For the three-dimensional convection-dominated problem of dynamics of fluids in porous media, the second order upwind finite difference fractional steps schemes applicable to parallel arithmetic are put forward. Fract...For the three-dimensional convection-dominated problem of dynamics of fluids in porous media, the second order upwind finite difference fractional steps schemes applicable to parallel arithmetic are put forward. Fractional steps techniques are needed to convert a multi-dimensional problem into a series of successive one-dimensional problems. Some techniques, such as calculus of variations, energy method, multiplicative commutation rule of difference operators, decomposition of high order difference operators, and the theory of prior estimates are adopted. Optimal order estimates are derived to determine the error in the second order approximate solution. These methods have already been applied to the numerical simulation of migration-accumulation of oil resources and predicting the consequences of seawater intrusion and protection projects.展开更多
For combinatorial system of multilayer dynamics of fluids in porous media, the second order and first order upwind finite difference fractional steps schemes applicable to parallel arithmetic are put forward and two-d...For combinatorial system of multilayer dynamics of fluids in porous media, the second order and first order upwind finite difference fractional steps schemes applicable to parallel arithmetic are put forward and two-dimensional and three-dimensional schemes are used to form a complete set. Some techniques, such as implicit-explicit difference scheme, calculus of variations, multiplicative commutation rule of difference operators, decomposition of high order difference operators and prior estimates, are adopted. Optimal order estimates in L 2 norm are derived to determine the error in the second order approximate solution. This method has already been applied to the numerical simulation of migration-accumulation of oil resources. Keywords: combinatorial system, multilayer dynamics of fluids in porous media, two-class upwind finite difference fractional steps method, convergence, numerical simulation of energy sources.展开更多
For the three-dimensional seawater intrusion and protection system, the model of dynamics of fluids in porous media and the modified upwind finite difference fractional steps schemes are put forward. Based on the nume...For the three-dimensional seawater intrusion and protection system, the model of dynamics of fluids in porous media and the modified upwind finite difference fractional steps schemes are put forward. Based on the numerical simulation of the practical situation in the Laizhou Bay Area of Shandong Province, predictive numerical simulation and analysis of the consequence of protection projects, underground dams, tidal barrage projects and the applied modular form of project adjustment have been finished. By using the theory and techniques of differential equation prior estimates, the convergence results have been got.展开更多
The coupled system of multilayer dynamics of fluids in porous media is to describe the history of oil-gas transport and accumulation in basin evolution.It is of great value in rational evaluation of prospecting and ex...The coupled system of multilayer dynamics of fluids in porous media is to describe the history of oil-gas transport and accumulation in basin evolution.It is of great value in rational evaluation of prospecting and exploiting oil-gas resources.The mathematical model can be described as a coupled system of nonlinear partial differential equations with moving boundary values.A kind of characteristic finite difference schemes is put forward,from which optimal order estimates in l~2 norm are derived for the error in the approximate solutions.The research is important both theoretically and practically for the model analysis in the field,the model numerical method and software development.展开更多
For a coupled system of multiplayer dynamics of fluids in porous media, the characteristic finite element domain decomposition procedures applicable to parallel arithmetic are put forward. Techniques such as calculus ...For a coupled system of multiplayer dynamics of fluids in porous media, the characteristic finite element domain decomposition procedures applicable to parallel arithmetic are put forward. Techniques such as calculus of variations, domain decomposition, characteristic method, negative norm estimate, energy method and the theory of prior estimates are adopted. Optimal order estimates in L^2 norm are derived for the error in the approximate solution.展开更多
