A Hybrid Dung Beetle Optimization Algorithm with Simulated Annealing for the Numerical Modeling of Asymmetric Wave Equations

In the generalized continuum mechanics(GCM)theory framework,asymmetric wave equations encompass the characteristic scale parameters of the medium,accounting for microstructure interactions.This study integrates two theoretical branches of the GCM,the modified couple stress theory(M-CST)and the one-parameter second-strain-gradient theory,to form a novel asymmetric wave equation in a unified framework.Numerical modeling of the asymmetric wave equation in a unified framework accurately describes subsurface structures with vital implications for subsequent seismic wave inversion and imaging endeavors.However,employing finite-difference(FD)methods for numerical modeling may introduce numerical dispersion,adversely affecting the accuracy of numerical modeling.The design of an optimal FD operator is crucial for enhancing the accuracy of numerical modeling and emphasizing the scale effects.Therefore,this study devises a hybrid scheme called the dung beetle optimization(DBO)algorithm with a simulated annealing(SA)algorithm,denoted as the SA-based hybrid DBO(SDBO)algorithm.An FD operator optimization method under the SDBO algorithm was developed and applied to the numerical modeling of asymmetric wave equations in a unified framework.Integrating the DBO and SA algorithms mitigates the risk of convergence to a local extreme.The numerical dispersion outcomes underscore that the proposed SDBO algorithm yields FD operators with precision errors constrained to 0.5‱while encompassing a broader spectrum coverage.This result confirms the efficacy of the SDBO algorithm.Ultimately,the numerical modeling results demonstrate that the new FD method based on the SDBO algorithm effectively suppresses numerical dispersion and enhances the accuracy of elastic wave numerical modeling,thereby accentuating scale effects.This result is significant for extracting wavefield perturbations induced by complex microstructures in the medium and the analysis of scale effects.

涡轮叶片气热耦合数值模拟方法

研究了气热耦合计算模型,建立了采用有限差分方法进行涡轮气热耦合计算的数值仿真平台,并利用该平台采用考虑转捩和不考虑转捩两类湍流模型对具有径向冷却通道的MARK II型叶片进行数值模拟,同时将结果与实验值进行比较,对比表明:考虑转捩的湍流模型能够准确的反映出边界层内的流态和热传导情况,因此壁面处温度和换热系数更接近于实验值,与实验值吻合较好。

Fracture identification based on remote detection acoustic reflection logging

Fracture identification is important for the evaluation of carbonate reservoirs. However, conventional logging equipment has small depth of investigation and cannot detect rock fractures more than three meters away from the borehole. Remote acoustic logging uses phase-controlled array-transmitting and long sound probes that increase the depth of investigation. The interpretation of logging data with respect to fractures is typically guided by practical experience rather than theory and is often ambiguous. We use remote acoustic reflection logging data and high-order finite-difference approximations in the forward modeling and prestack reverse-time migration to image fractures. First, we perform forward modeling of the fracture responses as a function of the fracture-borehole wall distance, aperture, and dip angle. Second, we extract the energy intensity within the imaging area to determine whether the fracture can be identified as the formation velocity is varied. Finally, we evaluate the effect of the fracture-borehole distance, fracture aperture, and dip angle on fracture identification.

Numerical simulation of intermediate phase growth in Ti/Al alternate foils

To investigate the diffusion reaction between Ti/Al solid diffusion couple, Ti/Al alternate foils formed by hot pressing were annealed at 525, 550, 575 and 600 °C for time ranging from 1 to 40 h. The experimental results show that TiAl3 was the only observed phase at Ti/Al interface. The interface thermodynamics favored the preferential formation of TiAl3 in Ti/Al couple. The growth of TiAl3 layer occurred mainly towards Al foil side and exhibited a parabolic law. Using the interdiffusion coefficients calculated based on the contribution of grain boundary diffusion, the growth of TiAl3 was simulated numerically with the finite difference method, and the simulated results were in good agreement with the experimental ones.

