With the development of industrial activities,global warming has accelerated due to excessive emission of CO_(2).Enhanced Geothermal System(EGS)utilizes deep geothermal heat for power generation.Although porous medium...With the development of industrial activities,global warming has accelerated due to excessive emission of CO_(2).Enhanced Geothermal System(EGS)utilizes deep geothermal heat for power generation.Although porous medium theory is commonly employed to model geothermal reservoirs in EGS,Hot Dry Rock(HDR)presents a challenge as it consists of impermeable granite with zero porosity,potentially distorting the physical interpretation.To address this,the Lattice Boltzmann Method(LBM)is employed to simulate CO_(2)flow within geothermal reservoirs and the Finite Volume Method(FVM)to solve the energy conservation equation for temperature distribution.This combined method of LBM and FVM is imple-mented using MATLAB.The results showed that the Reynolds numbers(Re)of 3,000 and 8,000 lead to higher heat extraction rates from geothermal reservoirs.However,higher Re values may accelerate thermal breakthrough,posing challenges to EGS operation.Meanwhile,non-equilibrium of density in fractures becomes more pronounced during the system's life cycle,with non-Darcy's law becoming significant at Re values of 3,000 and 8,000.Density stratification due to buoyancy effects significantly impacts temperature distribution within geothermal reservoirs,with buoyancy effects at Re=100 under gravitational influence being noteworthy.Larger Re values(3,000 and 8,000)induce stronger forced convection,leading to more uniform density distribution.The addition of proppant negatively affects heat transfer performance in geothermal reservoirs,especially in single fractures.Practical engineering considerations should determine the quantity of proppant through detailed numerical simulations.展开更多
A method to simulate processes of forging and subsequent heat treatment of an axial symmetric rod is formulated in eulerian description and the feasibility is investigated. This method uses finite volume mushes for t...A method to simulate processes of forging and subsequent heat treatment of an axial symmetric rod is formulated in eulerian description and the feasibility is investigated. This method uses finite volume mushes for troching material deformation and an automatically refined facet surface to accurately trace the free surface of the deforming material.In the method,the deforming work piece flows through fixed finite volume meshes using eulerian formulation to describe the conservation laws,Fixed finite volume meshing is particularly suitable for large three-dimensional deformation such as forging because remeshing techniques are not required, which are commonly considered to be the main bottelencek in the ssimulations of large defromation by using the finite element method,By means of this finite volume method, an approach has been developed in the framework of 'metallo-thermo-mechanics' to simulate metallic structure, temperature and stress/strain coupled in the heat treatment process.In a first step of simulation, the heat treatment solver is limited in small deformation hypothesis,and un- coupled with forging. The material is considered as elastic-plastic and takes into account of strain, strain rate and temperature effects on the yield stress.Heat generation due to deformation,heat con- duction and thermal stress are considered.Temperature - dependent phase transformation,stress-in- duced phase transformation,latent heat,transformation stress and strain are included.These ap- proaches are implemented into the commerical commercial computer program MSC/SuperForge and a verification example with experimental date is given as comparison.展开更多
The finite volume method （FVM） has many advantages in 2-D shallow water numerical simulation. In this study, the finite volume method is used with unstructured triangular grids to simulate the tidal currents. The Ro...The finite volume method （FVM） has many advantages in 2-D shallow water numerical simulation. In this study, the finite volume method is used with unstructured triangular grids to simulate the tidal currents. The Roe scheme is applied in the calculation of the intercell numerical flux, and the MUSCL method is introduced to improve its accuracy. The time integral is a two-step scheme of forecast and revision. For the verification of the present method, the Stoker＇s problem is calculated and the result is compared with the mathematically analytic solutions. The comparison indicates that the method is feasible. A sea area of a port is used as an example to test the method established here. The result shows that the present computational method is satisfactory, and it could be applied to the engineering fields.展开更多
The paper presents a finite volume numerical method universally applicable for solving both linear and nonlinear aeroacoustics problems on arbitrary unstructured meshes. It is based on the vertexcentered multi-paramet...The paper presents a finite volume numerical method universally applicable for solving both linear and nonlinear aeroacoustics problems on arbitrary unstructured meshes. It is based on the vertexcentered multi-parameter scheme offering up to the 6th accuracy order achieved on the Cartesian meshes. An adaptive dissipation is added for the numerical treatment of possible discontinuities. The scheme properties are studied on a series of test cases, its efficiency is demonstrated at simulating the noise suppression in resonance-type liners.展开更多
Based on the first-order upwind and second-order central type of finite volume (UFV and CFV) scheme, upwind and central type of perturbation finite volume (UPFV and CPFV) schemes of the Navier-Stokes equations were de...Based on the first-order upwind and second-order central type of finite volume (UFV and CFV) scheme, upwind and central type of perturbation finite volume (UPFV and CPFV) schemes of the Navier-Stokes equations were developed. In PFV method, the mass fluxes of across the cell faces of the control volume (CV) were expanded into power series of the grid spacing and the coefficients of the power series were determined by means of the conservation equation itself. The UPFV and CPFV scheme respectively uses the same nodes and expressions as those of the normal first-order upwind and second-order central scheme, which is apt to programming. The results of numerical experiments about the flow in a lid-driven cavity and the problem of transport of a scalar quantity in a known velocity field show that compared to the first-order UFV and second-order CFV schemes, upwind PFV scheme is higher accuracy and resolution, especially better robustness. The numerical computation to flow in a lid-driven cavity shows that the under-relaxation factor can be arbitrarily selected ranging from (0.3) to (0.8) and convergence perform excellent with Reynolds number variation from 10~2 to 10~4.展开更多
