The element energy projection （EEP） method for computation of super- convergent resulting in a one-dimensional finite element method （FEM） is successfully used to self-adaptive FEM analysis of various linear probl...The element energy projection （EEP） method for computation of super- convergent resulting in a one-dimensional finite element method （FEM） is successfully used to self-adaptive FEM analysis of various linear problems, based on which this paper presents a substantial extension of the whole set of technology to nonlinear problems. The main idea behind the technology transfer from linear analysis to nonlinear analysis is to use Newton＇s method to linearize nonlinear problems into a series of linear problems so that the EEP formulation and the corresponding adaptive strategy can be directly used without the need for specific super-convergence formulation for nonlinear FEM. As a re- sult, a unified and general self-adaptive algorithm for nonlinear FEM analysis is formed. The proposed algorithm is found to be able to produce satisfactory finite element results with accuracy satisfying the user-preset error tolerances by maximum norm anywhere on the mesh. Taking the nonlinear ordinary differential equation （ODE） of second-order as the model problem, this paper describes the related fundamental idea, the imple- mentation strategy, and the computational algorithm. Representative numerical exam- ples are given to show the efficiency, stability, versatility, and reliability of the proposed approach.展开更多
A novel flywheel energy storage （FES） motor/generator （M/G） was proposed for marine systems. The purpose was to improve the power quality of a marine power system （MPS） and strengthen the energy recycle. Two str...A novel flywheel energy storage （FES） motor/generator （M/G） was proposed for marine systems. The purpose was to improve the power quality of a marine power system （MPS） and strengthen the energy recycle. Two structures including the magnetic or non-magnetic inner-rotor were contrasted in the magnetostatic field by using finite element analysis （FEA）. By optimally designing the size parameters, the average speed of FEA results of was 17 200 r/m, and the current was controlled between 62 and 68 A in the transient field. The electrical machine electromagnetism design was further optimized by the FEA in the temperature field, to find the local overheating point under the normal operation condition and provide guidance for the cooling system. Finally, it can be concluded from the comprehensive physical field analysis that the novel redundant structure M/G can improve the efficiency of the M/G and maintain the stability of the MPS.展开更多
Prediction of vibration energy responses of structures with uncertainties is of interest in many fields. The energy density control equation for one-dimensional structure is provided firstly. Interval analysis method ...Prediction of vibration energy responses of structures with uncertainties is of interest in many fields. The energy density control equation for one-dimensional structure is provided firstly. Interval analysis method is applied to the control equation to obtain the range of energy density responses of structures with interval parameters. A cantilever beam with interval-valued damping coefficient is exemplified to carry out a simulation. The result shows that the mean value of energy density from the interval analysis method is the same as that from a probabilistic method which validates the interval analysis method. Besides, the response range from the interval analysis method is wider and includes that from the probabilistic method which indicates the interval analysis method is a more conservative method and is safer in realistic engineering structures.展开更多
To take into account the influence of uncetainties on the dynamic response of the vibro-acousitc structure, a hybrid modeling technique combining the finite element method（FE）and the statistic energy analysis（SEA）...To take into account the influence of uncetainties on the dynamic response of the vibro-acousitc structure, a hybrid modeling technique combining the finite element method（FE）and the statistic energy analysis（SEA） is proposed to analyze vibro-acoustics responses with uncertainties at middle frequencies. The mid-frequency dynamic response of the framework-plate structure with uncertainties is studied based on the hybrid FE-SEA method and the Monte Carlo（MC）simulation is performed so as to provide a benchmark comparison with the hybrid method. The energy response of the framework-plate structure matches well with the MC simulation results, which validates the effectiveness of the hybrid FE-SEA method considering both the complexity of the vibro-acoustic structure and the uncertainties in mid-frequency vibro-acousitc analysis. Based on the hybrid method, a vibroacoustic model of a construction machinery cab with random properties is established, and the excitations of the model are measured by experiments. The responses of the sound pressure level of the cab and the vibration power spectrum density of the front windscreen are calculated and compared with those of the experiment. At middle frequencies, the results have a good consistency with the tests and the prediction error is less than 3. 5dB.展开更多