Three-dimensional forward modeling of DC resistivity using the aggregation-based algebraic multigrid method

To speed up three-dimensional （3D） DC resistivity modeling, we present a new multigrid method, the aggregation-based algebraic multigrid method （AGMG）. We first discretize the differential equation of the secondary potential field with mixed boundary conditions by using a seven-point finite-difference method to obtain a large sparse system of linear equations. Then, we introduce the theory behind the pairwise aggregation algorithms for AGMG and use the conjugate-gradient method with the V-cycle AGMG preconditioner （AGMG-CG） to solve the linear equations. We use typical geoelectrical models to test the proposed AGMG-CG method and compare the results with analytical solutions and the 3DDCXH algorithm for 3D DC modeling （3DDCXH）. In addition, we apply the AGMG-CG method to different grid sizes and geoelectrical models and compare it to different iterative methods, such as ILU-BICGSTAB, ILU-GCR, and SSOR-CG. The AGMG-CG method yields nearly linearly decreasing errors, whereas the number of iterations increases slowly with increasing grid size. The AGMG-CG method is precise and converges fast, and thus can improve the computational efficiency in forward modeling of three-dimensional DC resistivity.

Three-dimensional acoustic wave equation modeling based on the optimal finite-difference scheme

Generally, FD coefficients can be obtained by using Taylor series expansion （TE） or optimization methods to minimize the dispersion error. However, the TE-based FD method only achieves high modeling precision over a limited range of wavenumbers, and produces large numerical dispersion beyond this range. The optimal FD scheme based on least squares （LS） can guarantee high precision over a larger range of wavenumbers and obtain the best optimization solution at small computational cost. We extend the LS-based optimal FD scheme from two-dimensional （2D） forward modeling to three-dimensional （3D） and develop a 3D acoustic optimal FD method with high efficiency, wide range of high accuracy and adaptability to parallel computing. Dispersion analysis and forward modeling demonstrate that the developed FD method suppresses numerical dispersion. Finally, we use the developed FD method to source wavefield extrapolation and receiver wavefield extrapolation in 3D RTM. To decrease the computation time and storage requirements, the 3D RTM is implemented by combining the efficient boundary storage with checkpointing strategies on GPU. 3D RTM imaging results suggest that the 3D optimal FD method has higher precision than conventional methods.

Modeling seismic wave propagation within complex structures

Seismic modeling is a useful tool for studying the propagation of seismic waves within complex structures. However, traditional methods of seismic simulation cannot meet the needs for studying seismic wavefields in the complex geological structures found in seismic exploration of the mountainous area in Northwestern China. More powerful techniques of seismic modeling are demanded for this purpose. In this paper, two methods of finite element-finite difference method （FE-FDM） and arbitrary difference precise integration （ADPI） for seismic forward modeling have been developed and implemented to understand the behavior of seismic waves in complex geological subsurface structures and reservoirs. Two case studies show that the FE-FDM and ADPI techniques are well suited to modeling seismic wave propagation in complex geology.

Numerical analysis of multicomponent responses of surface-hole transient electromagnetic method

We calculate the multicomponent responses of surface-hole transient electromagnetic method. The methods and models are unsuitable as geoelectric models of conductive surrounding rocks because they are based on regular local targets. We also propose a calculation and analysis scheme based on numerical simulations of the subsurface transient electromagnetic fields. In the modeling of the electromagnetic fields, the forward modeling simulations are performed by using the finite-difference time-domain method and the discrete image method, which combines the Gaver–Stehfest inverse Laplace transform with the Prony method to solve the initial electromagnetic fields. The precision in the iterative computations is ensured by using the transmission boundary conditions. For the response analysis, we customize geoelectric models consisting of near-borehole targets and conductive wall rocks and implement forward modeling simulations. The observed electric fields are converted into induced electromotive force responses using multicomponent observation devices. By comparing the transient electric fields and multicomponent responses under different conditions, we suggest that the multicomponent-induced electromotive force responses are related to the horizontal and vertical gradient variations of the transient electric field at different times. The characteristics of the response are determined by the varying the subsurface transient electromagnetic fields, i.e., diffusion, attenuation and distortion, under different conditions as well as the electromagnetic fields at the observation positions. The calculation and analysis scheme of the response consider the surrounding rocks and the anomalous field of the local targets. It therefore can account for the geological data better than conventional transient field response analysis of local targets.

