A wavelet finite-difference method for numerical simulation of wave propagation in fluid-saturated porous media

In this paper, we consider numerical simulation of wave propagation in fluidsaturated porous media. A wavelet finite-difference method is proposed to solve the 2-D elastic wave equation. The algorithm combines flexibility and computational efficiency of wavelet multi-resolution method with easy implementation of the finite-difference method. The orthogonal wavelet basis provides a natural framework, which adapt spatial grids to local wavefield properties. Numerical results show usefulness of the approach as an accurate and stable tool for simulation of wave propagation in fluid-saturated porous media.

Techniques for improving computational speed in numerical simulation of casting thermal stress based on finite difference method

Finite difference method (FDM) was applied to simulate thermal stress recently, which normally needs a long computational time and big computer storage. This study presents two techniques for improving computational speed in numerical simulation of casting thermal stress based on FDM, one for handling of nonconstant material properties and the other for dealing with the various coefficients in discretization equations. The use of the two techniques has been discussed and an application in wave-guide casting is given. The results show that the computational speed is almost tripled and the computer storage needed is reduced nearly half compared with those of the original method without the new technologies. The stress results for the casting domain obtained by both methods that set the temperature steps to 0.1 ℃ and 10 ℃, respectively are nearly the same and in good agreement with actual casting situation. It can be concluded that both handling the material properties as an assumption of stepwise profile and eliminating the repeated calculation are reliable and effective to improve computational speed, and applicable in heat transfer and fluid flow simulation.

Sloshing simulation of standing wave with time-independent finite difference method for Euler equations

The numerical solutions of standing waves for Euler equations with the nonlinear free surface boundary condition in a two-dimensional （2D） tank are studied. The irregular tank is mapped onto a fixed square domain through proper mapping functions. A staggered mesh system is employed in a 2D tank to calculate the elevation of the transient fluid. A time-independent finite difference method, which is developed by Bang- fuh Chen, is used to solve the Euler equations for incompressible and inviscid fluids. The numerical results agree well with the analytic solutions and previously published results. The sloshing profiles of surge and heave motion with initial standing waves are presented. The results show very clear nonlinear and beating phenomena.

Finite Difference Simulation of Implosive Collapsing for Aluminum Spherical Shell

Implosive collapsing for spherical metal shells is a kind of dynamic compressing method, in which high pressure and high compression degree of materials can be attained. In present work, the dynamic process of implosive collapsing for spherical metal shells was regard as spherical symmetry ideally, so one-dimensional spherical symmetric fluid dynamics conservation equations were established, and the finite difference schemes for solving these equations were given. An aluminum spherical shell was assumed, whose inner radius is 4cm and thickness is 2 cm. In numerical simulation, initial centripetal velocities (800, 1000 and 1200 m/s) were used to make aluminum spherical shell collapse. The simulation results show that during the process of implosive collapsing, the material exhibits a compression-expansion-compression pulsation process, and the internal pressure changes and distribution are consistent with the theoretical expectations. The simulation results can be used as a reference for relevant analysis.

Using finite difference method to simulate casting thermal stress

Thermal stress simulation can provide a scientific reference to eliminate defects such as crack,residual stress centralization and deformation etc.,caused by thermal stress during casting solidification.To study the thermal stress distribution during casting process,a unilateral thermal-stress coupling model was employed to simulate 3D casting stress using Finite Difference Method(FDM),namely all the traditional thermal-elastic-plastic equations are numerically and differentially discrete.A FDM/FDM numerical simulation system was developed to analyze temperature and stress fields during casting solidification process.Two practical verifications were carried out,and the results from simulation basically coincided with practical cases.The results indicated that the FDM/FDM stress simulation system can be used to simulate the formation of residual stress,and to predict the occurrence of hot tearing.Because heat transfer and stress analysis are all based on FDM,they can use the same FD model,which can avoid the matching process between different models,and hence reduce temperature-load transferring errors.This approach makes the simulation of fluid flow,heat transfer and stress analysis unify into one single model.

COMPACT FINITE DIFFERENCE-FOURIER SPECTRAL METHOD FOR THREE-DIMENSIONAL INCOMPRESSIBLE NAVIER-STOKES EQUATIONS

A new compact finite difference-Fourier spectral hybrid method for solving the three dimensional incompressible Navier-Stokes equations is developed in the present paper. The fifth-order upwind compact finite difference schemes for the nonlinear convection terms in the physical space, and the sixth-order center compact schemes for the derivatives in spectral space are described, respectively. The fourth-order compact schemes in a single nine-point cell for solving the Helmholtz equations satisfied by the velocities and pressure in spectral space is derived and its preconditioned conjugate gradient iteration method is studied. The treatment of pressure boundary conditions and the three dimensional non-reflecting outflow boundary conditions are presented. Application to the vortex dislocation evolution in a three dimensional wake is also reported.

