A 1D time-domain method for in-plane wave motions in a layered half-space

A 1D finite element method in time domain is developed in this paper and applied to calculate in-plane wave motions of free field exited by SV or P wave oblique incidence in an elastic layered half-space. First, the layered half-space is discretized on the basis of the propagation characteristic of elastic wave according to the Snell law. Then, the finite element method with lumped mass and the central difference method are incorporated to establish 2D wave motion equations, which can be transformed into 1D equations by discretization principle and explicit finite element method. By solving the 1D equations, the displacements of nodes in any vertical line can be obtained, and the wave motions in layered half-space are finally determined based on the characteristic of traveling wave. Both the theoretical analysis and the numerical results demonstrate that the proposed method has high accuracy and good stability.

Second-Order Wave Diffraction Around 3-D Bodies by A Time-Domain Method

A time-domain method is applied to simulate nonlinear wave diffraction around a surface piercing 3-D arbitrary body. The method involves the application of Taylor series expansions and the use of perturbation procedure to establish the corresponding boundary value problems with respect to a time-independent fluid domain. A boundary element method based on B-spline expansion is used to calculate the wave field at each time step, and the free surface boundary condition is satisfied to the second order of wave steepness by a numerical integration in time. An artificial damping layer is adopted on the free surface for the removal of wave reflection from the outer boundary. As an illustration, the method is used to compute the second-order wave forces and run-up on a surface-piercing circular cylinder. The present method is found to be accurate, computationally efficient, and numerically stable.

Investigation of three-pulse photon echo in thick crystal using finite-difference time-domain method

This paper investigates the phenomenon of three-pulse photon echo in thick rare-earth ions doped crystal whose thickness is far larger than 0.002 cm which is adopted in previous works.The influence of thickness on the three-pulse photon echo＇s amplitude and efficiency is analyzed with the Maxwell-Bloch equations solved by finite-difference timedomain method.We demonstrate that the amplitude of three-pulse echo will increase with the increasing of thickness and the optimum thickness to generate three-pulse photon echo is 0.3 cm for Tm^（3＋）：YAG when the attenuation of the input pulse is taken into account.Meanwhile,we find the expression 0.09 exp（α＇L）,which is previously employed to describe the relationship between echo＇s efficiency and thickness,should be modified as 1.3 · 0.09 exp（2.4 ·α＇L） with the propagation of echo considered.

Optical simulation of in-plane-switching blue phase liquid crystal display using the finite-difference time-domain method

The finite-difference time-domain method is used to simulate the optical characteristics of an in-plane switching blue phase liquid crystal display.Compared with the matrix optic methods and the refractive method,the finite-difference timedomain method,which is used to directly solve Maxwell＇s equations,can consider the lateral variation of the refractive index and obtain an accurate convergence effect.The simulation results show that e-rays and o-rays bend in different directions when the in-plane switching blue phase liquid crystal display is driven by the operating voltage.The finitedifference time-domain method should be used when the distribution of the liquid crystal in the liquid crystal display has a large lateral change.

Stochastic transient analysis of thermal stresses in solids by explicit time-domain method

Stochastic heat conduction and thermal stress analysis of structures has received considerable attention in recent years.The propagation of uncertain thermal environments will lead to stochastic variations in temperature fields and thermal stresses.Therefore,it is reasonable to consider the variability of thermal environments while conducting thermal analysis.However,for ambient thermal excitations,only stationary random processes have been investigated thus far.In this study,the highly efficient explicit time-domain method(ETDM)is proposed for the analysis of non-stationary stochastic transient heat conduction and thermal stress problems.The explicit time-domain expressions of thermal responses are first constructed for a thermoelastic body.Then the statistical moments of thermal displacements and stresses can be directly obtained based on the explicit expressions of thermal responses.A numerical example involving non-stationary stochastic internal heat generation rate is investigated.The accuracy and efficiency of the proposed method are validated by comparison with the Monte-Carlo simulation.

Uniform stable conformal convolutional perfectly matched layer for enlarged cell technique conformal finite-difference time-domain method

Based on conformal construction of physical model in a three-dimensional Cartesian grid,an integral-based conformal convolutional perfectly matched layer（CPML） is given for solving the truncation problem of the open port when the enlarged cell technique conformal finite-difference time-domain（ECT-CFDTD） method is used to simulate the wave propagation inside a perfect electric conductor（PEC） waveguide.The algorithm has the same numerical stability as the ECT-CFDTD method.For the long-time propagation problems of an evanescent wave in a waveguide,several numerical simulations are performed to analyze the reflection error by sweeping the constitutive parameters of the integral-based conformal CPML.Our numerical results show that the integral-based conformal CPML can be used to efficiently truncate the open port of the waveguide.