In the present work, the response of closed-cell aluminum foams under low-velocity impact has been studied numerically and experimentally. Computerized tomography is employed to access three-dimensional (3D) microstru...In the present work, the response of closed-cell aluminum foams under low-velocity impact has been studied numerically and experimentally. Computerized tomography is employed to access three-dimensional (3D) microstructure of the closed-cell aluminum foam. Effective parameters including foam density and the velocity of impactor on foam dynamic behavior are investigated. In order to show the validity and accuracy of results, some static experiments and low-velocity impact tests have been conducted. Results in dicate a remarkable agree me nt between the simulation and experimental data. Moreover, the results show that by increasing the density of foam samples, the highest difference between numerical and experimenidi results for peak stress and absorbed energy are 35.9% and 6.9%, respectively, which is related to the highest density. For impact velocities ranging from 3.1 to 4.2 m/s, the maximum discrepancy in peak stress and absorbed energy occur at an inipact velocity of 3.1 m/s in which corresponding errors are 33.3% and 6.6%, respectively. For the impact velocity of 40 m/s, the highest increase in peak stress and absorbed energy are 667.9% and 370.3% associated with the density of 0.5 and 0.3 g/cm^3, respectively.展开更多
The current research of supporting and transmission system in flywheel energy storage system(FESS) focuses on the low consumption design. However, friction loss is a non-negligible factor in the high-speed but lightwe...The current research of supporting and transmission system in flywheel energy storage system(FESS) focuses on the low consumption design. However, friction loss is a non-negligible factor in the high-speed but lightweight FESS energy and momentum storage with mechanical-type supporting system. In order to realize the support system without mechanical loss and to maximize the e ciency of the flywheel battery, a permanent magnet biased magnetic bearings(PMBMB) is applied to the FESS with the advantages of low loss, high critical speed, flexible controllability and compact structure. In this frame, the relevant research of three degrees of freedom(3-DOF) PMBMB for a new type FESS is carried out around the working principle, structural composition, coupling characteristics analysis, mathematical model, and structural design. In order to verify the performance of the 3-DOF PMBMB, the radial force mathematical model and the coupling determination equations of radial two DOF are calculated according to an equivalent magnetic circuit, and radial–axial coupling is analyzed through finite element analysis. Moreover, a control system is presented to solve the control problems in practical applications. The rotor returns to the balanced position in 0.05 s and maintains stable suspension. The displacement fluctuation is approximately 40 μm in the y direction and 30 μm in the x direction. Test results indicate that the dynamic rotor of the proposed flywheel energy storage system with PMBMB has excellent characteristics, such as good start-of-suspension performance and stable suspension characteristics. The proposed research provides the instruction to design and control a low loss support system for FESS.展开更多
In order to improve the mass efficiency of an automotive soundproof package, it is important to predict the middle to high frequency range of noise and vibration during vehicle operation. A hybrid method of experiment...In order to improve the mass efficiency of an automotive soundproof package, it is important to predict the middle to high frequency range of noise and vibration during vehicle operation. A hybrid method of experimental and analytical SEA （statistical energy analysis） has been applied for the prediction of air-borne noise. However, for predicting structure-borne noise, there are no definitive simulation methods that can address the soundproof specifications in an actual vehicle. Thus, in this paper, a FEM （finite element method）＇SEA hybrid method is used. The FEM＇SEA hybrid method predicts structure-borne noise in the middle to high frequency range. First, we explain the basic concept of the FEM＇SEA hybrid method; Second, we describe our experiment to verify the analytical results of the FEM＇SEA hybrid method; Third, we provide the details of the FEM model versus the FEM＇SEA hybrid model; Finally, we verify the validity and availability of the FEM＇SEA hybrid method through comparisons of the FEM analysis results, FEM-SEA analysis results and measured results.展开更多
In order to pursue good crushing load uniformity and enchance energy absorption efficiency of conventional honeycombs, a kind of bio-inspired hierarchical honeycomb model is proposed by mimicking the arched crab shell...In order to pursue good crushing load uniformity and enchance energy absorption efficiency of conventional honeycombs, a kind of bio-inspired hierarchical honeycomb model is proposed by mimicking the arched crab shell structures. Three bio-inspired hierarchical honeycombs(BHHs) with different topologies are designed by replacing each vertex of square honeycombs with smaller arc-shaped structures. The effects of hierarchical topologies and multi-material layout on in-plane dynamic crushings and absorbed-energy capacities of the BHHs are explored based on the explicit finite element(FE) analysis.Different deformation modes can be observed from the BHHs, which mainly depend upon hierarchical topologies and impact velocities. According to energy efficiency method and one-dimensional(1D) shock theory, calculation formulas of densification strains and plateau stresses for the BHHs are derived to characterize the dynamic bearing capacity, which is consistent well with FE results. Compared with conventional honeycombs, the crushing load efficiency and energy absorption capacity of the BHHs can be improved by changing the proper hierarchical topology and multi-material layout. These researches will provide theoretical guidance for innovative design and dynamic response performance controllability of honeycombs.展开更多