Two modes of gas-solid riser operation, i.e., fluid catalytic cracking （FCC） and circulating fluidized bed combustor （CFBC）, have been recognized in literature; particularly in the understanding of choking phenome...Two modes of gas-solid riser operation, i.e., fluid catalytic cracking （FCC） and circulating fluidized bed combustor （CFBC）, have been recognized in literature; particularly in the understanding of choking phenomena. This work compares these two modes of operation through computational fluid dynamics （CFD） simulation. In CFD simulations, the different operations are represented by fixing appropriate boundary conditions： solids flux or solids inventory. It is found that the FCC and CFBC modes generally have the same dependence of solids flux on the mean solids volume fraction or solids inventory. However, during the choking transition, the FCC mode of operation needs more time to reach a steady state; thus the FCC system may have insufficient time to respond to valve adjustments or flow state change, leading to the choking. The difference between FCC and CFBC systems is more pronounced for the systems with longer risers. A more detailed investigation of these two modes of riser operation may require a three-dimensional full loop simulation with dynamic valve adjustment.展开更多
Magnetic resonance imaging(MRI), magnetic resonance angiography(MRA) and magnetic resonance spectroscopy(MRS) are fundamental concepts used in modern medicine to improve health care. These concepts are based on the pr...Magnetic resonance imaging(MRI), magnetic resonance angiography(MRA) and magnetic resonance spectroscopy(MRS) are fundamental concepts used in modern medicine to improve health care. These concepts are based on the principle of nuclear magnetic resonance(NMR). Over the years, various laboratories around the world have applied different numerical techniques based on the Bloch NMR equations to solve specific problems in physics, biology, chemistry, engineering and medicine. The ultimate goal of any physician is to obtain maximum physical, biophysical, chemical and biological information on any tissue or cell under examination. This goal can be achieved by solving the Bloch NMR flow equations analytically. In this review, we present the basic principle of NMR/MRI in a way that can be easily understood by any researcher who needs an NMR concept to solve a specific medical problems. After a very brief history of the subject, a second order, non homogeneous, time-dependent differential equation derived from the Bloch NMR equation is presented. This equation has the basic intrinsic properties of MRI, MRA and MRS that can be extracted by means of classical and quantum mechanics for possible application in nanomedicine.展开更多
基金Project supported by the Major State Basic Research Program of China (No.G1999032803)the National Tackling Key Problems Program (No.20050200069)the National Natural Science Foundation of China (Nos.10372052, 10271066)the Doctoral Foundation of Ministry of Education of China (No.20030422047).
文摘For the three-dimensional convection-dominated problem of dynamics of fluids in porous media, the second order upwind finite difference fractional steps schemes applicable to parallel arithmetic are put forward. Fractional steps techniques are needed to convert a multi-dimensional problem into a series of successive one-dimensional problems. Some techniques, such as calculus of variations, energy method, multiplicative commutation rule of difference operators, decomposition of high order difference operators, and the theory of prior estimates are adopted. Optimal order estimates are derived to determine the error in the second order approximate solution. These methods have already been applied to the numerical simulation of migration-accumulation of oil resources and predicting the consequences of seawater intrusion and protection projects.
基金This work was supported by the Major State Basic Research Program of China(Grant No. 1990328) the National Tackling Key Problem Program, the National Natural Science Foundation of China (Grant Nos. 19871051 and 19972039) the Doctorate Foundation
文摘For combinatorial system of multilayer dynamics of fluids in porous media, the second order and first order upwind finite difference fractional steps schemes applicable to parallel arithmetic are put forward and two-dimensional and three-dimensional schemes are used to form a complete set. Some techniques, such as implicit-explicit difference scheme, calculus of variations, multiplicative commutation rule of difference operators, decomposition of high order difference operators and prior estimates, are adopted. Optimal order estimates in L 2 norm are derived to determine the error in the second order approximate solution. This method has already been applied to the numerical simulation of migration-accumulation of oil resources. Keywords: combinatorial system, multilayer dynamics of fluids in porous media, two-class upwind finite difference fractional steps method, convergence, numerical simulation of energy sources.