The finite volume method has been successfully applied in several engineering fields and has shown outstanding performance in fluid dynamics simulation. In this paper, the general framework for the simulation ofnear-w...The finite volume method has been successfully applied in several engineering fields and has shown outstanding performance in fluid dynamics simulation. In this paper, the general framework for the simulation ofnear-wellbore systems using the finite volume method is described. The mathematical model and the numerical model developed by the authors are presented and discussed. A radial geometry in the vertical plane was implemented so as to thoroughly describe near-wellbore phenomena. The model was then used to simulate injection tests in an oil reservoir through a horizontal well and proved very powerful to correctly reproduce the transient pressure behavior. The reason for this is the robustness of the method, which is independent of the gridding options because the discretization is performed in the physical space. The model is able to describe the phenomena taking place in the reservoir even in complex situations, i.e. in the presence of heterogeneities and permeability barriers, demonstrating the flexibility of the finite volume method when simulating non-conventional tests. The results are presented in comparison with those obtained with the finite difference numerical approach and with analytical methods, if possible.展开更多
Global electromagnetic induction provides an efficient way to probe the electrical conductivity in the Earth’s deep interior.Owing to the increasing geomagnetic data especially from high-accuracy geomagnetic satellit...Global electromagnetic induction provides an efficient way to probe the electrical conductivity in the Earth’s deep interior.Owing to the increasing geomagnetic data especially from high-accuracy geomagnetic satellites,inverting the Earth’s three-dimensional conductivity distribution on a global scale becomes attainable.A key requirement in the global conductivity inversion is to have a forward solver with high-accuracy and efficiency.In this study,a finite volume method for global electromagnetic induction forward modeling is developed based on unstructured grids.Arbitrary polyhedral grids are supported in our algorithms to obtain high geometric adaptability.We employ a cell-centered collocated variable arrangement which allows convenient discretization for complex geometries and straightforward implementation of multigrid technique.To validate the method,we test our code with two synthetic models and compare our finite volume results with an analytical solution and a finite element numerical solution.Good agreements are observed between our solution and other results,indicating acceptable accuracy of the proposed method.展开更多
The examination of an unstructured finite volume method for structural dynamics is assessed for simulations of systematic impact dynamics. A robust display dual-time stepping method is utilized to obtain time accurate...The examination of an unstructured finite volume method for structural dynamics is assessed for simulations of systematic impact dynamics. A robust display dual-time stepping method is utilized to obtain time accurate solutions. The study of impact dynamics is a complex problem that should consider strength models and state equations to describe the mechanical behavior of materials. The current method has several features, l） Discrete equations of unstructured finite volume method naturally follow the conservation law. 2） Display dual-time stepping method is suitable for the analysis of impact dynamic problems of time accurate solutions. 3） The method did not produce grid distortion when large deformation appeared. The method is validated by the problem of impact dynamics of an elastic plate with initial conditions and material properties. The results validate the finite element numerical data展开更多
In order to simulate the flowing of shale gas in multi-scale media,we established a mathematical model for the unsteady seepage of multi-stage fractured horizontal wells in shale gas reservoirs in consideration of the...In order to simulate the flowing of shale gas in multi-scale media,we established a mathematical model for the unsteady seepage of multi-stage fractured horizontal wells in shale gas reservoirs in consideration of the flowing characteristics of shale gas in matrix,natural fractures and large-scale artificial fractures.Grid division in the simulation region was carried out by means of nonstructural tetrahedral grid.Then,a 3D numerical model for the seepage of shale gas was established discretely using finite volume method and solved using sequence solution method.Finally,the production performance of multi-stage fractured horizontal wells in shale gas reservoirs and the reservoir pressure distribution were simulated,and the simulation results were analyzed.And the following research results were obtained.First,the gas production rates of multi-stage fractured horizontal wells calculated by this newly established numerical simulation method are basically consistent with the calculation results by the commercial numerical simulation software Eclipse,which proves that this new model is accurate and feasible.Second,the gas production rates of horizontal wells calculated by the sequential solution method are different from those calculated by the fully implicit solution method in the early production stages,but as the calculation progresses,both of them tend to be consistent,which further verifies the accuracy of this new model.Third,desorbed gas plays a supplementary role to reservoir pressure,but its function is limited,and its effect on gas production is little.As the production goes on,the percentage of desorbed gas increases gradually.Fourth,the key to the stimulation of shale-gas horizontal wells is to determine the number of fractured sections rationally and create longer artificial fractures.In conclusion,the research results are conducive to the design of stimulated reservoir volumes(SRVs)of shale gas reservoirs and the prediction of production performance of multi-stage fractured horizontal wells.展开更多
