Efficient finite-volume simulation of the LWD orthogonal azimuth electromagnetic response in a three-dimensional anisotropic formation using potentials on cylindrical meshes

In this study,the cylindrical finite-volume method(FVM)is advanced for the efficient and high-precision simulation of the logging while drilling(LWD)orthogonal azimuth electromagnetic tool(OAEMT)response in a three-dimensional(3 D)anisotropic formation.To overcome the ill-condition and convergence problems arising from the low induction number,Maxwell’s equations are reformulated into a mixed Helmholtz equation for the coupled potentials in a cylindrical coordinate system.The electrical fi eld continuation method is applied to approximate the perfectly electrical conducting(PEC)boundary condition,to improve the discretization accuracy of the Helmholtz equation on the surface of metal mandrels.On the base,the 3 D FVM on Lebedev’s staggered grids in the cylindrical coordinates is employed to discretize the mixed equations to ensure good conformity with typical well-logging tool geometries.The equivalent conductivity in a non-uniform element is determined by a standardization technique.The direct solver,PARDISO,is applied to efficiently solve the sparse linear equation systems for the multi-transmitter problem.To reduce the number of calls to PARDISO,the whole computational domain is divided into small windows that contain multiple measuring points.The electromagnetic(EM)solutions produced by all the transmitters per window are simultaneously solved because the discrete matrix,relevant to all the transmitters in the same window,is changed.Finally,the 3 D FVM is validated against the numerical mode matching method(NMM),and the characteristics of both the coaxial and coplanar responses of the EM field tool are investigated using the numerical results.

An insulated-gate bipolar transistor model based on the finite-volume charge method

A finite-volume charge method has been proposed to simulate PIN diodes and insulated-gate bipolar transistor(IGBT)devices using SPICE simulators by extending the lumped-charge method.The new method assumes local quasi-neutrality in the undepleted N^(-)base region and uses the total collector current,the nodal hole density and voltage as the basic quantities.In SPICE implementation,it makes clear and accurate definitions of three kinds of nodes—the carrier density nodes,the voltage nodes and the current generator nodes—in the undepleted N^(-)base region.It uses central finite difference to approximate electron and hole current generators and sets up the current continuity equation in a control volume for every carrier density node in the undepleted N^(-)base region.It is easy to increase the number of nodes to describe the fast spatially varying carrier density in transient processes.We use this method to simulate IGBT devices in SPICE simulators and get a good agreement with technology computer-aided design simulations.

Upwind Finite-Volume Solution of Stochastic Burgers’ Equation

In this paper, a stochastic finite-volume solver based on polynomial chaos expansion is developed. The upwind scheme is used to avoid the numerical instabilities. The Burgers’ equation subjected to deterministic boundary conditions and random viscosity is solved. The solution uncertainty is quantified for different values of viscosity. Monte-Carlo simulations are used to validate and compare the developed solver. The mean, standard deviation and the probability distribution function (p.d.f) of the stochastic Burgers’ solution is quantified and the effect of some parameters is investigated. The large sparse linear system resulting from the stochastic solver is solved in parallel to enhance the performance. Also, Monte-Carlo simulations are done in parallel and the execution times are compared in both cases.

An Unconventional Divergence Preserving Finite-Volume Discretization of Lagrangian Ideal MHD

We construct an unconventional divergence preserving discretization of updated Lagrangian ideal magnetohydrodynamics(MHD)over simplicial grids.The cell-centered finite-volume(FV)method employed to discretize the conservation laws of volume,momentum,and total energy is rigorously the same as the one developed to simulate hyperelasticity equations.By construction this moving mesh method ensures the compatibility between the mesh displacement and the approximation of the volume flux by means of the nodal velocity and the attached unit corner normal vector which is nothing but the partial derivative of the cell volume with respect to the node coordinate under consideration.This is precisely the definition of the compatibility with the Geometrical Conservation Law which is the cornerstone of any proper multi-dimensional moving mesh FV discretization.The momentum and the total energy fluxes are approximated utilizing the partition of cell faces into sub-faces and the concept of sub-face force which is the traction force attached to each sub-face impinging at a node.We observe that the time evolution of the magnetic field might be simply expressed in terms of the deformation gradient which characterizes the Lagrange-to-Euler mapping.In this framework,the divergence of the magnetic field is conserved with respect to time thanks to the Piola formula.Therefore,we solve the fully compatible updated Lagrangian discretization of the deformation gradient tensor for updating in a simple manner the cell-centered value of the magnetic field.Finally,the sub-face traction force is expressed in terms of the nodal velocity to ensure a semi-discrete entropy inequality within each cell.The conservation of momentum and total energy is recovered prescribing the balance of all the sub-face forces attached to the sub-faces impinging at a given node.This balance corresponds to a vectorial system satisfied by the nodal velocity.It always admits a unique solution which provides the nodal velocity.The robustness and the accuracy of this unconventional FV scheme have been demonstrated by employing various representative test cases.Finally,it is worth emphasizing that once you have an updated Lagrangian code for solving hyperelasticity you also get an almost free updated Lagrangian code for solving ideal MHD ensuring exactly the compatibility with the involution constraint for the magnetic field at the discrete level.