Multicomponent seismic forward modeling of gas hydrates beneath the seafloor

We investigated the effect of microscopic distribution modes of hydrates in porous sediments, and the saturation of hydrates and free gas on the elastic properties of saturated sediments. We simulated the propagation of seismic waves in gas hydrate-bearing sediments beneath the seafloor, and obtained the common receiver gathers of compressional waves（P-waves） and shear waves（S-waves）. The numerical results suggest that the interface between sediments containing gas hydrates and free gas produces a large-amplitude bottomsimulating reflector. The analysis of multicomponent common receiver data suggests that ocean-bottom seismometers receive the converted waves of upgoing P- and S-waves, which increases the complexity of the wavefield record.

Stability of finite difference numerical simulations of acoustic logging-while-drilling with different perfectly matched layer schemes

In acoustic logging-while-drilling （ALWD） finite difference in time domain （FDTD） simulations, large drill collar occupies, most of the fluid-filled borehole and divides the borehole fluid into two thin fluid columns （radius -27 mm）. Fine grids and large computational models are required to model the thin fluid region between the tool and the formation. As a result, small time step and more iterations are needed, which increases the cumulative numerical error. Furthermore, due to high impedance contrast between the drill collar and fluid in the borehole （the difference is 〉30 times）, the stability and efficiency of the perfectly matched layer （PML） scheme is critical to simulate complicated wave modes accurately. In this paper, we compared four different PML implementations in a staggered grid finite difference in time domain （FDTD） in the ALWD simulation, including field-splitting PML （SPML）, multiaxial PML（M- PML）, non-splitting PML （NPML）, and complex frequency-shifted PML （CFS-PML）. The comparison indicated that NPML and CFS-PML can absorb the guided wave reflection from the computational boundaries more efficiently than SPML and M-PML. For large simulation time, SPML, M-PML, and NPML are numerically unstable. However, the stability of M-PML can be improved further to some extent. Based on the analysis, we proposed that the CFS-PML method is used in FDTD to eliminate the numerical instability and to improve the efficiency of absorption in the PML layers for LWD modeling. The optimal values of CFS-PML parameters in the LWD simulation were investigated based on thousands of 3D simulations. For typical LWD cases, the best maximum value of the quadratic damping profile was obtained using one do. The optimal parameter space for the maximum value of the linear frequency-shifted factor （a0） and the scaling factor （β0） depended on the thickness of the PML layer. For typical formations, if the PML thickness is 10 grid points, the global error can be reduced to 〈1% using the optimal PML parameters, and the error will decrease as the PML thickness increases.

Application of the double absorbing boundary condition in seismic modeling

We apply the newly proposed double absorbing boundary condition（DABC）（Hagstrom et al., 2014） to solve the boundary reflection problem in seismic finite-difference（FD） modeling. In the DABC scheme, the local high-order absorbing boundary condition is used on two parallel artificial boundaries, and thus double absorption is achieved. Using the general 2D acoustic wave propagation equations as an example, we use the DABC in seismic FD modeling, and discuss the derivation and implementation steps in detail. Compared with the perfectly matched layer（PML）, the complexity decreases, and the stability and fl exibility improve. A homogeneous model and the SEG salt model are selected for numerical experiments. The results show that absorption using the DABC is considerably improved relative to the Clayton–Engquist boundary condition and nearly the same as that in the PML.