Ionosphere is the layer of atmosphere which plays an important role both in space based navigation,positioning and communication systems and HF signals. The structure of the electron density is a function of spatio-te...Ionosphere is the layer of atmosphere which plays an important role both in space based navigation,positioning and communication systems and HF signals. The structure of the electron density is a function of spatio-temporal variables. The electrodynamic medium is also influenced with earth’s magnetic field, atmospheric chemistry and plasma flow and diffusion under earth’s gravitation. Thus, the unified dynamo equation for the ionosphere is a second order partial differential equation for quasi-static electric potential with variable spatial coefficients. In this study, the inhomogeneous and anisotropic nature of ionosphere that can be formulated as a divergence equation is solved numerically using Finite Volume Method for the first time. The ionosphere and the operators are discretized for the midlatitude region and the solution domain is investigated for Dirichlet type boundary conditions that are built in into the diffusion equation. The analysis indicates that FVM can be a powerful tool in obtaining parametric electrostatic potential distribution in ionosphere.展开更多
In this paper, we present a finite volume framework for second order elliptic equations with variable coefficients based on cubic Hermite element. We prove the optimal H1 norm error estimates. A numerical example is g...In this paper, we present a finite volume framework for second order elliptic equations with variable coefficients based on cubic Hermite element. We prove the optimal H1 norm error estimates. A numerical example is given at the end to show the feasibility of the method.展开更多
The fluid-structure interaction may occur in space launch vehicles,which would lead to bad performance of vehicles,damage equipments on vehicles,or even affect astronauts＇ health.In this paper,analysis on dynamic beh...The fluid-structure interaction may occur in space launch vehicles,which would lead to bad performance of vehicles,damage equipments on vehicles,or even affect astronauts＇ health.In this paper,analysis on dynamic behavior of liquid oxygen （LOX） feeding pipe system in a large scale launch vehicle is performed,with the effect of fluid-structure interaction （FSI） taken into consideration.The pipe system is simplified as a planar FSI model with Poisson coupling and junction coupling.Numerical tests on pipes between the tank and the pump are solved by the finite volume method.Results show that restrictions weaken the interaction between axial and lateral vibrations.The reasonable results regarding frequencies and modes indicate that the FSI affects substantially the dynamic analysis,and thus highlight the usefulness of the proposed model.This study would provide a reference to the pipe test,as well as facilitate further studies on oscillation suppression.展开更多
Three-dimensional simulations of ferroelectric hysteresis and butterfly loops are carried out based on solving the time dependent Ginzburg-Landau equations using a finite volume method. The influence of externally mec...Three-dimensional simulations of ferroelectric hysteresis and butterfly loops are carried out based on solving the time dependent Ginzburg-Landau equations using a finite volume method. The influence of externally mechanical loadings with a tensile strain and a compressive strain on the hysteresis and butterfly loops is studied numerically. Different from the traditional finite element and finite difference methods, the finite volume method is applicable to simulate the ferroelectric phase transitions and properties of ferroelectric materials even for more realistic and physical problems.展开更多
Efficient recycling of lithium metasilicate(Li_(2)SiO_(3))from lithium-containing slag via a pyrometallurgical route demands a comprehensive understanding of its solidification process in the slag reactor.A simulation...Efficient recycling of lithium metasilicate(Li_(2)SiO_(3))from lithium-containing slag via a pyrometallurgical route demands a comprehensive understanding of its solidification process in the slag reactor.A simulation framework is developed to predict the heterogeneous phase distribution of Li_(2)SiO_(3),the temperature and velocity fields considering density changes in the solidifying melt,on the apparatus scale.This framework integrates thermodynamic models via calculation of phase diagrams with the enthalpy-porosity technique and the volume of fluid method within a finite volume approach,ensuring thermodynamic consistency and adherence to mass balance.Thus,the formation of Li_(2)SiO_(3)from the liquid slag composed of Li_(2)O-SiO_(2)is described in space and temporal fields.Thereby,the interrelationship between the temperature field,enthalpy field,velocity field,and phase distribution of Li_(2)SiO_(3)is revealed.It is shown that the lower temperature on reactor boundaries prompts the earlier formation of Li_(2)SiO_(3)in the vicinity of the boundaries,which subsequently induces a downward flow due to the higher density of Li_(2)SiO_(3).The predicted global mass fraction of Li_(2)SiO_(3)under non-equilibrium conditions is 11.5 wt%lower than that calculated using the global equilibrium assumption.This demonstrates the global non-equilibrium behavior on the process scale and its consequences on slag solidification.展开更多
In this paper,we concentrate on high-order boundary treatments for finite volume methods solving hyperbolic conservation laws.The complex geometric physical domain is covered by a Cartesian mesh,resulting in the bound...In this paper,we concentrate on high-order boundary treatments for finite volume methods solving hyperbolic conservation laws.The complex geometric physical domain is covered by a Cartesian mesh,resulting in the boundary intersecting the grids in various fashions.We propose two approaches to evaluate the cell averages on the ghost cells near the boundary.Both of them start from the inverse Lax-Wendroff(ILW)procedure,in which the normal spatial derivatives at inflow boundaries can be obtained by repeatedly using the governing equations and boundary conditions.After that,we can get an accurate evaluation of the ghost cell average by a Taylor expansion joined with high-order extrapolation,or by a Hermite extrapolation coupling with the cell averages on some“artificial”inner cells.The stability analysis is provided for both schemes,indicating that they can avoid the so-called“small-cell”problem.Moreover,the second method is more efficient under the premise of accuracy and stability.We perform numerical experiments on a collection of examples with the physical boundary not aligned with the grids and with various boundary conditions,indicating the high-order accuracy and efficiency of the proposed schemes.展开更多