Unconditional Bound-Preserving and Energy-Dissipating Finite-Volume Schemes for the Cahn-Hilliard Equation

We propose finite-volume schemes for the Cahn-Hilliard equation which unconditionally and discretely preserve the boundedness of the phase field and the dissipation of the free energy.Our numerical framework is applicable to a variety of free-energy potentials,including Ginzburg-Landau and Flory-Huggins,to general wetting boundary conditions,and to degenerate mobilities.Its central thrust is the upwind methodology,which we combine with a semi-implicit formulation for the freeenergy terms based on the classical convex-splitting approach.The extension of the schemes to an arbitrary number of dimensions is straightforward thanks to their dimensionally split nature,which allows to efficiently solve higher-dimensional problems with a simple parallelisation.The numerical schemes are validated and tested through a variety of examples,in different dimensions,and with various contact angles between droplets and substrates.

AN UNSTRUCTURED FINITE-VOLUME ALGORITHM FOR NONLINEAR TWO-DIMENSIOAL SHALLOW WATER EQUATION

An unstructured finite-volume numerical algorithm was presented for solution of the two-dimensional shallow water equations, based on triangular or arbitrary quadrilateral meshes. The Roe type approximate Riemann solver was used to the system. A second-order TVD scheme with the van Leer limiter was used in the space discretization and a two-step Runge-Kutta approach was used in the time discretization. An upwind, as opposed to a pointwise, treatment of the slope source terms was adopted and the semi-implicit treatment was used for the friction source terms. Verification for two-dimension dam-break problems are carried out by comparing the present results with others and very good agreement is shown.

FINITE-VOLUME TVD ALGORITHM FOR DAM-BREAK FLOWS IN OPEN CHANNELS

A finite-volume Total Variation Diminishing (TVD) scheme is presented formodeling dam-break flows in open channels. This method is used for solving the 2D shallow waterequations on arbitrary quadrilateral meshes, based upon a second-order hybrid TVD scheme with anoptimum-selected limiter in the space discretization and a two-step Runge-Kutta approach in the timediscretization. Verification for a circular dam-break problem is carried out by comparing thepresent results with others and very good agreement is shown. The present algorithm is then used topredict dam-break flow characteristics in open channels such as in furcated channels. Morecomplicated unsteady flow characteristics in these furcated channels than in the regular channelsstudied previously can observed in this work.

A Finite-Volume Method for Nonlinear Nonlocal Equations with a Gradient Flow Structure

We propose a positivity preserving entropy decreasing finite volume scheme for nonlinear nonlocal equations with a gradient flow structure.These properties allow for accurate computations of stationary states and long-time asymptotics demonstrated by suitably chosen test cases in which these features of the scheme are essential.The proposed scheme is able to cope with non-smooth stationary states,different time scales including metastability,as well as concentrations and self-similar behavior induced by singular nonlocal kernels.We use the scheme to explore properties of these equations beyond their present theoretical knowledge.

Challenges in Developing Finite-Volume Global Weather and Climate Models with Focus on Numerical Accuracy

High-resolution global non-hydrostatic gridded dynamic models have drawn significant attention in recent years in conjunction with the rising demand for improving weather forecasting and climate predictions.By far it is still challenging to build a high-resolution gridded global model,which is required to meet numerical accuracy,dispersion relation,conservation,and computation requirements.Among these requirements,this review focuses on one significant topic—the numerical accuracy over the entire non-uniform spherical grids.The paper discusses all the topic-related challenges by comparing the schemes adopted in well-known finite-volume-based operational or research dynamical cores.It provides an overview of how these challenges are met in a summary table.The analysis and validation in this review are based on the shallow-water equation system.The conclusions can be applied to more complicated models.These challenges should be critical research topics in the future development of finite-volume global models.

