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.

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.

Decoupling Conditions for Elasto-plastic Consolidation Question Based on Numerical Modeling Method

Elasto-plastic consolidation is one of the classic coupling questions in geomechanics. To solve this problem, an elasto-plastic constitutive model is derived based on the numerical modeling method. The model is applied to Blot＇s consolidation theory. Incremental governing partial differential equations are established using this method. According to the stress path, the decoupling condition of these equations is discussed. Based on these conditions, an incremental diffusion equation and uncoupling governing equations are presented. The method is then applied to numerical analyses of three examples. The results show that （1） the effect of the stress path should be taken into account in the simulation of the soil consolidation question; （2） this decoupling method can predict the evolvement of pore water pressure; （3） the settlement using cam-clay model is less than that using numerical model because of dilatancy.

Numerical Modeling of the Hyperbolic Mild-Slope Equation in Curvilinear Coordinates

The mild-slope equation is familiar to coastal engineers as it can effectively describe wave propagation in nearshore regions. However, its computational method in Cartesian coordinates often renders the model inaccurate in areas with irregular shorelines, such as estuaries and harbors. Based on the hyperbolic mild-slope equation in Cartesian coordinates, the numerical model in orthogonal curvilinear coordinates is developed. The transformed model is discretized by the finite difference method and solved by the ADI method with space-staggered grids. The numerical predictions in curvilinear co- ordinates show good agreemenl with the data obtained in three typical physical expedments, which demonstrates that the present model can be used to simulate wave propagation, for normal incidence and oblique incidence, in domains with complicated topography and boundary conditions.

Surrogate modeling for unsaturated infiltration via the physics and equality-constrained artificial neural networks

Machine learning(ML)provides a new surrogate method for investigating groundwater flow dynamics in unsaturated soils.Traditional pure data-driven methods(e.g.deep neural network,DNN)can provide rapid predictions,but they do require sufficient on-site data for accurate training,and lack interpretability to the physical processes within the data.In this paper,we provide a physics and equalityconstrained artificial neural network(PECANN),to derive unsaturated infiltration solutions with a small amount of initial and boundary data.PECANN takes the physics-informed neural network(PINN)as a foundation,encodes the unsaturated infiltration physical laws(i.e.Richards equation,RE)into the loss function,and uses the augmented Lagrangian method to constrain the learning process of the solutions of RE by adding stronger penalty for the initial and boundary conditions.Four unsaturated infiltration cases are designed to test the training performance of PECANN,i.e.one-dimensional(1D)steady-state unsaturated infiltration,1D transient-state infiltration,two-dimensional(2D)transient-state infiltration,and 1D coupled unsaturated infiltration and deformation.The predicted results of PECANN are compared with the finite difference solutions or analytical solutions.The results indicate that PECANN can accurately capture the variations of pressure head during the unsaturated infiltration,and present higher precision and robustness than DNN and PINN.It is also revealed that PECANN can achieve the same accuracy as the finite difference method with fewer initial and boundary training data.Additionally,we investigate the effect of the hyperparameters of PECANN on solving RE problem.PECANN provides an effective tool for simulating unsaturated infiltration.

A Comparative Study of Adomian Decomposition Method with Variational Iteration Method for Solving Linear and Nonlinear Differential Equations

This study compares the Adomian Decomposition Method (ADM) and the Variational Iteration Method (VIM) for solving nonlinear differential equations in engineering. Differential equations are essential for modeling dynamic systems in various disciplines, including biological processes, heat transfer, and control systems. This study addresses first, second, and third-order nonlinear differential equations using Mathematica for data generation and graphing. The ADM, developed by George Adomian, uses Adomian polynomials to handle nonlinear terms, which can be computationally intensive. In contrast, VIM, developed by He, directly iterates the correction functional, providing a more straightforward and efficient approach. This study highlights VIM’s rapid convergence and effectiveness of VIM, particularly for nonlinear problems, where it simplifies calculations and offers direct solutions without polynomial derivation. The results demonstrate VIM’s superior efficiency and rapid convergence of VIM compared with ADM. The VIM’s minimal computational requirements make it practical for real-time applications and complex system modeling. Our findings align with those of previous research, confirming VIM’s efficiency of VIM in various engineering applications. This study emphasizes the importance of selecting appropriate methods based on specific problem requirements. While ADM is valuable for certain nonlinearities, VIM’s approach is ideal for many engineering scenarios. Future research should explore broader applications and hybrid methods to enhance the solution’s accuracy and efficiency. This comprehensive comparison provides valuable guidance for selecting effective numerical methods for differential equations in engineering.