In this paper,we consider the electromagnetic wave scattering problem from a periodic chiral structure.The scattering problem is simplified to a two-dimensional problem,and is discretized by a finite volume method com...In this paper,we consider the electromagnetic wave scattering problem from a periodic chiral structure.The scattering problem is simplified to a two-dimensional problem,and is discretized by a finite volume method combined with the perfectly matched layer(PML)technique.A residual-type a posteriori error estimate of the PML finite volume method is analyzed and the upper and lower bounds on the error are established in the H^(1)-norm.The crucial part of the a posteriori error analysis is to derive the error representation formula and use a L^(2)-orthogonality property of the residual which plays a similar role as the Galerkin orthogonality.An adaptive PML finite volume method is proposed to solve the scattering problem.The PML parameters such as the thickness of the layer and the medium property are determined through sharp a posteriori error estimate.Finally,numerical experiments are presented to illustrate the efficiency of the proposed method.展开更多
The discrete version of solute transport equation for porous matrix depicted with the continuum model and the discrete fractured-network model are derived for fractured rocks with the Finite Volume Method （FVM）. The...The discrete version of solute transport equation for porous matrix depicted with the continuum model and the discrete fractured-network model are derived for fractured rocks with the Finite Volume Method （FVM）. The two models are coupled according to the continuity condition of hydraulic head and concentration and the conservation of flow flux and mass flux in the contact plane between porous matrix and fractures. Numerical results show that the simulated concentration of the coupling model based on the FVM agrees well with that from analytical solution, which demonstrates that the coupling model can effectively be applied to the simulation of solute transport in fractured rocks.展开更多
A finite volume method for the numerical solution of viscoelastic flows is given. The flow of a differential Upper-Convected Maxwell （UCM） fluid through an abrupt expansion has been chosen as a prototype example. Th...A finite volume method for the numerical solution of viscoelastic flows is given. The flow of a differential Upper-Convected Maxwell （UCM） fluid through an abrupt expansion has been chosen as a prototype example. The conservation and constitutive equations are solved using the Finite Volume Method （FVM） in a staggered grid with an upwind scheme for the viscoelastic stresses and a hybrid scheme for the velocities. An enhanced-in-speed pressure-correction algorithm is used and a method for handling the source term in the momentum equations is employed. Improved accuracy is achieved by a special discretization of the boundary conditions. Stable solutions are obtained for higher Weissenberg number （We）, further extending the range of simulations with the FVM. Numerical results show the viscoelasticity of polymer solutions is the main factor influencing the sweeo efficiency.展开更多
The purpose of this study is to set up a dynamically linked 1D and 2D hydrodynamic and sediment transport models for dam break flow.The 1D-2D coupling model solves the generalized shallow water equations,the non-equil...The purpose of this study is to set up a dynamically linked 1D and 2D hydrodynamic and sediment transport models for dam break flow.The 1D-2D coupling model solves the generalized shallow water equations,the non-equilibrium sediment transport and bed change equations in a coupled fashion using an explicit finite volume method.It considers interactions among transient flow,strong sediment transport and rapid bed change by including bed change and variable flow density in the flow continuity and momentum equations.An unstructured Quadtree rectangular grid with local refinement is used in the 2D model.The intercell flux is computed by the HLL approximate Riemann solver with shock captured capability for computing the dry-to-wet interface for all models.The effects of pressure and gravity are included in source term in this coupling model which can simplify the computation and eliminate numerical imbalance between source and flux terms.The developed model has been tested against experimental and real-life case of dam-break flow over fix bed and movable bed.The results are compared with analytical solution and measured data with good agreement.The simulation results demonstrate that the coupling model is capable of calculating the flow,erosion and deposition for dam break flows in complicated natural domains.展开更多
Under the interval uncertainties, by incorporating the discretization form offinite volume method and interval algebra theory, an Interval Finite Volume Method (IF-VM) wasdeveloped to solve water quality simulation is...Under the interval uncertainties, by incorporating the discretization form offinite volume method and interval algebra theory, an Interval Finite Volume Method (IF-VM) wasdeveloped to solve water quality simulation issues for two-dimensional river when lacking effectivedata of flow velocity and flow quantity. The IFVM was practically applied to a segment of theXiangjiang River because the Project of Hunan Inland Waterway Multipurpose must be started workingafter the environmental impact assessment for it. The simulation results suggest that there existrather apparent pollution zones of BOD_5 downstream the Dongqiaogang discharger and that of CODdownstream Xiaoxiangjie discharger, but the pollution sources have no impact on the safety of thethree water plants located in this river segment. Although the developed IFVM is to be perfected, itis still a powerful tool under interval uncertainties for water environmental impact assessment,risk analysis, and water quality planning, etc. besides water quality simulation studied in thispaper.展开更多
基金supported by the Hebei Province Graduate Innovation Funding Project(CXZZBS2022029).