A simple method of depressing numerical dissipation effects during wave simulation within the Euler model

Numerical wave tanks are widely-acknowledged tools in studying waves and wave-structure interactions. They can generate waves under realistic scales and offers more information on the fluid field. However, most numerical wave tanks suffer from issues known as the numerical dissipation and numerical dispersion. The former causes wave energy to be slowly dissipated and the latter shifts wave frequencies during wave propagation. This paper proposes a simple method of depressing numerical dissipation effects on the basis of solving Euler equations using the finite difference method(FDM). The wave propagation solutions are solved analytically taking into account the influence of the damping terms. The main idea of the method is to append a source term to the momentum equation, whose strength is determined by how strong the numerical damping effect is. The method is verified by successfully depressing numerical effects during the simulation of regular linear waves, Stokes waves and irregular waves. By applying the method, wave energy is able to be close to its initial value after long distance of travel.

Numerical Simulation of Groundwater Pollution Problems Based on Convection Diffusion Equation

The analytical solution of the convection diffusion equation is considered by two-dimensional Fourier transform and the inverse Fourier transform. To get the numerical solution, the Crank-Nicolson finite difference method is constructed, which is second-order accurate in time and space. Numerical simulation shows excellent agreement with the analytical solution. The dynamic visualization of the simulating results is realized on ArcGIS platform. This work provides a quick and intuitive decision-making basis for water resources protection, especially in dealing with water pollution emergencies.

Characteristic finite difference method and application for moving boundary value problem of coupled system

The coupled system of multilayer dynamics of fluids in porous media is to describe the history of oil-gas transport and accumulation in basin evolution.It is of great value in rational evaluation of prospecting and exploiting oil-gas resources.The mathematical model can be described as a coupled system of nonlinear partial differential equations with moving boundary values.A kind of characteristic finite difference schemes is put forward,from which optimal order estimates in l~2 norm are derived for the error in the approximate solutions.The research is important both theoretically and practically for the model analysis in the field,the model numerical method and software development.

Borehole-GPR numerical simulation of full wave field based on convolutional perfect matched layer boundary

The absorbing boundary is the key in numerical simulation of borehole radar.Perfect match layer(PML) was chosen as the absorbing boundary in numerical simulation of GPR.But CPML(convolutional perfect match layer) approach that we have chosen has the advantage of being media independent.Beginning with the Maxwell equations in a two-dimensional structure,numerical formulas of finite-difference time-domain(FDTD) method with CPML boundary condition for transverse electric(TE) or transverse magnetic(TM) wave are presented in details.Also,there are three models for borehole-GPR simulation.By analyzing the simulation results,the features of targets in GPR are obtained,which can provide a better interpretation of real radar data.The results show that CPML is well suited for the simulation of borehole-GPR.

A numerical simulation of surface wave excitation in a rectangular planar-type plasma source

The principle of surface wave plasma discharge in a rectangular cavity is introduced simply based on surface plasmon polariton theory. The distribution of surface-wave electric field at the interface of the plasma-dielectric slab is investigated by using the three-dimensional finite-difference time-domain method （3D-FDTD） with different slotantenna structures. And the experimental image of discharge with a novel slot antenna array and the simulation of the electric field with this slot antenna array are both displayed. Combined with the distribution of surface wave excitation and experimental results, the numerical simulation performed by using 3D-FDTD is shown to be a useful tool in the computer-aided antenna design for large area planar-type surface-wave plasma sources.

Numerical Simulation of 2D and 3D Sloshing Waves in a Regularly and Randomly Excited Container

在这份报纸， 2D 和 3D 的各种各样的方面在垂直地激动的集装箱的非线性的液体 sloshing 问题与修改转变的帮助一起数字地被学习了。基于这个新数字算法，在垂直方向的一只定期并且随机激动的集装箱上的数字研究被进行利用四个不同盒子：第一个盒子被执行与常规刺激利用一只 2D 集装箱。下一个盒子为液体与二个不同起始的条件检验了一只定期激动的 3D 集装箱免费表面，并且最后，有在垂直方向的随机的刺激的 3D 容器。格子独立研究与一系列确认测试一起被执行。一个重复错误评价方法被用来停止反复的解答者(使用解决在计算领域管理方程的 discretized ) 在到达结果的稳定的状态在之上每次走。在现在的盒子中，这个方法被发现生产相当精确的结果并且作为与为反复的解答者的另外的常规停止过程相比更多的倍有效。结果与基准结果被验证。波浪举起时间历史，阶段飞机图和表面阴谋在它的运动期间代表波浪非线性。

Numerical Simulation of Microstructure Formation and Forecast of Mechanical Properties for Spheroidal Graphite Iron

The numerical simulation can overcome the hardship of mathematical analysis and experimental research, explicate the mechanism of microstructure shaping, predict mechanical properties and operating life of castings and then optimize technology and control microstructure formation to obtain the qualified castings. The finite difference method (FDM) is applied to the simulation of temperature field based on all kinds of nucleation and growth models on all stages of solidification of spheroidal graphite cast iron. Visual C++ is used to program the numerical simulation software, QTstructure-1 to simulate the solidification process of spheroidal graphite cast iron and the formation of all phases in solidification process. Finally, the result of simulation is well agreed with the experimental result.