A High-Order Conservative Numerical Method for Gross-Pitaevskii Equation with Time-Varying Coefficients in Modeling BEC

We propose a high-order conservative method for the nonlinear Sehodinger/Gross-Pitaevskii equation with time- varying coefficients in modeling Bose Einstein condensation （BEC）. This scheme combined with the sixth-order compact finite difference method and the fourth-order average vector field method, finely describes the condensate wave function and physical characteristics in some small potential wells. Numerical experiments are presented to demonstrate that our numerical scheme is efficient by the comparison with the Fourier pseudo-spectral method. Moreover, it preserves several conservation laws well and even exactly under some specific conditions.

Numerical Models of Higher-Order Boussinesq Equations and Comparisons with Laboratory Measurement

Nonlinear water wave propagation passing a submerged shelf is studied experimentally and numerically. The applicability of two different wave propagation models has been investigated. One is higher-order Boussinesq equations derived by Zou (1999) and the other is the classic Boussinesq equations, Physical experiments are conducted, three different front slopes (1:10, 1:5 and 1:2) of the shelf are set up in the experiment and their effects on wave propagation are investigated. Comparisons of numerical results with test data are made, the model of higher-order Boussinesq equations agrees much better with the measurements than the model of the classical Boussinesq equations, The results show that the higher-order Boussinesq equations can also be applied to the steeper slope case although the mild slope assumption is employed in the derivation of the higher order terms of higher order Boussinesq equations.

3-D acoustic wave equation forward modeling with topography

In order to model the seismic wave field with surface topography, we present a method of transforming curved grids into rectangular grids in two different coordinate systems. Then the 3D wave equation in the transformed coordinate system is derived. The wave field is modeled using the finite-difference method in the transformed coordinate system. The model calculation shows that this method is able to model the seismic wave field with fluctuating surface topography and achieve good results. Finally, the energy curves of the direct and reflected waves are analyzed to show that surface topography has a great influence on the seismic wave＇s dynamic properties.

Bubble size modeling approach for the simulation of bubble columns

The constant bubble size modeling approach(CBSM)and variable bubble size modeling approach(VBSM)are frequently employed in Eulerian–Eulerian simulation of bubble columns.However,the accuracy of CBSM is limited while the computational efficiency of VBSM needs to be improved.This work aims to develop method for bubble size modeling which has high computational efficiency and accuracy in the simulation of bubble columns.The distribution of bubble sizes is represented by a series of discrete points,and the percentage of bubbles with various sizes at gas inlet is determined by the results of computational fluid dynamics(CFD)–population balance model(PBM)simulations,whereas the influence of bubble coalescence and breakup is neglected.The simulated results of a 0.15 m diameter bubble column suggest that the developed method has high computational speed and can achieve similar accuracy as CFD–PBM modeling.Furthermore,the convergence issues caused by solving population balance equations are addressed.

AN INTEGRATION METHOD WITH FITTING CUBIC SPLINE FUNCTIONS TO A NUMERICAL MODEL OF 2ND-ORDER SPACE-TIME DIFFERENTIAL REMAINDER——FOR AN IDEAL GLOBAL SIMULATION CASE WITH PRIMITIVE ATMOSPHERIC EQUATIONS

In this paper,the forecasting equations of a 2nd-order space-time differential remainder are deduced from the Navier-Stokes primitive equations and Eulerian operator by Taylor-series expansion.Here we introduce a cubic spline numerical model(Spline Model for short),which is with a quasi-Lagrangian time-split integration scheme of fitting cubic spline/bicubic surface to all physical variable fields in the atmospheric equations on spherical discrete latitude-longitude mesh.A new algorithm of"fitting cubic spline—time step integration—fitting cubic spline—……"is developed to determine their first-and2nd-order derivatives and their upstream points for time discrete integral to the governing equations in Spline Model.And the cubic spline function and its mathematical polarities are also discussed to understand the Spline Model’s mathematical foundation of numerical analysis.It is pointed out that the Spline Model has mathematical laws of"convergence"of the cubic spline functions contracting to the original functions as well as its 1st-order and 2nd-order derivatives.The"optimality"of the 2nd-order derivative of the cubic spline functions is optimal approximation to that of the original functions.In addition,a Hermite bicubic patch is equivalent to operate on a grid for a 2nd-order derivative variable field.Besides,the slopes and curvatures of a central difference are identified respectively,with a smoothing coefficient of 1/3,three-point smoothing of that of a cubic spline.Then the slopes and curvatures of a central difference are calculated from the smoothing coefficient 1/3 and three-point smoothing of that of a cubic spline,respectively.Furthermore,a global simulation case of adiabatic,non-frictional and"incompressible"model atmosphere is shown with the quasi-Lagrangian time integration by using a global Spline Model,whose initial condition comes from the NCEP reanalysis data,along with quasi-uniform latitude-longitude grids and the so-called"shallow atmosphere"Navier-Stokes primitive equations in the spherical coordinates.The Spline Model,which adopted the Navier-Stokes primitive equations and quasi-Lagrangian time-split integration scheme,provides an initial ideal case of global atmospheric circulation.In addition,considering the essentially non-linear atmospheric motions,the Spline Model could judge reasonably well simple points of any smoothed variable field according to its fitting spline curvatures that must conform to its physical interpretation.

