRESSIBLE TURBULENCE BY SPECTRAL METHOD

The numerical and physical issues of simulations on compressible turbulence are reviewed in the present paper. An outline of the global spectral methods and the progress of recent local spectral methods are illustrated. Several typical subjects in this field are studied, including homogeneous isotropic turbulence, autoignition in premixed turbulence, interaction between flames and turbulence, and shock wave in turbulence. The results of the numerical simulations are discussed, enabling us to discover and to understand the physical phenomena which have not been solved by experiments.

NUMERICAL STUDY OF TWO INTERFACE METHODS FOR COMPRESSIBLE MULTI-FLUID FLOWS

Two interface capturing methods are studied for multi fluid flows, governed by the stiffened gas equation of state. The mixture type interface capturing algorithm uses a simple volume fraction model Euler equations written in a quasi conservative form, which is solved by a standard high resolution piecewise parabolic method (PPM) with multi fluid Riemann solver. The level set interface capturing method uses a narrow band ghost fluid method (GFM) with no numerical smearing. Several examples are presented and compared for one and two dimensions, which show the feasibility of the two methods applied to various multi fluid problems.

基于有限相似方法的轴压加筋板极限强度相似缩比准则研究

在对船体结构进行相似缩比试验设计时,通常采用方向性量纲分析法。然而,传统的基于弹性理论的量纲分析法不能反映结构材料非线性过程,因而限制了其在船体结构缩比模型极限强度试验中的应用。本文基于有限相似方法,通过匹配物理空间与试验空间中的输运方程,获得结构几何尺寸、材料密度和时间的比例因子,推导得到加筋板结构缩比模型与原模型的非线性过程相似关系,分析材料参数对非线性相似过程的影响。通过开展不同缩比比例、不同材料参数的加筋板轴压极限强度数值计算,验证基于有限相似方法缩比准则的有效性。分析表明,基于有限相似方法的轴压加筋板极限强度缩比准则可以很好地体现材料的非线性特性,可以通过缩比模型结果对原模型的极限强度取得良好的预报效果。

干湿循环与加载先后顺序对砂泥岩混合料压缩特性的影响

为研究干湿循环与加载先后顺序对砂泥岩混合料压缩特性的影响,针对不同干湿循环次数、浸水时间和水温处置下的砂泥岩混合料,开展先干湿循环后加载、先加载后干湿循环的单向压缩试验。结果表明,两种试验方法所得砂泥岩混合料压缩量均随干湿循环次数增加、浸水时间增长、水温增高而增大;压缩量与干湿循环次数呈对数关系、与浸水时间呈幂函数关系、与水温呈线性关系,并推导出相应的压缩量计算公式;试验结果及理论分析均得出先干湿循环后加载的压缩量大于先加载后干湿循环的压缩量。

The discontinuous Petrov-Galerkin method for one-dimensional compressible Euler equations in the Lagrangian coordinate

In this paper, a Petrov-Galerkin scheme named the Runge-Kutta control volume （RKCV） discontinuous finite ele- ment method is constructed to solve the one-dimensional compressible Euler equations in the Lagrangian coordinate. Its advantages include preservation of the local conservation and a high resolution. Compared with the Runge-Kutta discon- tinuous Galerkin （RKDG） method, the RKCV method is easier to implement. Moreover, the advantages of the RKCV and the Lagrangian methods are combined in the new method. Several numerical examples are given to illustrate the accuracy and the reliability of the algorithm.