THEORETICAL ANALYSES ON DISCRETE FORMULAE OF DIRECTIONAL DIFFERENTIALS IN THE FINITE POINT METHOD

For the five-point discrete formulae of directional derivatives in the finite point method,overcoming the challenge resulted from scattered point sets and making full use of the explicit expressions and accuracy of the formulae,this paper obtains a number of theoretical results:(1)a concise expression with definite meaning of the complicated directional difference coefficient matrix is presented,which characterizes the correlation between coefficients and the connection between coefficients and scattered geometric characteristics;(2)various expressions of the discriminant function for the solvability of numerical differentials along with the estimation of its lower bound are given,which are the bases for selecting neighboring points and making analysis;(3)the estimations of combinatorial elements and of each element in the directional difference coefficient matrix are put out,which exclude the existence of singularity.Finally,the theoretical analysis results are verified by numerical calculations.The results of this paper have strong regularity,which lay the foundation for further research on the finite point method for solving partial differential equations.

Lattice Boltzmann Method for Conduction and Radiation Heat Transfer in Composite Materials

In this work,the utilization of lattice Boltzmann method(LBM)in the simulation of coupled conduction and radiation heat transfer in composite materials is studied.The novel D3Q30-LBM and D3Q38-LBM models are proposed for the simulation of radiative transfer equation(RTE).The LBM-LBM model,coupled finite volume method(FVM)and LBM are compared with the coupled FVM and discrete ordinate method(DOM)for 2D and 3D simulations.The results show that the original D3Q26-LBM is insufficient for the simulation of radiation,and both the D3Q30-LBM and D3Q38-LBM are close to the DOM for the RTE.The LBM can have large errors in the simulation of heat conduction when the relaxation time is large.Thus,its application in the composite materials is limited when the ratio between thermal conductivities of different components is large.The models with LBM for RTE can be more efficient than the FVM-DOM for the simulation of conduction-radiation heat transfer in composite materials.The FVM-D3Q30-LBM model is suggested because of its accuracy and efficiency.

The research of space-time coupled spectral element method for acoustic wave equations

A space-time coupled spectral element method based on Chebyshev polynomials is presented for solving time-dependent wave equations.Acoustic propagation problems in1＋1,2＋1,3＋1 dimensions with the Dirichlet boundary conditions are simulated via space-time coupled spectral element method using quadrilateral,hexahedral and tesseractic elements respectively.Space-time coupled spectral element method can obtain high-order precision over time.With the same total number of nodes,higher numerical precision is obtained if the higher-order Chebyshev polynomials in space directions and lower-order Chebyshev polynomials in time direction are adopted.Numerical illustrations have indicated that the space-time algorithm provides higher precision than the semi-discretization.When space-time coupled spectral element method is used,time subdomain-by-subdomain approach is more economical than time domain approach.

Macro- and micromechanical evaluation of cyclic simple shear test by discrete element method

Direct simple shear tests are considered to be simple laboratory tests that are capable of imposing a cyclic loading that is analogous to that induced by earthquakes. A realistic evaluation of the test results demands a profound micromechanical investigation of specimens. Three-dimensional discrete element method models of a stacked-ring simple shear test were constructed, in which monotonic and cyclic loadings were applied under constant-volume conditions, and good agreement between the monotonic and cyclic macromechanical behaviors was noted. Micromechanical properties of specimens that were subjected to a cyclic loading are discussed in terms of lateral and intermediate principal stress development, fabric anisotropy, and principal stress rotation. The stress and strain states inside the specimen were investigated and it was shown that despite the uniform stress distribution inside the specimen, the volumetric strain distributes non-uniformly during loading and the non-uniformity grows with cycling, which leads to localized zones of dilative and contractive behavior.