Conical Sonic-Supersonic Solutions for the 3-D Steady Full Euler Equations

This paper concerns the sonic-supersonic structures of the transonic crossflow generated by the steady supersonic flow past an infinite cone of arbitrary cross section.Under the conical assumption,the three-dimensional(3-D)steady Euler equations can be projected onto the unit sphere and the state of fluid can be characterized by the polar and azimuthal angles.Given a segment smooth curve as a conical-sonic line in the polar-azimuthal angle plane,we construct a classical conical-supersonic solution near the curve under some reasonable assumptions.To overcome the difficulty caused by the parabolic degeneracy,we apply the characteristic decomposition technique to transform the Euler equations into a new degenerate hyperbolic system in a partial hodograph plane.The singular terms are isolated from the highly nonlinear complicated system and then can be handled successfully.We establish a smooth local solution to the new system in a suitable weighted metric space and then express the solution in terms of the original variables.

3D elastic waveform modeling with an optimized equivalent staggered-grid finite-difference method

Equivalent staggered-grid(ESG) as a new family of schemes has been utilized in seismic modeling,imaging,and inversion.Traditionally,the Taylor series expansion is often applied to calculate finite-difference(FD) coefficients on spatial derivatives,but the simulation results suffer serious numerical dispersion on a large frequency zone.We develop an optimized equivalent staggered-grid(OESG) FD method that can simultaneously suppress temporal and spatial dispersion for solving the second-order system of the 3 D elastic wave equation.On the one hand,we consider the coupling relations between wave speeds and spatial derivatives in the elastic wave equation and give three sets of FD coefficients with respect to the P-wave,S-wave,and converted-wave(C-wave) terms.On the other hand,a novel plane wave solution for the 3 D elastic wave equation is derived from the matrix decomposition method to construct the time-space dispersion relations.FD coefficients of the OESG method can be acquired by solving the new dispersion equations based on the Newton iteration method.Finally,we construct a new objective function to analyze P-wave,S-wave,and C-wave dispersion concerning frequencies.The dispersion analyses show that the presented method produces less modeling errors than the traditional ESG method.The synthetic examples demonstrate the effectiveness and superiority of the presented method.

THE INVISCID AND NON-RESISTIVE LIMIT IN THE CAUCHY PROBLEM FOR 3-D NONHOMOGENEOUS INCOMPRESSIBLE MAGNETO-HYDRODYNAMICS

In this paper,the inviscid and non-resistive limit is justified for the local-in-time solutions to the equations of nonhomogeneous incompressible magneto-hydrodynamics （MHD）in R3.We prove that as the viscosity and resistivity go to zero,the solution of the Cauchy problem for the nonhomogeneous incompressible MHD system converges to the solution of the ideal MHD system.The convergence rate is also obtained simultaneously.

Propagation of traveling wave solutions for nonlinear evolution equation through the implementation of the extended modi ed direct algebraic method

In this work,di erent kinds of traveling wave solutions and uncategorized soliton wave solutions are obtained in a three dimensional(3-D)nonlinear evolution equations(NEEs)through the implementation of the modi ed extended direct algebraic method.Bright-singular and dark-singular combo solitons,Jacobi's elliptic functions,Weierstrass elliptic functions,constant wave solutions and so on are attained beside their existing conditions.Physical interpretation of the solutions to the 3-D modi ed KdV-Zakharov-Kuznetsov equation are also given.

On Completeness for a 3-D Linear Theory of Composite Laminate

In Ref [1] a model of 3-D composite laminate theory was described In the present paper,based on the basic equations about 3-D linear elasticity and classicalrariational principles,by the block matrix operation and the Lagrange's method of multipliers a series of basic equations and variational principles are obtained whichare more complere and more systematic than that in Ref [1]

Preliminary Report on the Theory of Elastic Circular Plate with no Kirchhoff-Love Assumptions

In this paper, the theory of elastic circular plate with no classical Kirchhoff-Love assumptions is established on the basis of a previous paper. In this theory, no classical Kirchhoff-Love assumptions are pre-assumed and the axial symmetrical analytic solution of fixed circular plate under the action of uniform pressure is obtained. Comparison of this solution and the known classical solution shows that this new solution agrees better than classical solution with the experiment measurement.This gives also the quantitative effect of the thickness on the deflection of circular plate with moderate thickness.

A SIMPLIFIED NUMERICAL MODEL OF 3-D GROUNDWATER AND SOLUTE TRANSPORT AT LARGE SCALE AREA

A simplified numerical model of groundwater and solute transport is developed. At large scale area there exists a big spatial scale difference between horizontal and vertical length scales. In the resultant model, the seepage region is particularly divided into several virtual layers along the z direction and vertical 1-D columns covering x-y 2-D area according to stratum properties. The numerical algorithm is replacing the full 3-D water and mass balance analysis as the 2-D Galerkin finite element method in x- and y-directions and 1-D finite differential approach in the z direction. The reasonable method of giving minimum thickness is successfully used to handle transient change of water table, drying cells and problem of rewetting. The solution of the simplified model is preconditioned conjugate gradient and ORTHOMIN method. The validity of the developed 3-D groundwater model is tested with the typical pumping and backwater scenarios. Results of water balance of the computed example reveal the model computation reliability. Based on a representative 3-D pollution case, the solute transport module is tested against computing results using the MT3DMS. The capability and high efficiency to predict non-stationary situations of free groundwater surface and solute plume in regional scale problem is quantitatively investigated. It is shown that the proposed model is computationally effective.