Simulation of Turbulent Flows Using a Finite-Volume Based Lattice Boltzmann Flow Solver

In this study,the Lattice Boltzmann Method(LBM)is implemented through a finite-volume approach to perform 2-D,incompressible,and turbulent fluid flow analyses on structured grids.Even though the approach followed in this study necessitates more computational effort compared to the standard LBM(the so called stream and collide scheme),using the finite-volume method,the known limitations of the stream and collide scheme on lattice to be uniform and Courant-Friedrichs-Lewy(CFL)number to be one are removed.Moreover,the curved boundaries in the computational domain are handled more accurately with less effort.These improvements pave the way for the possibility of solving fluid flow problems with the LBM using coarser grids that are refined only where it is necessary and the boundary layers might be resolved better.

Regularity of Fluxes in Nonlinear Hyperbolic Balance Laws

This paper addresses the issue of the formulation of weak solutions to systems of nonlinear hyperbolic conservation laws as integral balance laws.The basic idea is that the“meaningful objects”are the fluxes,evaluated across domain boundaries over time intervals.The fundamental result in this treatment is the regularity of the flux trace in the multi-dimensional setting.It implies that a weak solution indeed satisfies the balance law.In fact,it is shown that the flux is Lipschitz continuous with respect to suitable perturbations of the boundary.It should be emphasized that the weak solutions considered here need not be entropy solutions.Furthermore,the assumption imposed on the flux f(u)is quite minimal-just that it is locally bounded.

胶州湾高分辨率三维风暴潮漫滩数值模拟

基于海表气压项改进的FVCOM(Finite-Volume Coastal Ocean Model)海洋模式,研发胶州湾高分辨率三维风暴潮漫滩数值模式(JS-FVCOM)。利用JS-FVCOM模式通过对天文潮、台风强度和径流3要素的不同组合,共设计了5个试验,分别进行风暴潮漫滩模拟实验。分析各试验结果得到如下结论:(1)随着台风最大风速的增加,风暴潮增水迅速增加,当综合水位超过防潮堤高程后增水速度明显减慢。海水淹没范围和淹没深度受综合水位超防潮堤高程时间影响明显。(2)在入海河流的河口区,当洪水位与高潮位相遇时,由于高潮位的顶托作用,洪水下泄不畅,造成综合水位上升明显,极易发生海水漫溢现象。JS-FVCOM的模拟结果清楚地再现了海水漫堤的淹没过程,可为紧急情况下的人员疏散提供科学的基础数据。

蓬莱19-3油田事故溢油数值模拟

利用FVCOM(Finite-volume coastal ocean numerical model)数值模型和MM5风场预报模式,在对渤海海域水动力场进行数值模拟的基础上,基于"油粒子"的欧拉-拉格朗日跟踪法和随机走动原理,并考虑风对溢油油膜漂移扩散的直接作用,建立了海洋溢油油膜漂移轨迹和扩散的数值预测模型。利用建立的模型对2011年6月蓬莱19-3油田事故溢油进行了数值模拟,模拟结果与RADARSAT卫星遥感监测数据相吻合。研究结果表明:在渤海中部地区夏季事故溢油模拟预测中,风漂移因子取0.024最为合理,模型可用于渤海蓬莱19-3油田附近事故溢油轨迹和扩散的快速预报,从而为该区域的溢油事故应急响应提供科学依据。

实际气象场驱动下太湖悬浮物浓度的模拟研究

本文利用高频变化的实际气象数据,在考虑波浪作用的前提下利用FVCOM Finite-volume Coastal Ocean Model模式模拟了太湖底泥再悬浮的情况。模拟结果表明,FVCOM模式在考虑波浪作用下对太湖悬浮物浓度的模拟结果与卫星反演结果吻合较好。在模拟时刻,湖心区和西南湖区是悬浮物浓度的大值区,其原因在于:湖心区虽然底泥较少,但其流场的分布总是有利于周围悬浮物向湖心区输送;而西南湖区本身有底泥的分布,在上升运动和流场的配合下,一方面有悬浮物向该区域输送,另一方面该区域有沉积物悬浮。模拟时刻切应力和悬浮物浓度的空间配置是不一致的,说明了底部切应力并不是影响悬浮物浓度的唯一因子,还与湖流的输移和底泥的分布有关。

N-S EQUATION CALCULATIONS ON MULTI-ELEMENT AIRFOILS WITH ZONAL PATCHED GRIDS

For a complex flow about multi-element airfoils a mixed grid method is set up. C-type grids are produced on each element′s body and in their wakes at first, O-type grids are given in the outmost area, and H-type grids are used in middle additional areas. An algebra method is used to produce the initial grids in each area. And the girds are optimized by elliptical differential equation method. Then C-O-H zonal patched grids around multi-element airfoils are produced automatically and efficiently. A time accurate finite-volume integration method is used to solve the compressible laminar and turbulent Navier-Stokes (N-S) equations on the grids. Computational results prove the method to be effective.