Seismic wavefield modeling in media with fluid-filled fractures and surface topography

We present a finite difference （FD） method for the simulation of seismic wave fields in fractured medium with an irregular （non-fiat） free surface which is beneficial for interpreting exploration data acquired in mountainous regions. Fractures are introduced through the Coates-Schoenberg approach into the FD scheme which leads to local anisotropic properties of the media where fractures are embedded. To implement surface topography, we take advantage of the boundary-conforming grid and map a rectangular grid onto a curved one. We use a stable and explicit second-order accurate finite difference scheme to discretize the elastic wave equations （in a curvilinear coordinate system） in a 2D heterogeneous transversely isotropic medium with a horizontal axis of symmetry （HTI）. Efficiency tests performed by different numerical experiments clearly illustrate the influence of an irregular free surface on seismic wave propagation in fractured media which may be significant to mountain seismic exploration. The tests also illustrate that the scattered waves induced by the tips of the fracture are re-scattered by the features of the free surface topography. The scattered waves provoked by the topography are re-scattered by the fractures, especially Rayleigh wave scattering whose amplitudes are much larger than others and making it very difficult to identify effective information from the fractures.

Application of Padé Approximation in Simulating Photonic Crystals

To save finite-difference time-domain（FDTD） computing time, several methods are proposed to convert the time domain FDTD output into frequency domain. The Pad6 approximation with Baker＇s algorithm and the program are introduced to simulate photonic crystal structures. For a simple pole system with frequency 160THz and quality factor of 5000, the intensity spectrum obtained by the Padé approximation from a 2^8-item sequence output is more exact than that obtained by fast Fourier transformation from a 2^20-item sequence output. The mode frequencies and quality factors are calculated at different wave vectors for the photonic crystal slab from a much shorter FDTD output than that required by the FFT method, and then the band diagrams are obatined. In addition, mode frequencies and Q-factors are calculated for photonic crystal microcavity.

Finite-difference numerical modeling with even-order accuracy in two-phase anisotropic media

To improve the accuracy of the conventional finite-difference method, finitedifference numerical modeling methods of any even-order accuracy are recommended. We introduce any even-order accuracy difference schemes of any-order derivatives derived from Taylor series expansion. Then, a finite-difference numerical modeling method with any evenorder accuracy is utilized to simulate seismic wave propagation in two-phase anisotropic media. Results indicate that modeling accuracy improves with the increase of difference accuracy order number. It is essential to find the optimal order number, grid size, and time step to balance modeling precision and computational complexity. Four kinds of waves, static mode in the source point, SV wave cusps, reflection and transmission waves are observed in two-phase anisotropic media through modeling.

Improved absorbing boundary condition based on linear interpolation for ADI-FDTD method

With the linear interpolation method, an improved absorbing boundary condition（ABC）is introduced and derived, which is suitable for the alternating-direction-implicit finite- difference time-domain （ADI-FDTD） method. The reflection of the ABC caused by both the truncated error and the phase velocity error is analyzed. Based on the phase velocity estimation and the nonuniform cell, two methods are studied and then adopted to improve the performance of the ABC. A calculation case of a rectangular waveguide which is a typical dispersive transmission line is carried out using the ADI-FDTD method with the improved ABC for evaluation. According to the calculated case, the comparison is given between the reflection coefficients of the ABC with and without the velocity estimation and also the comparison between the reflection coefficients of the ABC with and without the nonuniform processing. The reflection variation of the ABC under different time steps is also analyzed and the acceptable worsening will not obscure the improvement on the absorption. Numerical results obviously show that efficient improvement on the absorbing performance of the ABC is achieved based on these methods for the ADI-FDTD.