An efficient locally one-dimensional finite-difference time-domain method based on the conformal scheme

An efficient conformal locally one-dimensional finite-difference time-domain（LOD-CFDTD） method is presented for solving two-dimensional（2D） electromagnetic（EM） scattering problems. The formulation for the 2D transverse-electric（TE） case is presented and its stability property and numerical dispersion relationship are theoretically investigated. It is shown that the introduction of irregular grids will not damage the numerical stability. Instead of the staircasing approximation, the conformal scheme is only employed to model the curve boundaries, whereas the standard Yee grids are used for the remaining regions. As the irregular grids account for a very small percentage of the total space grids, the conformal scheme has little effect on the numerical dispersion. Moreover, the proposed method, which requires fewer arithmetic operations than the alternating-direction-implicit（ADI） CFDTD method, leads to a further reduction of the CPU time. With the total-field/scattered-field（TF/SF） boundary and the perfectly matched layer（PML）, the radar cross section（RCS） of two2 D structures is calculated. The numerical examples verify the accuracy and efficiency of the proposed method.

Conformal Multi-resolution Time-Domain Method for Scattering Curved Dielectric Objects

A conformal multi-resolution time-domain( CMRTD) method is presented for modeling curved objects. The effective dielectric constant and area weighting are used to derive the update equations of CMRTD. The backward scattering bistatic radar cross sections( RCS) of the dielectric cylinder and ellipsoid are used to validate the proposed method. The results show that the proposed conformal method is more accurate to deal with the complex curved objects in electromagnetic simulations.

IMPROVED LOCALLY CONFORMAL FINITE-DIFFERENCE TIME-DOMAIN METHOD FOR EDGE INCLINED SLOTS IN A FINITE WALL THICKNESS WAVEGUIDE

An Improved Locally Conformal Finite-Difference Time-Domain (ILC-FDTD) method is presented in this paper, which is used to analyze the edge inclined slots penetrating adjacent broadwalls of a finite wall thickness waveguide. ILC-FDTD not only removes the instability of the original locally conformal FDTD algorithm, but also improves the computational accuracy by locally modifying magnetic field update equations and the virtual iterative electric fields according to the complexity of the slot fringe fields. The mutual coupling between two edge inclined slots can also be analyzed by ILC-FDTD effectively.

A leap-frog discontinuous Galerkin time-domain method of analyzing electromagnetic scattering problems

Several major challenges need to be faced for efficient transient multiscale electromagnetic simulations, such as flex- ible and robust geometric modeling schemes, efficient and stable time-stepping algorithms, etc. Fortunately, because of the versatile choices of spatial discretization and temporal integration, a discontinuous Galerkin time-domain （DGTD） method can be a very promising method of solving transient multiscale electromagnetic problems. In this paper, we present the application of a leap-frog DGTD method to the analyzing of the multiscale electromagnetic scattering problems. The uniaxial perfect matching layer （UPML） truncation of the computational domain is discussed and formulated in the leap-frog DGTD context. Numerical validations are performed in the challenging test cases demonstrating the accuracy and effectiveness of the method in solving transient multiscale electromagnetic problems compared with those of other numerical methods.

Runge-Kutta Multi-resolution Time-Domain Method for Modeling 3D Dielectric Curved Objects

A conformal Runge-Kutta multi-resolution time-domain(C-RKMRTD)method is present and applied to model and analyze curved objects.Compared with the non-conformal method,the proposed method is more accurate.The scattering analyses of the cylinder and ellipsoid are presented to validate the proposed method.The numerical results demonstrate that the proposed scheme perform better than the MRTD method and other higher order methods with a higher accuracy.

USE OF FINITE-DIFFERENCE TIME-DOMAIN METHOD FOR CALCULATING EM ABSORPTION IN LOSSY DIELECTRIC SCATTERER

The problem for calculating EM energy absorption by lossy dielectric scatterer ir-radiated by plane wave are discussed.The factors affecting the accuracy of computation arediscussed.The calculated results of EM energy absorption and its distribution in homogeneousand layered homogenous lossy dielectric spheres are presented,and a comparison of these resultswith analytical solution is given.The calculation is carried out for dielectric cylinder on conduct-ing ground as well,and the results are compared with the image theory.All the computationsshew that the finite-difference time-domain method can give satisfactory results.