文摘With the development of industrial activities,global warming has accelerated due to excessive emission of CO_(2).Enhanced Geothermal System(EGS)utilizes deep geothermal heat for power generation.Although porous medium theory is commonly employed to model geothermal reservoirs in EGS,Hot Dry Rock(HDR)presents a challenge as it consists of impermeable granite with zero porosity,potentially distorting the physical interpretation.To address this,the Lattice Boltzmann Method(LBM)is employed to simulate CO_(2)flow within geothermal reservoirs and the Finite Volume Method(FVM)to solve the energy conservation equation for temperature distribution.This combined method of LBM and FVM is imple-mented using MATLAB.The results showed that the Reynolds numbers(Re)of 3,000 and 8,000 lead to higher heat extraction rates from geothermal reservoirs.However,higher Re values may accelerate thermal breakthrough,posing challenges to EGS operation.Meanwhile,non-equilibrium of density in fractures becomes more pronounced during the system's life cycle,with non-Darcy's law becoming significant at Re values of 3,000 and 8,000.Density stratification due to buoyancy effects significantly impacts temperature distribution within geothermal reservoirs,with buoyancy effects at Re=100 under gravitational influence being noteworthy.Larger Re values(3,000 and 8,000)induce stronger forced convection,leading to more uniform density distribution.The addition of proppant negatively affects heat transfer performance in geothermal reservoirs,especially in single fractures.Practical engineering considerations should determine the quantity of proppant through detailed numerical simulations.
文摘A method to simulate processes of forging and subsequent heat treatment of an axial symmetric rod is formulated in eulerian description and the feasibility is investigated. This method uses finite volume mushes for troching material deformation and an automatically refined facet surface to accurately trace the free surface of the deforming material.In the method,the deforming work piece flows through fixed finite volume meshes using eulerian formulation to describe the conservation laws,Fixed finite volume meshing is particularly suitable for large three-dimensional deformation such as forging because remeshing techniques are not required, which are commonly considered to be the main bottelencek in the ssimulations of large defromation by using the finite element method,By means of this finite volume method, an approach has been developed in the framework of 'metallo-thermo-mechanics' to simulate metallic structure, temperature and stress/strain coupled in the heat treatment process.In a first step of simulation, the heat treatment solver is limited in small deformation hypothesis,and un- coupled with forging. The material is considered as elastic-plastic and takes into account of strain, strain rate and temperature effects on the yield stress.Heat generation due to deformation,heat con- duction and thermal stress are considered.Temperature - dependent phase transformation,stress-in- duced phase transformation,latent heat,transformation stress and strain are included.These ap- proaches are implemented into the commerical commercial computer program MSC/SuperForge and a verification example with experimental date is given as comparison.
基金This paper was supported bythe Natural Science Foundation of Shandong Province (Grant No.y2004f13)
文摘The finite volume method （FVM） has many advantages in 2-D shallow water numerical simulation. In this study, the finite volume method is used with unstructured triangular grids to simulate the tidal currents. The Roe scheme is applied in the calculation of the intercell numerical flux, and the MUSCL method is introduced to improve its accuracy. The time integral is a two-step scheme of forecast and revision. For the verification of the present method, the Stoker＇s problem is calculated and the result is compared with the mathematically analytic solutions. The comparison indicates that the method is feasible. A sea area of a port is used as an example to test the method established here. The result shows that the present computational method is satisfactory, and it could be applied to the engineering fields.
基金Russian Foundation of Basic Research(No. 04-01-08034, 06-01-00293-a)
文摘The paper presents a finite volume numerical method universally applicable for solving both linear and nonlinear aeroacoustics problems on arbitrary unstructured meshes. It is based on the vertexcentered multi-parameter scheme offering up to the 6th accuracy order achieved on the Cartesian meshes. An adaptive dissipation is added for the numerical treatment of possible discontinuities. The scheme properties are studied on a series of test cases, its efficiency is demonstrated at simulating the noise suppression in resonance-type liners.
文摘Based on the first-order upwind and second-order central type of finite volume (UFV and CFV) scheme, upwind and central type of perturbation finite volume (UPFV and CPFV) schemes of the Navier-Stokes equations were developed. In PFV method, the mass fluxes of across the cell faces of the control volume (CV) were expanded into power series of the grid spacing and the coefficients of the power series were determined by means of the conservation equation itself. The UPFV and CPFV scheme respectively uses the same nodes and expressions as those of the normal first-order upwind and second-order central scheme, which is apt to programming. The results of numerical experiments about the flow in a lid-driven cavity and the problem of transport of a scalar quantity in a known velocity field show that compared to the first-order UFV and second-order CFV schemes, upwind PFV scheme is higher accuracy and resolution, especially better robustness. The numerical computation to flow in a lid-driven cavity shows that the under-relaxation factor can be arbitrarily selected ranging from (0.3) to (0.8) and convergence perform excellent with Reynolds number variation from 10~2 to 10~4.