New numerical algorithm of gas-liquid two-phase flow considering characteristics of liquid metal during mold filling

A new program is developed for gas-liquid two-phase mold filling simulation in casting. The gas fluid, the superheated liquid metal and the liquid metal containing solid grains are assumed to be governed by Navier-Stokes equations and solved through Projection method. The Level set method is used to track the gas-liquid interface boundary. In order to demonstrate the correctness of this new program for simulation of gas-liquid two-phase mold filling in casting, a benchmark filling experiment is simulated （this benchmark test is designed by XU and the filling process is recorded by a 16-mm film camera）. The simulated results agree very well with the experimental results, showing that this new program can be used to properly predicate the gas-liquid two-phase mold filling simulation in casting.

New algorithm for solving 3D incompressible viscous equations based on projection method

A new algorithm based on the projection method with the implicit finite difference technique was established to calculate the velocity fields and pressure.The calculation region can be divided into different regions according to Reynolds number.In the far-wall region,the thermal melt flow was calculated as Newtonian flow.In the near-wall region,the thermal melt flow was calculated as non-Newtonian flow.It was proved that the new algorithm based on the projection method with the implicit technique was correct through nonparametric statistics method and experiment.The simulation results show that the new algorithm based on the projection method with the implicit technique calculates more quickly than the solution algorithm-volume of fluid method using the explicit difference method.

Numerical prediction of the long- term soil temperature variations around shallowsections of cross-river road tunnels

Considering the coupled heat transfer effect induced by parallel cross-river road tunnels, the long-term soil temperature variations of shallow sections of cross-river tunnels under the river beach are predicted using the finite difference method for numerical simulation. The boundary conditions and the initial values are determined by in situ observations and numerical iterations.The simulation results indicate that the ultimate calculated steady heat transfer time is 68 years, and most of the heat transfer is completed in 20 years.The initial constant temperature soil surrounding the tunnels is transformed to an annually variable one.An obvious temperature-varying region of the surrounding soil is discovered within 5 m from the tunnel exterior, as well as within the entire range of soil between the two tunnels.The maximum temperature increase value reaches 7.14 ℃ and the maximum peak-to-valley value of annual temperature increase reaches 10 ℃.The temperature variation of soils surrounding tunnels below 10 m is completely controlled by the heat transfer from the tunnels.The coupled heat transfer effect is confirmed because the ultimate steady temperature of soil between the two tunnels is higher than the ones along other positions.Moreover, the regression model comprising a series of univariate functions is proposed for the annual soil temperature fluctuation estimation for the locations varied distances around the tunnel.This investigation is beneficial to gain an insight into the long-term variation tendencies of local engineering geological conditions of the river beach above shallow sections of the cross-river road tunnels.

Finite-difference modeling of surface waves in poroelastic media and stress mirror conditions

During seismic wave propagation on a free surface, a strong material contrast boundary develops in response to interference by P- and S- waves to create a surface-wave phenomenon. To accurately determine the effects of this interface on surface-wave propagation, the boundary conditions must be accurately modeled. In this paper, we present a numerical approach based on the dynamic poroelasticity for a space–time-domain staggered-grid finite-difference simulation in porous media that contain a free-surface boundary. We propose a generalized stess mirror formulation of the free-surface boundary for solids and fluids in porous media for the grid mesh on which lays the free-surface plane. Its analog is that used for elastic media, which is suitable for precise and stable Rayleigh-type surface-wave modeling. The results of our analysis of first kind of Rayleigh （R1） waves obtained by this model demonstrate that the discretization of the mesh in a similar way to that for elastic media can realize stable numerical solutions with acceptable precision. We present numerical examples demonstrating the efficiency and accuracy of our proposed method.

Full-Wave Analysis of Slotline Using Time-Domain Finite-Difference Method

The transmission and dispersive characteristics of slotline are calculated in this paper. The tail of Gaussion pulse is improved because a modified dispersive boundary condition (DBC) is adopted. It leads to a reduction in computer memory requirements and computational time. The computational domain is greatly reduced to enable performance in personal computer. At the same time because edges of a boundary and summits are treated well, the computational results is more accurate and more collector.