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 w...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.展开更多
In order to reduce casualties and property losses in a collision accident, thin-walled structure has been extensively used as energy absorber in crashworthiness design of train. With the help of energy absorber, colli...In order to reduce casualties and property losses in a collision accident, thin-walled structure has been extensively used as energy absorber in crashworthiness design of train. With the help of energy absorber, collision kinetic energy can be controllably dissipated by the plastic deformation of structures. A new kind of multi-cell thin-walled structure called as bitubular polygonal tubes with internal walls(BPTIW) was constructed. The crashworthiness characteristics of BPTIWs were investigated by LS-DYNA. It can be found that the BPTIW with 12 sides has the most excellent crashworthiness characteristics. Therefore, based on response surface method(RSM) and multiobjective particle optimization(MOPSO) algorithm, the BPTIW with 12 sides was selected to optimize the dimensions of cross-sectional configuration under different constraints of energy absorption(EA) and crushing peak force(CPF). The results show that the optimal designs of BPTIW12 under different constraints present excellent crashworthiness characteristics and can be used in the practical engineering.展开更多
At present, the development of the traditional car is more and more troubled by the high cost of environmental pollution and oil prices, many countries have paid increasingly attention to the research and development ...At present, the development of the traditional car is more and more troubled by the high cost of environmental pollution and oil prices, many countries have paid increasingly attention to the research and development of electric vehicles. And vehicle battery box, as the heart of the automobile power system, and many difficulties still exist in its research and development. This paper is based on ANSYS. By using the finite element theory, it is to analyze the modal characteristics of the battery box and frequency vibration characteristics. Having a more comprehensive grasp of the dynamic performance of the battery box is the key to solve the new energy automotive research and development of issues.展开更多
In this paper the authors discuss a numerical simulation problem of three-dimensional compressible contamination treatment from nuclear waste. The mathematical model, a nonlinear convection-diffusion system of four PD...In this paper the authors discuss a numerical simulation problem of three-dimensional compressible contamination treatment from nuclear waste. The mathematical model, a nonlinear convection-diffusion system of four PDEs, determines four major physical unknowns: the pressure, the concentrations of brine and radionuclide, and the temperature. The pressure is solved by a conservative mixed finite volume element method, and the computational accuracy is improved for Darcy velocity. Other unknowns are computed by a composite scheme of upwind approximation and mixed finite volume element. Numerical dispersion and nonphysical oscillation are eliminated, and the convection-dominated diffusion problems are solved well with high order computational accuracy. The mixed finite volume element is conservative locally, and get the objective functions and their adjoint vector functions simultaneously. The conservation nature is an important character in numerical simulation of underground fluid. Fractional step difference is introduced to solve the concentrations of radionuclide factors, and the computational work is shortened significantly by decomposing a three-dimensional problem into three successive one-dimensional problems. By the theory and technique of a priori estimates of differential equations, we derive an optimal order estimates in L2norm. Finally, numerical examples show the effectiveness and practicability for some actual problems.展开更多
基金supported by the National Natural Science Foundation of China(Nos.51378293,51078199,50678093,and 50278046)the Program for Changjiang Scholars and the Innovative Research Team in University of China(No.IRT00736)
文摘The element energy projection （EEP） method for computation of super- convergent resulting in a one-dimensional finite element method （FEM） is successfully used to self-adaptive FEM analysis of various linear problems, based on which this paper presents a substantial extension of the whole set of technology to nonlinear problems. The main idea behind the technology transfer from linear analysis to nonlinear analysis is to use Newton＇s method to linearize nonlinear problems into a series of linear problems so that the EEP formulation and the corresponding adaptive strategy can be directly used without the need for specific super-convergence formulation for nonlinear FEM. As a re- sult, a unified and general self-adaptive algorithm for nonlinear FEM analysis is formed. The proposed algorithm is found to be able to produce satisfactory finite element results with accuracy satisfying the user-preset error tolerances by maximum norm anywhere on the mesh. Taking the nonlinear ordinary differential equation （ODE） of second-order as the model problem, this paper describes the related fundamental idea, the imple- mentation strategy, and the computational algorithm. Representative numerical exam- ples are given to show the efficiency, stability, versatility, and reliability of the proposed approach.