Numerical Simulation of Freak Waves Based on the Four-Order Nonlinear Schrdinger Equation

A numerical wave model based on the modified four-order nonlinear Schoedinger （NKS） equation in deep water is developed to simulate freak waves. A standard split-step, pseudo-spectral method is used to solve NLS equation. The validation of the model is firstly verified, and then the simulation of freak waves is perforated by changing sideband condi- tions. Results show that freak waves entirely consistent with the definition in the evolution of wave trains are obtained. The possible occurrence mechanism of freak waves is discussed and the relevant characteristics are also analyzed.

Numerical Modeling of Three-Phase Mass Transition with an Application in Atmospheric Chemistry

This work presents a software tool for modeling of mass transfer physicochemical processes occurring in the atmosphere. The implemented algorithms provide an efficient theoretical frame for the interpretation of the results obtained from Coated Wall Flow Tube (CWFT) reactor experiments, which is one of the most adequate techniques to study heterogeneous kinetics. The numerical simulations are based on the fundamental Langmuir adsorption theory by ordinary differential equations and the second Fick’s law described by partial differential equations. The main application of the system is to estimate the basic parameters that characterize the processes. The best parameter estimation is found by minimizing the difference between experimental signals from the CWFT reactors and the obtained numerical simulations. A numerical example for an experimental data fit is given.

An alternating direction implicit （ADI） numerical model for two－dimensional hydrodynamic equations

A two-dimensional computational model is develope for the calulation of tides, storm surges and otherlong-period waves in coastal and shelf waters. The Partial differental equations are approximated by two sets of difference equations on a space-staggered grid system. Both sets are explicit with one set for water level and x-component velocity, and another for water level and y-component velocity. These two sets are used successively for stepby-step solution in time. An analytical investigation on the linearized sets of the difference equations indicates that thecomputational scheme is unconditionally stable. The model is of second order accuracy both in space and in time andconserves mass and momentum. Simulations of surface elevation caused by periodic forcing in one-opening rectangularbasin with flat topography and by steady wind stress in the basin with flat or slope topography show that the computed results are in excellent agreement with the corresponding analytic solutions. The steady-tate wind-induced setupin a ofed basin with discontinuous topography computed with the present model are also in excellent agreement withthe results from Leendertse's model. Finally, the model is applied to hindcast a storm surge in the South China Seaand reproduces the surge elevation satisfactorily.

Solution of Self-similar Equations of the k-ε Model in the Shear Turbulent Mixing Problem and Its Numerical Simulation

The paper presents the k-ε model equations of turbulence with a single set of constants chosen by the authors, which is appropriate to simulate a wide range of turbulent flows. The model validation has been performed for a number of flows and its main results are given in the paper. The turbulent mixing of flow with shear in the tangential velocity component is discussed in details. An analytical solution to the system of ordinary differential equations of the k-ε model of turbulent mixing has been found for the self-similar regime of flow. The model coefficients were chosen using simulation results for some simplest turbulent flows. The solution can be used for the verification of codes. The numerical simulation of the problem has been performed by the 2D code EGAK using this model. A good agreement of the numerical simulation results with the self-similar solution, 3D DNS results and known experimental data has been achieved. This allows stating that the k-ε model constants chosen by the authors are acceptable for the considered flow.