文摘The finite volume method has been successfully applied in several engineering fields and has shown outstanding performance in fluid dynamics simulation. In this paper, the general framework for the simulation ofnear-wellbore systems using the finite volume method is described. The mathematical model and the numerical model developed by the authors are presented and discussed. A radial geometry in the vertical plane was implemented so as to thoroughly describe near-wellbore phenomena. The model was then used to simulate injection tests in an oil reservoir through a horizontal well and proved very powerful to correctly reproduce the transient pressure behavior. The reason for this is the robustness of the method, which is independent of the gridding options because the discretization is performed in the physical space. The model is able to describe the phenomena taking place in the reservoir even in complex situations, i.e. in the presence of heterogeneities and permeability barriers, demonstrating the flexibility of the finite volume method when simulating non-conventional tests. The results are presented in comparison with those obtained with the finite difference numerical approach and with analytical methods, if possible.
基金supported by the National Natural Science Foundation of China(41922027,4214200052)by the Macao Foundation+1 种基金by the Pre-research Project on Civil Aerospace Technologies No.D020308/D020303 funded by China National Space Administrationby the Macao Science and Technology Development Fund,grant No.0001/2019/A1。
文摘Global electromagnetic induction provides an efficient way to probe the electrical conductivity in the Earth’s deep interior.Owing to the increasing geomagnetic data especially from high-accuracy geomagnetic satellites,inverting the Earth’s three-dimensional conductivity distribution on a global scale becomes attainable.A key requirement in the global conductivity inversion is to have a forward solver with high-accuracy and efficiency.In this study,a finite volume method for global electromagnetic induction forward modeling is developed based on unstructured grids.Arbitrary polyhedral grids are supported in our algorithms to obtain high geometric adaptability.We employ a cell-centered collocated variable arrangement which allows convenient discretization for complex geometries and straightforward implementation of multigrid technique.To validate the method,we test our code with two synthetic models and compare our finite volume results with an analytical solution and a finite element numerical solution.Good agreements are observed between our solution and other results,indicating acceptable accuracy of the proposed method.
文摘The examination of an unstructured finite volume method for structural dynamics is assessed for simulations of systematic impact dynamics. A robust display dual-time stepping method is utilized to obtain time accurate solutions. The study of impact dynamics is a complex problem that should consider strength models and state equations to describe the mechanical behavior of materials. The current method has several features, l） Discrete equations of unstructured finite volume method naturally follow the conservation law. 2） Display dual-time stepping method is suitable for the analysis of impact dynamic problems of time accurate solutions. 3） The method did not produce grid distortion when large deformation appeared. The method is validated by the problem of impact dynamics of an elastic plate with initial conditions and material properties. The results validate the finite element numerical data
基金supported by National Natural Science Foundation of China“Numerical simulation of fractured reservoirs based on nonstructural hexahedral grid model and parallel computation”(No.:51474179).
文摘In order to simulate the flowing of shale gas in multi-scale media,we established a mathematical model for the unsteady seepage of multi-stage fractured horizontal wells in shale gas reservoirs in consideration of the flowing characteristics of shale gas in matrix,natural fractures and large-scale artificial fractures.Grid division in the simulation region was carried out by means of nonstructural tetrahedral grid.Then,a 3D numerical model for the seepage of shale gas was established discretely using finite volume method and solved using sequence solution method.Finally,the production performance of multi-stage fractured horizontal wells in shale gas reservoirs and the reservoir pressure distribution were simulated,and the simulation results were analyzed.And the following research results were obtained.First,the gas production rates of multi-stage fractured horizontal wells calculated by this newly established numerical simulation method are basically consistent with the calculation results by the commercial numerical simulation software Eclipse,which proves that this new model is accurate and feasible.Second,the gas production rates of horizontal wells calculated by the sequential solution method are different from those calculated by the fully implicit solution method in the early production stages,but as the calculation progresses,both of them tend to be consistent,which further verifies the accuracy of this new model.Third,desorbed gas plays a supplementary role to reservoir pressure,but its function is limited,and its effect on gas production is little.As the production goes on,the percentage of desorbed gas increases gradually.Fourth,the key to the stimulation of shale-gas horizontal wells is to determine the number of fractured sections rationally and create longer artificial fractures.In conclusion,the research results are conducive to the design of stimulated reservoir volumes(SRVs)of shale gas reservoirs and the prediction of production performance of multi-stage fractured horizontal wells.