3-D Lightning Location Solution and Precision Analysis of Cloud Flash

Using the spatial coordinates of detection stations and the time of arrival of lightning wave, the observation equations can be expressed. For the large lightning detection network, the least square method is used to process the adjustment of observation data to find the most probable value of lightning position, and the result is assessed by the mean error and dilution of precision. Lightning location precision is affected by figure factor. The conclusion can be used in the design of location network, data processing, and data analysis.

复合材料层合板的热应力分析

基于Reissner-Mindlin型全局位移场模型和有限元预测-修正分析过程,数值计算和分析了复 合材料层合板受热载荷作用下的横向剪应力．计算结果与三维弹性解比较表明横向剪应力的计算精 度是满意的．

TEMPORAL AND SPATIAL DISCRETIZATION ON QUASI-3-D GROUNDWATER FINITE ELEMENT MODELLING TO AVOID SPURIOUS OSCILLATION

In this article, the fmite element solution of quasi-three-dimensional （quasi-3-D） groundwater flow was mathematically analyzed. The research shows that the spurious oscillation solution to the Finite Element Model （FEM） is the results choosing the small time step △t or the large element size L and using the non-diagonal storage matrix. The mechanism for this phenomenon is explained by the negative weighting factor of implicit part in the discretized equations. To avoid spurious oscillation solution, the criteria on the selection of △t and L for quasi-3-D groundwater flow simulations were identified. An application example of quasi-3-D groundwater flow simulation was presented to verify the criteria. The results indicate that temporal discretization scale has significant impact on the spurious oscillations in the finite-element solutions, and the spurious oscillations can be avoided in solving practical quasi-3-D groundwater flow problems if the criteria are satisfied.

Viscous Approximations and Decay Rate of Maximal Vorticity Function for 3-D Axisymmetric Euler Equations

In this paper, we are first concerned with viscous approximations for the three-dimensional axisymmetric incompressible Euler equations. It is proved that the viscous approximations, which are the solutions of the corresponding Navier-Stokes equations, converge strongly in provided that they have strong convergence in the region away from the symmetry axis. This result has been proved by the authors for the approximate solutions generated by smoothing the initial data, with no restriction of the sign of the initial data. Then we discuss the decay rate for maximal vorticity function, which is established for both approximate solutions generated by smoothing the initial data and viscous approximations respectively. One sufficient condition to guarantee the strong convergence in the region away from the symmetry axis is given, and a decay rate for maximal vorticity function in the region away from the symmetry axis is obtained for non-negative initial vorticity.

FORECAST OF WATER TEMPERATURE IN RESERVOIR BASED ON ANALYTICAL SOLUTION

The water temperature in reservoirs is difficult to be predicted by numerical simulations. In this article, a statistical model of forecasting the water temperature was proposed. In this model, the 3-D thermal conduction-diffusion equations were converted into a system consisting of 2-D equations with the Fourier expansion and some hypotheses. Then the statistical model of forecasting the water temperature was developed based on the analytical solution to the 2-D thermal equations. The~ simplified statistical model can elucidate the main physical mechanism of the temperature variation much more clearly than the numerical simulation with the Navier-Stokes equations. Finally, with the presented statistical model, the distribution of water temperature in the Shangyoujiang reservoir was determined.

Formulation of elastic multi-structures

Based on the creative and groundbreaking work done by Feng and Shi, some further work has been carried out comprehensively by the first author on the formulation of elastic multi-structures. The main contribution of this paper can be summarized as follows: The work of Feng and Shi has been extended to an elastic multi-structures with nonlinear structural element: shell in both linear and nonlinear case. Three general combinations of multi-structures have been formulated, that is, Case 1: linear elements of 3-D body, 1-D bar/beam, 2-D plates and 2-D shell; Case 2: nonlinear elements of 3-D body, 1-D bar/beam, 2-D plates and 2-D shell; and Case 3: the linear-nonlinear mix problem of 3-D body (nonlinear), 1-D bar/beam (linear), 2-D plates (linear) and 2-D shell (linear). From the investigation, it has proved that the higher dimensional element will have a strong influence on the lower one with the inner linkage boundaries, and also proved that solution uniqueness of elastic multi-structures is different from a single 3-D body.

考虑竖向荷载的桩基水平振动响应解析解

针对粘弹性土中桩土水平耦合振动问题,考虑土体竖向应力梯度变化以及竖向荷载二阶效应的影响,通过微分变换及分离变量法解耦土体波动方程,求得桩周土体位移和应力解析表达式,结合桩土耦合连续性条件,推导出桩身位移、内力解析表达式,讨论了竖向荷载及桩土模量比对桩身位移、内力的影响。研究结果表明,竖向荷载超过某一临界值时,会使桩基位移和内力发生重分布,桩身最大位移和剪力由桩顶向桩底转移;桩土模量比对桩身位移和内力具有明显影响,位移和内力随桩土模量比的变化而变化,具体变化趋势与深度有关。