三维TI和OA介质中优化黏滞纯声波方程及其数值模拟

各向异性和黏滞性在地球介质中广泛存在,会对地震波的运动学和动力学特征产生影响,因此研究地震波在地下空间中传播时应该对其予以充分考虑.现有的各向异性波场外推方法主要采用基于声学近似的伪声波方程,该类方程在非声学假设条件下容易出现伪横波污染及传播不稳定.针对此问题,本文应用优化方案对原始的耦合各向异性纯声波频散关系式进行近似展开,进而发展了针对三维TI(横向各向同性)介质和OA(正交各向异性)介质的优化纯声波方程,结合有限差分和泊松算法对其进行了有效求解.同时,考虑到介质对地震波的吸收衰减效应,本文结合发展的纯声波方程和标准线性体模型,推导了黏滞各向异性优化纯声波方程.相速度分析表明优化方案能够产生高精度近似结果.数值模型算例证明优化黏滞纯声波方程在产生精确稳定P波响应的前提下,能够有效模拟各向异性介质中纯声波的振幅衰减和相位频散.整体而言,本文推导的方程能够为各向异性衰减介质成像和反演提供有效帮助.

综合能源系统建模与仿真:综述、思考与展望

建模和仿真将真实系统及其物理性质抽象化为适当的数学形式,并采用数学方法求解以模拟真实系统行为或性能。为综合能源系统在各时间尺度的物理过程建立恰当的数学模型并进行仿真验证,是分析系统运行规律、优化运行策略以及评估运行性能的基础。文中围绕电气热综合能源系统建模和仿真问题,首先介绍了电、气、热子系统和耦合设备的机理模型,总结了建模的研究进展与技术难点。进一步,从仿真框架、算法以及改进策略3个方面介绍了综合能源系统仿真技术所取得的研究进展。特别地,总结了仿真算法中数值法、半解析法、解析法的原理、应用现状及其难点。最后,围绕现存技术难点,从建模和仿真算法2个方面对未来研究进行了展望。

鄂尔多斯盆地黄土塬区地震波场数值模拟及传播规律

为研究鄂尔多斯盆地黄土塬区地震波的传播规律和噪声的产生机理,根据庆城北三维工区实际地表高程和速度结构,建立准确反映黄土塬区近地表结构的三维数字模型(速度和品质因子Q),以基于Q显式表达的黏滞声波方程为基础,采用坐标变换法实现起伏地表条件下的三维黏滞声波方程数值模拟。该方法可以将复杂近地表引起的近炮点强能量噪声和强衰减效应较客观地模拟出来,模拟结果与实际资料的吻合度较高。通过不同复杂程度模型的三维数值模拟和波场分析,厘清了黄土塬区地震资料近炮点强能量噪声和多次反射、多次折射的产生机理,并结合实际资料分析了黄土塬区不同位置(塬、梁、坡、沟)及不同炮点深度的波场特征差异,认为:沟中激发时,近炮点强能量噪声较弱,资料品质相对较好;随着炮点深度增大,信号的高频端成分逐步增加;黄土塬地区野外地震采集时,应避免在干黄土层中激发,尽可能选择胶泥层或更深层激发。波场分析结论对黄土塬区实际资料采集和处理具有一定的指导意义。

电子束发射诱发航天器充电的数值模拟研究

通过发射电子束测量空间地磁场是一种新的有效的地磁场高精度测量方法,但电子束发射对在轨航天器自身状态和安全存在影响。为了研究这一影响,从同步轨道充电机制出发,基于轨道限制机制和朗缪尔方程研究了航天器发射高能电子束时的诱发充电模型,推导了不同初始电位情况下束流发射的平衡电位公式,并编制程序研究了这一过程中粒子束电流、能量、光照等因素对航天器充电电位的影响,得到了航天器对外发射高能电子束时诱发航天器自身或平台的充电电位随时间变化规律,并通过部分解析解对比验证了模拟结果的正确性。

带有最优流量信息中断期望影响的一类新格子模型

交通中断是导致交通扰动的一个重要因素.为研究最优流量信息中断的期望行为对交通流稳定性的影响,基于Nagatani’s模型考虑最优流量中断概率的影响,提出一类新的格子流体力学模型.首先,根据线性稳定分析方法,得到新模型的线性稳定条件;其次,通过非线性稳定理论,获得该模型的modified Korteweg-de Vries(mKdV)方程,并根据求解方程得到的扭结-反扭结孤立波解描述交通堵塞的演变过程;最后,通过仿真算例验证了理论分析结果.结果表明,考虑最优流量中断期望影响的新格子流体力学模型比Nagatani’s模型更稳定,当添加最优流量信息中断的期望影响时,交通流的稳定性得到显著提高.