THE UPWIND FINITE DIFFERENCE METHOD FOR MOVING BOUNDARY VALUE PROBLEM OF COUPLED SYSTEM

Coupled system of multilayer dynamics of fluids in porous media is to describe the history of oil-gas transport and accumulation in basin evolution.It is of great value in rational evaluation of prospecting and exploiting oil-gas resources.The mathematical model can be described as a coupled system of nonlinear partial differential equations with moving boundary values.The upwind finite difference schemes applicable to parallel arithmetic are put forward and two-dimensional and three-dimensional schemes are used to form a complete set.Some techniques,such as change of variables,calculus of variations, multiplicative commutation rule of difference operators,decomposition of high order difference operators and prior estimates,are adopted.The estimates in l~2 norm are derived to determine the error in the approximate solution.This method was already applied to the numerical simulation of migration-accumulation of oil resources.

Modified characteristic finite difference fractional step method for moving boundary value problem of nonlinear percolation system

A fractional step scheme with modified characteristic finite differences run- ning in a parallel arithmetic is presented to simulate a nonlinear percolation system of multilayer dynamics of fluids in a porous medium with moving boundary values. With the help of theoretical techniques including the change of regions, piecewise threefold quadratic interpolation, calculus of variations, multiplicative commutation rule of differ- ence operators, multiplicative commutation rule of difference operators, decomposition of high order difference operators, induction hypothesis, and prior estimates, an optimal order in 12 norm is displayed to complete the convergence analysis of the numerical algo- rithm. Some numerical results arising in the actual simulation of migration-accumulation of oil resources by this method are listed in the last section.

High accuracy compact finite difference methods and their applications

Numerical simulation of complex flow fields with multi-scale structures is one of the most important and challenging branches of computational fluid dynamics. From linear analysis and numerical experiments it has been discovered that the higher-order accurate method can give reliable and efficient computational results, as well as better resolution of the complex flow fields with multi-scale structures. Compact finite difference schemes, which feature higher-order accuracy and spectral-like resolution with smaller stencils and easier application of boundary conditions, has attracted more and more interest and attention.

Numerical simulation of tungsten alloy in powder injection molding process

The flow behavior of feedstock for the tungsten alloy powder in the mold cavity was approximately described using Hele-Shaw flow model. The math model consisting of momentum equation, consecutive equation and thermo-conduction equation for describing the injection process was established. The equations are solved by the finite element/finite difference hybrid method that means dispersing the feedstock model with finite element method, resolving the model along the depth with finite difference method, and tracking the movable boundary with control volume method, then the pressure equation and energy equation can be resolved in turn. The numerical simulation of the injection process and the identification of the process parameters were realized by the Moldflow software. The results indicate that there is low temperature gradient in the cavity while the pressure and shear rate gradient are high at high flow rate. The selection of the flow rate is affected by the structure of the gate. The shear rate and the pressure near the gate can be decreased by properly widening the dimension of the gate. There is a good agreement between the process parameters obtained by the numerical simulation and the actual ones.

Characteristic Finite Difference Methods for Moving Boundary Value Problem of Numerical Simulation of Oil Deposit

The software for oil-gas transport and accumulation is to describe the history of oil-gas transport and accumulation in basin evolution. It is of great value in rational evaluation of prospecting and exploiting oil-gas resources. The mathematical model can be described as a coupled system of nonlinear partial differential equations with moving boundary value problem. This paper puts forward a kind of characteristic finite difference schemes, and derives from them optimal order estimates in l^2 norm for the error in the approximate solutions. The research is important both theoretically and practically for the model analysis in the field, for model numerical method and for software development.

Finite difference numerical simulation of guided wave propagation in the full grouted rock bolt

Based on guided wave theory and considering the grouted rock bolt as waveguide medium, we have constructed a three dimensional model of grouted rock bolt with the dynamics of finite difference numerical simulation software FLAC3D4.0, and simulated the propagation behavior of the guided wave in the full grouted rock bolt. The simulated waveform and wave velocity matched well with the experimental results. We have made a more in-depth and comprehensive study of the wave velocity, wave component and attenuation characteristics of the guided wave propagating in rock bolt, and found some new characteristics and phenomena. In addition, some phenomena that haven’t been explained in the previous researches have also been discussed in this paper. The result showed that when guided wave propagates in grouted rock bolt, after the body wave decays, there is still the interface wave-Stoneley wave that does not decay in the axial direction of the bolt. The findings can provide some reference for rock bolt testing and the selection of the optimal excitation wave of testing.