基金Supported by the Fundamental Research Funds for the Central Universities under Grants Nos. HEUCF101706 and HEUCF111705
文摘A novel flywheel energy storage （FES） motor/generator （M/G） was proposed for marine systems. The purpose was to improve the power quality of a marine power system （MPS） and strengthen the energy recycle. Two structures including the magnetic or non-magnetic inner-rotor were contrasted in the magnetostatic field by using finite element analysis （FEA）. By optimally designing the size parameters, the average speed of FEA results of was 17 200 r/m, and the current was controlled between 62 and 68 A in the transient field. The electrical machine electromagnetism design was further optimized by the FEA in the temperature field, to find the local overheating point under the normal operation condition and provide guidance for the cooling system. Finally, it can be concluded from the comprehensive physical field analysis that the novel redundant structure M/G can improve the efficiency of the M/G and maintain the stability of the MPS.
基金Sponsored by the National Natural Science Foundation of China(Grant No.11072066)
文摘Prediction of vibration energy responses of structures with uncertainties is of interest in many fields. The energy density control equation for one-dimensional structure is provided firstly. Interval analysis method is applied to the control equation to obtain the range of energy density responses of structures with interval parameters. A cantilever beam with interval-valued damping coefficient is exemplified to carry out a simulation. The result shows that the mean value of energy density from the interval analysis method is the same as that from a probabilistic method which validates the interval analysis method. Besides, the response range from the interval analysis method is wider and includes that from the probabilistic method which indicates the interval analysis method is a more conservative method and is safer in realistic engineering structures.
基金Science and Technology Support Planning of Jiangsu Province(No.BE2014133)the Open Foundation of Key Laboratory of Underw ater Acoustic Signal Processing(No.UASP1301)the Prospective Joint Research Project of Jiangsu province(No.BY2014127-01)
文摘To take into account the influence of uncetainties on the dynamic response of the vibro-acousitc structure, a hybrid modeling technique combining the finite element method（FE）and the statistic energy analysis（SEA） is proposed to analyze vibro-acoustics responses with uncertainties at middle frequencies. The mid-frequency dynamic response of the framework-plate structure with uncertainties is studied based on the hybrid FE-SEA method and the Monte Carlo（MC）simulation is performed so as to provide a benchmark comparison with the hybrid method. The energy response of the framework-plate structure matches well with the MC simulation results, which validates the effectiveness of the hybrid FE-SEA method considering both the complexity of the vibro-acoustic structure and the uncertainties in mid-frequency vibro-acousitc analysis. Based on the hybrid method, a vibroacoustic model of a construction machinery cab with random properties is established, and the excitations of the model are measured by experiments. The responses of the sound pressure level of the cab and the vibration power spectrum density of the front windscreen are calculated and compared with those of the experiment. At middle frequencies, the results have a good consistency with the tests and the prediction error is less than 3. 5dB.