A comparison study on structure-function relationship of polysaccharides obtained from sea buckthorn berries using different methods:antioxidant and bile acid-binding capacity

In this study,the structural characters,antioxidant activities and bile acid-binding ability of sea buckthorn polysaccharides(HRPs)obtained by the commonly used hot water(HRP-W),pressurized hot water(HRP-H),ultrasonic(HRP-U),acid(HRP-C)and alkali(HRP-A)assisted extraction methods were investigated.The results demonstrated that extraction methods had significant effects on extraction yield,monosaccharide composition,molecular weight,particle size,triple-helical structure,and surface morphology of HRPs except for the major linkage bands.Thermogravimetric analysis showed that HRP-U with filamentous reticular microstructure exhibited better thermal stability.The HRP-A with the lowest molecular weight and highest arabinose content possessed the best antioxidant activities.Moreover,the rheological analysis indicated that HRPs with higher galacturonic acid content and molecular weight showed higher viscosity and stronger crosslinking network(HRP-C,HRP-W and HRP-U),which exhibited stronger bile acid binding capacity.The present findings provide scientific evidence in the preparation technology of sea buckthorn polysaccharides with good antioxidant and bile acid binding capacity which are related to the structure affected by the extraction methods.

Drilling-based measuring method for the c-φ parameter of rock and its field application

The technology of drilling tests makes it possible to obtain the strength parameter of rock accurately in situ. In this paper, a new rock cutting analysis model that considers the influence of the rock crushing zone(RCZ) is built. The formula for an ultimate cutting force is established based on the limit equilibrium principle. The relationship between digital drilling parameters(DDP) and the c-φ parameter(DDP-cφ formula, where c refers to the cohesion and φ refers to the internal friction angle) is derived, and the response of drilling parameters and cutting ratio to the strength parameters is analyzed. The drillingbased measuring method for the c-φ parameter of rock is constructed. The laboratory verification test is then completed, and the difference in results between the drilling test and the compression test is less than 6%. On this basis, in-situ rock drilling tests in a traffic tunnel and a coal mine roadway are carried out, and the strength parameters of the surrounding rock are effectively tested. The average difference ratio of the results is less than 11%, which verifies the effectiveness of the proposed method for obtaining the strength parameters based on digital drilling. This study provides methodological support for field testing of rock strength parameters.

Time-Domain Analysis of Body Freedom Flutter Based on 6DOF Equation

The reduced weight and improved efficiency of modern aeronautical structures result in a decreasing separation of frequency ranges of rigid and elastic modes.Particularly,a high-aspect-ratio flexible flying wing is prone to body freedomflutter(BFF),which is a result of coupling of the rigid body short-periodmodewith 1st wing bendingmode.Accurate prediction of the BFF characteristics is helpful to reflect the attitude changes of the vehicle intuitively and design the active flutter suppression control law.Instead of using the rigid body mode,this work simulates the rigid bodymotion of the model by using the six-degree-of-freedom(6DOF)equation.A dynamicmesh generation strategy particularly suitable for BFF simulation of free flying aircraft is developed.An accurate Computational Fluid Dynamics/Computational Structural Dynamics/six-degree-of-freedom equation(CFD/CSD/6DOF)-based BFF prediction method is proposed.Firstly,the time-domain CFD/CSD method is used to calculate the static equilibrium state of the model.Based on this state,the CFD/CSD/6DOF equation is solved in time domain to evaluate the structural response of themodel.Then combinedwith the variable stiffnessmethod,the critical flutter point of the model is obtained.This method is applied to the BFF calculation of a flyingwing model.The calculation results of the BFF characteristics of the model agree well with those fromthe modalmethod andNastran software.Finally,the method is used to analyze the influence factors of BFF.The analysis results show that the flutter speed can be improved by either releasing plunge constraint or moving the center ofmass forward or increasing the pitch inertia.