文摘Ionosphere is the layer of atmosphere which plays an important role both in space based navigation,positioning and communication systems and HF signals. The structure of the electron density is a function of spatio-temporal variables. The electrodynamic medium is also influenced with earth’s magnetic field, atmospheric chemistry and plasma flow and diffusion under earth’s gravitation. Thus, the unified dynamo equation for the ionosphere is a second order partial differential equation for quasi-static electric potential with variable spatial coefficients. In this study, the inhomogeneous and anisotropic nature of ionosphere that can be formulated as a divergence equation is solved numerically using Finite Volume Method for the first time. The ionosphere and the operators are discretized for the midlatitude region and the solution domain is investigated for Dirichlet type boundary conditions that are built in into the diffusion equation. The analysis indicates that FVM can be a powerful tool in obtaining parametric electrostatic potential distribution in ionosphere.
基金The Major State Basic Research (1999032803) of China, the NNSF (10372052, 10271066)of China and the Doctorate Foundation (20030422047) of the Ministry of Education of China.
文摘In this paper, we present a finite volume framework for second order elliptic equations with variable coefficients based on cubic Hermite element. We prove the optimal H1 norm error estimates. A numerical example is given at the end to show the feasibility of the method.
文摘The fluid-structure interaction may occur in space launch vehicles,which would lead to bad performance of vehicles,damage equipments on vehicles,or even affect astronauts＇ health.In this paper,analysis on dynamic behavior of liquid oxygen （LOX） feeding pipe system in a large scale launch vehicle is performed,with the effect of fluid-structure interaction （FSI） taken into consideration.The pipe system is simplified as a planar FSI model with Poisson coupling and junction coupling.Numerical tests on pipes between the tank and the pump are solved by the finite volume method.Results show that restrictions weaken the interaction between axial and lateral vibrations.The reasonable results regarding frequencies and modes indicate that the FSI affects substantially the dynamic analysis,and thus highlight the usefulness of the proposed model.This study would provide a reference to the pipe test,as well as facilitate further studies on oscillation suppression.
基金Supported by the Research Starting Funds for Imported Talents of Ningxia University under Grant No BQD2012011
文摘Three-dimensional simulations of ferroelectric hysteresis and butterfly loops are carried out based on solving the time dependent Ginzburg-Landau equations using a finite volume method. The influence of externally mechanical loadings with a tensile strain and a compressive strain on the hysteresis and butterfly loops is studied numerically. Different from the traditional finite element and finite difference methods, the finite volume method is applicable to simulate the ferroelectric phase transitions and properties of ferroelectric materials even for more realistic and physical problems.
基金funded by the German Federal Ministry of Education and Research within the Competence Cluster Recycling&Green Battery(greenBatt)under the grant number 03XP0336A.The authors are responsible for the contents of this publication.
文摘Efficient recycling of lithium metasilicate(Li_(2)SiO_(3))from lithium-containing slag via a pyrometallurgical route demands a comprehensive understanding of its solidification process in the slag reactor.A simulation framework is developed to predict the heterogeneous phase distribution of Li_(2)SiO_(3),the temperature and velocity fields considering density changes in the solidifying melt,on the apparatus scale.This framework integrates thermodynamic models via calculation of phase diagrams with the enthalpy-porosity technique and the volume of fluid method within a finite volume approach,ensuring thermodynamic consistency and adherence to mass balance.Thus,the formation of Li_(2)SiO_(3)from the liquid slag composed of Li_(2)O-SiO_(2)is described in space and temporal fields.Thereby,the interrelationship between the temperature field,enthalpy field,velocity field,and phase distribution of Li_(2)SiO_(3)is revealed.It is shown that the lower temperature on reactor boundaries prompts the earlier formation of Li_(2)SiO_(3)in the vicinity of the boundaries,which subsequently induces a downward flow due to the higher density of Li_(2)SiO_(3).The predicted global mass fraction of Li_(2)SiO_(3)under non-equilibrium conditions is 11.5 wt%lower than that calculated using the global equilibrium assumption.This demonstrates the global non-equilibrium behavior on the process scale and its consequences on slag solidification.
基金supported in part by the NSFC Grant 12271499supported in part by the R&D project of Pazhou Lab(Huangpu)under Grant 2023K0609 and the NSFC Grant 12126604.
文摘In this paper,we concentrate on high-order boundary treatments for finite volume methods solving hyperbolic conservation laws.The complex geometric physical domain is covered by a Cartesian mesh,resulting in the boundary intersecting the grids in various fashions.We propose two approaches to evaluate the cell averages on the ghost cells near the boundary.Both of them start from the inverse Lax-Wendroff(ILW)procedure,in which the normal spatial derivatives at inflow boundaries can be obtained by repeatedly using the governing equations and boundary conditions.After that,we can get an accurate evaluation of the ghost cell average by a Taylor expansion joined with high-order extrapolation,or by a Hermite extrapolation coupling with the cell averages on some“artificial”inner cells.The stability analysis is provided for both schemes,indicating that they can avoid the so-called“small-cell”problem.Moreover,the second method is more efficient under the premise of accuracy and stability.We perform numerical experiments on a collection of examples with the physical boundary not aligned with the grids and with various boundary conditions,indicating the high-order accuracy and efficiency of the proposed schemes.