文摘In the present work, the response of closed-cell aluminum foams under low-velocity impact has been studied numerically and experimentally. Computerized tomography is employed to access three-dimensional (3D) microstructure of the closed-cell aluminum foam. Effective parameters including foam density and the velocity of impactor on foam dynamic behavior are investigated. In order to show the validity and accuracy of results, some static experiments and low-velocity impact tests have been conducted. Results in dicate a remarkable agree me nt between the simulation and experimental data. Moreover, the results show that by increasing the density of foam samples, the highest difference between numerical and experimenidi results for peak stress and absorbed energy are 35.9% and 6.9%, respectively, which is related to the highest density. For impact velocities ranging from 3.1 to 4.2 m/s, the maximum discrepancy in peak stress and absorbed energy occur at an inipact velocity of 3.1 m/s in which corresponding errors are 33.3% and 6.6%, respectively. For the impact velocity of 40 m/s, the highest increase in peak stress and absorbed energy are 667.9% and 370.3% associated with the density of 0.5 and 0.3 g/cm^3, respectively.
基金Supported by National Natural Science Foundation of China(Grant Nos.51707082,51877101,51607080)Jiangsu Provincial Natural Science Foundation of China(Grant Nos.BK20170546,BK20150510)+1 种基金China Postdoctoral Science Foundation(Grant No.2017M620192)Priority Academic Program Development of Jiangsu Higher Education Institutions
文摘The current research of supporting and transmission system in flywheel energy storage system(FESS) focuses on the low consumption design. However, friction loss is a non-negligible factor in the high-speed but lightweight FESS energy and momentum storage with mechanical-type supporting system. In order to realize the support system without mechanical loss and to maximize the e ciency of the flywheel battery, a permanent magnet biased magnetic bearings(PMBMB) is applied to the FESS with the advantages of low loss, high critical speed, flexible controllability and compact structure. In this frame, the relevant research of three degrees of freedom(3-DOF) PMBMB for a new type FESS is carried out around the working principle, structural composition, coupling characteristics analysis, mathematical model, and structural design. In order to verify the performance of the 3-DOF PMBMB, the radial force mathematical model and the coupling determination equations of radial two DOF are calculated according to an equivalent magnetic circuit, and radial–axial coupling is analyzed through finite element analysis. Moreover, a control system is presented to solve the control problems in practical applications. The rotor returns to the balanced position in 0.05 s and maintains stable suspension. The displacement fluctuation is approximately 40 μm in the y direction and 30 μm in the x direction. Test results indicate that the dynamic rotor of the proposed flywheel energy storage system with PMBMB has excellent characteristics, such as good start-of-suspension performance and stable suspension characteristics. The proposed research provides the instruction to design and control a low loss support system for FESS.
文摘In order to improve the mass efficiency of an automotive soundproof package, it is important to predict the middle to high frequency range of noise and vibration during vehicle operation. A hybrid method of experimental and analytical SEA （statistical energy analysis） has been applied for the prediction of air-borne noise. However, for predicting structure-borne noise, there are no definitive simulation methods that can address the soundproof specifications in an actual vehicle. Thus, in this paper, a FEM （finite element method）＇SEA hybrid method is used. The FEM＇SEA hybrid method predicts structure-borne noise in the middle to high frequency range. First, we explain the basic concept of the FEM＇SEA hybrid method; Second, we describe our experiment to verify the analytical results of the FEM＇SEA hybrid method; Third, we provide the details of the FEM model versus the FEM＇SEA hybrid model; Finally, we verify the validity and availability of the FEM＇SEA hybrid method through comparisons of the FEM analysis results, FEM-SEA analysis results and measured results.
基金the financial support provided by the Natural Science Foundation of Hebei Province of China [No. A2020502005]the Fundamental Research Funds for the Central Universities [No. 2020MS113]Science & Technology Program of Baoding [No. 1911ZG019]。
文摘In order to pursue good crushing load uniformity and enchance energy absorption efficiency of conventional honeycombs, a kind of bio-inspired hierarchical honeycomb model is proposed by mimicking the arched crab shell structures. Three bio-inspired hierarchical honeycombs(BHHs) with different topologies are designed by replacing each vertex of square honeycombs with smaller arc-shaped structures. The effects of hierarchical topologies and multi-material layout on in-plane dynamic crushings and absorbed-energy capacities of the BHHs are explored based on the explicit finite element(FE) analysis.Different deformation modes can be observed from the BHHs, which mainly depend upon hierarchical topologies and impact velocities. According to energy efficiency method and one-dimensional(1D) shock theory, calculation formulas of densification strains and plateau stresses for the BHHs are derived to characterize the dynamic bearing capacity, which is consistent well with FE results. Compared with conventional honeycombs, the crushing load efficiency and energy absorption capacity of the BHHs can be improved by changing the proper hierarchical topology and multi-material layout. These researches will provide theoretical guidance for innovative design and dynamic response performance controllability of honeycombs.