A 3D Nonhydrostatic Compressible Atmospheric Dynamic Core by Multi-moment Constrained Finite Volume Method

A 3D compressible nonhydrostatic dynamic core based on a three-point multi-moment constrained finite-volume (MCV) method is developed by extending the previous 2D nonhydrostatic atmospheric dynamics to 3D on a terrainfollowing grid. The MCV algorithm defines two types of moments: the point-wise value (PV) and the volume-integrated average (VIA). The unknowns (PV values) are defined at the solution points within each cell and are updated through the time evolution formulations derived from the governing equations. Rigorous numerical conservation is ensured by a constraint on the VIA moment through the flux form formulation. The 3D atmospheric dynamic core reported in this paper is based on a three-point MCV method and has some advantages in comparison with other existing methods, such as uniform third-order accuracy, a compact stencil, and algorithmic simplicity. To check the performance of the 3D nonhydrostatic dynamic core, various benchmark test cases are performed. All the numerical results show that the present dynamic core is very competitive when compared to other existing advanced models, and thus lays the foundation for further developing global atmospheric models in the near future.

墨西哥湾海洋环境对蓝蟹(Callinectes sapidus)幼体分布和扩散的影响

本文以蓝蟹为例,研究海洋环境对甲壳动物幼体迁移规律和机制的影响。利用不规则三角形网格和有限体积模型(finite-volume coastal ocean model,FVCOM)耦合kinesis模型的方法,分析研究了墨西哥湾物理环境对蓝蟹(Callinectes sapidus)幼体的分布和扩散途径的影响。蓝蟹在每年的四、五月份海水落潮期间产卵,通过跟踪算法从产卵区域沿着墨西哥湾海域进行模拟,获得了80天内蓝蟹幼体的粒子移动轨迹,记录并分析了幼体经过海域的盐度值。研究结果证明了该方法可有效模拟蓝蟹幼体在特定海域的迁移规律和扩散机制,进一步研究可为了解海洋物理环境对蓝蟹和其他渔业资源的影响提供借鉴。

Progressive failure analysis of composite structure based on micro- and macro-mechanics models

Based on parameter design language, a program of progressive failure analysis in composite structures is proposed. In this program, the relationship between macro- and micro-mechanics is established and the macro stress distribution of the composite structure is calculated by commercial finite element software. According to the macro-stress, the damaged point is found and the micro-stress distribution of representative volume element is calculated by finite-volume direct averaging micromechanics(FVDAM). Compared with the results calculated by failure criterion based on macro-stress field(the maximum stress criteria and Hashin criteria) and micro-stress field(Huang model), it is proven that the failure analysis based on macro- and micro-mechanics model is feasible and efficient.

Adaptive Moving Mesh Central-Upwind Schemes for Hyperbolic System of PDEs:Applications to Compressible Euler Equations and Granular Hydrodynamics

We introduce adaptive moving mesh central-upwind schemes for one-and two-dimensional hyperbolic systems of conservation and balance laws.The proposed methods consist of three steps.First,the solution is evolved by solving the studied system by the second-order semi-discrete central-upwind scheme on either the one-dimensional nonuniform grid or the two-dimensional structured quadrilateral mesh.When the evolution step is complete,the grid points are redistributed according to the moving mesh differential equation.Finally,the evolved solution is projected onto the new mesh in a conservative manner.The resulting adaptive moving mesh methods are applied to the one-and two-dimensional Euler equations of gas dynamics and granular hydrodynamics systems.Our numerical results demonstrate that in both cases,the adaptive moving mesh central-upwind schemes outperform their uniform mesh counterparts.

COMPUTATION OF UNSTEADY AERODYNAMIC FORCES ON WINGS WITH NAVIER-STOCKS EQUATIONS

A "dual time" method for the solution of unsteady three dimensional Navier Stocks equations is described in this paper. An implicit real time discretisation is used, and then the equations are integrated in a fictitious pseudo time. When marching in a pseudo time, the finite volume method, multi grid scheme and other acceleration techniques used in steady flow calculations can be used. Balwin Lomax turbulence model is applied to simulate the turbulence.