基金supported in part by the NSF of China(Grant No.12171141)by the Science and Technology Attack Plan Project of Henan province(Grant No.222102210049)supported in part by the NSF of China(Grant No.62102134).
文摘In this paper,we consider the electromagnetic wave scattering problem from a periodic chiral structure.The scattering problem is simplified to a two-dimensional problem,and is discretized by a finite volume method combined with the perfectly matched layer(PML)technique.A residual-type a posteriori error estimate of the PML finite volume method is analyzed and the upper and lower bounds on the error are established in the H^(1)-norm.The crucial part of the a posteriori error analysis is to derive the error representation formula and use a L^(2)-orthogonality property of the residual which plays a similar role as the Galerkin orthogonality.An adaptive PML finite volume method is proposed to solve the scattering problem.The PML parameters such as the thickness of the layer and the medium property are determined through sharp a posteriori error estimate.Finally,numerical experiments are presented to illustrate the efficiency of the proposed method.
基金supported by the Program for Changjiang Scholars and Innovative Research Team in University (Grant No.IRT0717)the Scientific Research Foundation for the Returned Overseas Chinese Scholars,State Education Ministrysupported by the Natural Science Foundation of Hohai University (Grant No.2008433111)
文摘The discrete version of solute transport equation for porous matrix depicted with the continuum model and the discrete fractured-network model are derived for fractured rocks with the Finite Volume Method （FVM）. The two models are coupled according to the continuity condition of hydraulic head and concentration and the conservation of flow flux and mass flux in the contact plane between porous matrix and fractures. Numerical results show that the simulated concentration of the coupling model based on the FVM agrees well with that from analytical solution, which demonstrates that the coupling model can effectively be applied to the simulation of solute transport in fractured rocks.
基金supported by the National Basic Research Program of China (973 Program, Grant No. 2005CB221304)the Scientific Research Project of the Heilongjiang Education Department (Grant No.11521003)the Graduate Innovation Scientific Research Funds Project of Heilongjiang (Grant No.YJSCX2008-047HLJ)
文摘A finite volume method for the numerical solution of viscoelastic flows is given. The flow of a differential Upper-Convected Maxwell （UCM） fluid through an abrupt expansion has been chosen as a prototype example. The conservation and constitutive equations are solved using the Finite Volume Method （FVM） in a staggered grid with an upwind scheme for the viscoelastic stresses and a hybrid scheme for the velocities. An enhanced-in-speed pressure-correction algorithm is used and a method for handling the source term in the momentum equations is employed. Improved accuracy is achieved by a special discretization of the boundary conditions. Stable solutions are obtained for higher Weissenberg number （We）, further extending the range of simulations with the FVM. Numerical results show the viscoelasticity of polymer solutions is the main factor influencing the sweeo efficiency.
基金supported by the National Basic Research Program of China(Grant No.2013CB430403)the Public Science and Technology Research Funds Projects of Ocean(Grant No.201205023)+3 种基金the Program for Liaoning Excellent Talents in University(Grant No.LJQ2013077)the Science and Technology Foundation of Dalian City(Grant No.2013J21DW009)the Special Funds for Postdoctoral Innovative Projects of Liaoning Province(Grant No.2011921018)the Special Funds for Talent Projects of Dalian Ocean University(Grant No.SYYJ2011004)
文摘The purpose of this study is to set up a dynamically linked 1D and 2D hydrodynamic and sediment transport models for dam break flow.The 1D-2D coupling model solves the generalized shallow water equations,the non-equilibrium sediment transport and bed change equations in a coupled fashion using an explicit finite volume method.It considers interactions among transient flow,strong sediment transport and rapid bed change by including bed change and variable flow density in the flow continuity and momentum equations.An unstructured Quadtree rectangular grid with local refinement is used in the 2D model.The intercell flux is computed by the HLL approximate Riemann solver with shock captured capability for computing the dry-to-wet interface for all models.The effects of pressure and gravity are included in source term in this coupling model which can simplify the computation and eliminate numerical imbalance between source and flux terms.The developed model has been tested against experimental and real-life case of dam-break flow over fix bed and movable bed.The results are compared with analytical solution and measured data with good agreement.The simulation results demonstrate that the coupling model is capable of calculating the flow,erosion and deposition for dam break flows in complicated natural domains.
文摘Under the interval uncertainties, by incorporating the discretization form offinite volume method and interval algebra theory, an Interval Finite Volume Method (IF-VM) wasdeveloped to solve water quality simulation issues for two-dimensional river when lacking effectivedata of flow velocity and flow quantity. The IFVM was practically applied to a segment of theXiangjiang River because the Project of Hunan Inland Waterway Multipurpose must be started workingafter the environmental impact assessment for it. The simulation results suggest that there existrather apparent pollution zones of BOD_5 downstream the Dongqiaogang discharger and that of CODdownstream Xiaoxiangjie discharger, but the pollution sources have no impact on the safety of thethree water plants located in this river segment. Although the developed IFVM is to be perfected, itis still a powerful tool under interval uncertainties for water environmental impact assessment,risk analysis, and water quality planning, etc. besides water quality simulation studied in thispaper.