基金Project supported by the Major State Basic Research Program of China (No. 19990328)the National Tackling Key Problems Program (No. 20050200069)+4 种基金the National Natural Science Foundation of China (Nos. 10771124, 10372052, 11101244, and 11271231)the Doctorate Foundation of the Ministry of Education of China (No. 20030422047)the Shandong Province Natural Science Foundation (No. ZR2009AQ012)the Independent Innovation Foundation of Shandong University(No. 2010TS031)the Scientific Research Award Fund for Excellent Middle-Aged and Young Scientists of Shandong Province (No. BS2009NJ003)
文摘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.
基金Project(CX2016B047)supported by Hunan Provincial Innovation Foundation For Postgraduate,ChinaProjects(U1334208,51405516,51275532)supported by the National Natural Science Foundation of ChinaProject(2016YFB1200403)supported by the National Key Research and Development Proguam of China
文摘In order to reduce casualties and property losses in a collision accident, thin-walled structure has been extensively used as energy absorber in crashworthiness design of train. With the help of energy absorber, collision kinetic energy can be controllably dissipated by the plastic deformation of structures. A new kind of multi-cell thin-walled structure called as bitubular polygonal tubes with internal walls(BPTIW) was constructed. The crashworthiness characteristics of BPTIWs were investigated by LS-DYNA. It can be found that the BPTIW with 12 sides has the most excellent crashworthiness characteristics. Therefore, based on response surface method(RSM) and multiobjective particle optimization(MOPSO) algorithm, the BPTIW with 12 sides was selected to optimize the dimensions of cross-sectional configuration under different constraints of energy absorption(EA) and crushing peak force(CPF). The results show that the optimal designs of BPTIW12 under different constraints present excellent crashworthiness characteristics and can be used in the practical engineering.
文摘At present, the development of the traditional car is more and more troubled by the high cost of environmental pollution and oil prices, many countries have paid increasingly attention to the research and development of electric vehicles. And vehicle battery box, as the heart of the automobile power system, and many difficulties still exist in its research and development. This paper is based on ANSYS. By using the finite element theory, it is to analyze the modal characteristics of the battery box and frequency vibration characteristics. Having a more comprehensive grasp of the dynamic performance of the battery box is the key to solve the new energy automotive research and development of issues.
基金supported by the Natural Science Foundation of Shangdong Province (Grant No.ZR2021MA019)Natural Science Foundation of Hunan Province (Grant No.2018JJ2028)。
文摘In this paper the authors discuss a numerical simulation problem of three-dimensional compressible contamination treatment from nuclear waste. The mathematical model, a nonlinear convection-diffusion system of four PDEs, determines four major physical unknowns: the pressure, the concentrations of brine and radionuclide, and the temperature. The pressure is solved by a conservative mixed finite volume element method, and the computational accuracy is improved for Darcy velocity. Other unknowns are computed by a composite scheme of upwind approximation and mixed finite volume element. Numerical dispersion and nonphysical oscillation are eliminated, and the convection-dominated diffusion problems are solved well with high order computational accuracy. The mixed finite volume element is conservative locally, and get the objective functions and their adjoint vector functions simultaneously. The conservation nature is an important character in numerical simulation of underground fluid. Fractional step difference is introduced to solve the concentrations of radionuclide factors, and the computational work is shortened significantly by decomposing a three-dimensional problem into three successive one-dimensional problems. By the theory and technique of a priori estimates of differential equations, we derive an optimal order estimates in L2norm. Finally, numerical examples show the effectiveness and practicability for some actual problems.