基金Supported by the Major State Basic Research Program of China (Grant No.19990328)the National Tackling Key Problem (Grant No. 2005020069)+1 种基金the Na-tional Natural Sciences Foundation of China (Grant Nos.10771124 and 10372052)the Doctorate Foundation of the Ministry of Education of China (Grant No.20030422047)
文摘For the three-dimensional seawater intrusion and protection system, the model of dynamics of fluids in porous media and the modified upwind finite difference fractional steps schemes are put forward. Based on the numerical simulation of the practical situation in the Laizhou Bay Area of Shandong Province, predictive numerical simulation and analysis of the consequence of protection projects, underground dams, tidal barrage projects and the applied modular form of project adjustment have been finished. By using the theory and techniques of differential equation prior estimates, the convergence results have been got.
基金the Major State Basic Research Program of China(No.G19990328)the National Tackling Key Problem Program(No.20050200069)+1 种基金the National Natural Science Foundation of China(Nos.10771124,10372052)the Ph.D.Programs Foundation of Ministry of Education of China(No.20030422047)
文摘The coupled system of multilayer dynamics of fluids in porous media is to describe the history of oil-gas transport and accumulation in basin evolution.It is of great value in rational evaluation of prospecting and exploiting oil-gas resources.The mathematical model can be described as a coupled system of nonlinear partial differential equations with moving boundary values.A kind of characteristic finite difference schemes is put forward,from which optimal order estimates in l~2 norm are derived for the error in the approximate solutions.The research is important both theoretically and practically for the model analysis in the field,the model numerical method and software development.
基金Supported by the Major State Basic Research Program of China (No. 1999032803)the National Tackling Key Problems Program (No. 2002020094)+1 种基金the National Natural Scicnccs Foundation of China (Nos.19972039,10271066)the Doctorate Foundation of the Ministry of Education of China (No.2003042047)
文摘For a coupled system of multiplayer dynamics of fluids in porous media, the characteristic finite element domain decomposition procedures applicable to parallel arithmetic are put forward. Techniques such as calculus of variations, domain decomposition, characteristic method, negative norm estimate, energy method and the theory of prior estimates are adopted. Optimal order estimates in L^2 norm are derived for the error in the approximate solution.
基金This work is financially supported by the National Natural Science Foundation of China under Grant Nos. 91334204 and 21576263, the Chinese Academy of Sciences under Grant No. XDA07080100, and the Ministry of Science and Technology of the People＇s Republic of China under Grant No. 2012CB215003.
文摘Two modes of gas-solid riser operation, i.e., fluid catalytic cracking （FCC） and circulating fluidized bed combustor （CFBC）, have been recognized in literature; particularly in the understanding of choking phenomena. This work compares these two modes of operation through computational fluid dynamics （CFD） simulation. In CFD simulations, the different operations are represented by fixing appropriate boundary conditions： solids flux or solids inventory. It is found that the FCC and CFBC modes generally have the same dependence of solids flux on the mean solids volume fraction or solids inventory. However, during the choking transition, the FCC mode of operation needs more time to reach a steady state; thus the FCC system may have insufficient time to respond to valve adjustments or flow state change, leading to the choking. The difference between FCC and CFBC systems is more pronounced for the systems with longer risers. A more detailed investigation of these two modes of riser operation may require a three-dimensional full loop simulation with dynamic valve adjustment.
文摘Magnetic resonance imaging(MRI), magnetic resonance angiography(MRA) and magnetic resonance spectroscopy(MRS) are fundamental concepts used in modern medicine to improve health care. These concepts are based on the principle of nuclear magnetic resonance(NMR). Over the years, various laboratories around the world have applied different numerical techniques based on the Bloch NMR equations to solve specific problems in physics, biology, chemistry, engineering and medicine. The ultimate goal of any physician is to obtain maximum physical, biophysical, chemical and biological information on any tissue or cell under examination. This goal can be achieved by solving the Bloch NMR flow equations analytically. In this review, we present the basic principle of NMR/MRI in a way that can be easily understood by any researcher who needs an NMR concept to solve a specific medical problems. After a very brief history of the subject, a second order, non homogeneous, time-dependent differential equation derived from the Bloch NMR equation is presented. This equation has the basic intrinsic properties of MRI, MRA and MRS that can be extracted by means of classical and quantum mechanics for possible application in nanomedicine.