Dynamic Coupling Analysis of Semisubmersible Platform Float-over Method for Docking Case

In this paper,the multi-body coupled dynamic characteristics of a semisubmersible platform and an HYSY 229 barge were investigated.First,coupled hydrodynamic analysis of the HYSY 229 barge and the semisubmersible platform was performed.Relevant hydrodynamic parameters were obtained using the retardation function method of three-dimensional frequency-domain potential flow theory.The results of the hydrodynamic analysis were highly consistent with the test findings,verifying the accuracy of the multifloating hydrodynamic coupling analysis,and key hydrodynamic parameters were solved for different water depths and the coupling effect.According to the obtained results,the hydrodynamic influence was the largest in shallow waters when the coupling effect was considered.Furthermore,the coupled motion equation combined with viscous damping,fender system,and mooring system was established,and the hydrodynamics,floating body motion,and dynamic response of the fender system were analyzed.Motion analysis revealed good agreement among the surge,sway,and yaw motions of the two floating bodies.However,when the wave period reached 10 s,the motion of the two floating bodies showed severe shock,and a relative motion was also observed.Therefore,excessive constraints should be added between the two floating bodies during construction to ensure construction safety.The numerical analysis and model test results of the semisubmersible platform and HYSY 229 barge at a water depth of 42 m and sea conditions of 0°,45°,and 90° were in good agreement,and the error was less than 5%.The maximum movement of the HYSY 229 barge reached 2.61 m in the sway direction,whereas that of the semisubmersible platform was 2.11 m.During construction,excessive constraints should be added between the two floating bodies to limit their relative movement and ensure construction safety.

Volumetric lattice Boltzmann method for pore-scale mass diffusionadvection process in geopolymer porous structures

Porous materials present significant advantages for absorbing radioactive isotopes in nuclear waste streams.To improve absorption efficiency in nuclear waste treatment,a thorough understanding of the diffusion-advection process within porous structures is essential for material design.In this study,we present advancements in the volumetric lattice Boltzmann method(VLBM)for modeling and simulating pore-scale diffusion-advection of radioactive isotopes within geopolymer porous structures.These structures are created using the phase field method(PFM)to precisely control pore architectures.In our VLBM approach,we introduce a concentration field of an isotope seamlessly coupled with the velocity field and solve it by the time evolution of its particle population function.To address the computational intensity inherent in the coupled lattice Boltzmann equations for velocity and concentration fields,we implement graphics processing unit(GPU)parallelization.Validation of the developed model involves examining the flow and diffusion fields in porous structures.Remarkably,good agreement is observed for both the velocity field from VLBM and multiphysics object-oriented simulation environment(MOOSE),and the concentration field from VLBM and the finite difference method(FDM).Furthermore,we investigate the effects of background flow,species diffusivity,and porosity on the diffusion-advection behavior by varying the background flow velocity,diffusion coefficient,and pore volume fraction,respectively.Notably,all three parameters exert an influence on the diffusion-advection process.Increased background flow and diffusivity markedly accelerate the process due to increased advection intensity and enhanced diffusion capability,respectively.Conversely,increasing the porosity has a less significant effect,causing a slight slowdown of the diffusion-advection process due to the expanded pore volume.This comprehensive parametric study provides valuable insights into the kinetics of isotope uptake in porous structures,facilitating the development of porous materials for nuclear waste treatment applications.

Material point method simulation of hydro-mechanical behaviour in twophase porous geomaterials: A state-of-the-art review

The material point method(MPM)has been gaining increasing popularity as an appropriate approach to the solution of coupled hydro-mechanical problems involving large deformation.In this paper,we survey the current state-of-the-art in the MPM simulation of hydro-mechanical behaviour in two-phase porous geomaterials.The review covers the recent advances and developments in the MPM and their extensions to capture the coupled hydro-mechanical problems involving large deformations.The focus of this review is aiming at providing a clear picture of what has or has not been developed or implemented for simulating two-phase coupled large deformation problems,which will provide some direct reference for both practitioners and researchers.

Sparse Modal Decomposition Method Addressing Underdetermined Vortex-Induced Vibration Reconstruction Problem for Marine Risers

When investigating the vortex-induced vibration(VIV)of marine risers,extrapolating the dynamic response on the entire length based on limited sensor measurements is a crucial step in both laboratory experiments and fatigue monitoring of real risers.The problem is conventionally solved using the modal decomposition method,based on the principle that the response can be approximated by a weighted sum of limited vibration modes.However,the method is not valid when the problem is underdetermined,i.e.,the number of unknown mode weights is more than the number of known measurements.This study proposed a sparse modal decomposition method based on the compressed sensing theory and the Compressive Sampling Matching Pursuit(Co Sa MP)algorithm,exploiting the sparsity of VIV in the modal space.In the validation study based on high-order VIV experiment data,the proposed method successfully reconstructed the response using only seven acceleration measurements when the conventional methods failed.A primary advantage of the proposed method is that it offers a completely data-driven approach for the underdetermined VIV reconstruction problem,which is more favorable than existing model-dependent solutions for many practical applications such as riser structural health monitoring.