Convection-dispersion of fluids flowing through porous media is an important phenomenon in immiscible and miscible displacement in hydrocarbon reservoirs. Exact calculation of this problem leads to perform more robust...Convection-dispersion of fluids flowing through porous media is an important phenomenon in immiscible and miscible displacement in hydrocarbon reservoirs. Exact calculation of this problem leads to perform more robust reservoir simulation and reliable prediction. There are various techniques that have been proposed to solve convection-dispersion equation. To check the validity of these techniques, the convection-dispersion equation was solved numerically using a series of well known numerical techniques. Such techniques that employed in this study include method of line, explicit, implicit, Crank-Nicolson and Barakat-Clark. Several cases were considered as input, and convection-dispersion equation was solved using the aforementioned techniques. Moreover the error analysis was also carried out based on the comparison of numerical and analytical results. Finally it was observed that method of line and explicit methods are not capable of simulating the convection-dispersion equation for wide range of input parameters. The Barakat-Clark method was also failed to predict accurate results and in some cases it had large deviation from analytical solution. On the other hand, the simulation results of implicit and Crank-Nicolson have more qualitative and quantitative agreement with those obtained by the analytical solutions.展开更多
Mathematically, the Black-Scholes model of American option pricing is a free boundary problem of partial differential equation. It is well known that this model is a nonlinear problem, and it has no closed form soluti...Mathematically, the Black-Scholes model of American option pricing is a free boundary problem of partial differential equation. It is well known that this model is a nonlinear problem, and it has no closed form solution. We can only obtain an approximate solution by numerical method, but the precision and stability are hard to control, because the singularity at the exercise boundary near expiration date has a great effect on precision and stability for numerical method. We propose a new numerical method, FDA method, to solve the American option pricing problem, which combines advantages the Semi-Analytical Method and the Front-Fixed Difference Method. Using the FDA method overcomes the difficulty resulting from the singularity at the terminal of optimal exercise boundary. A large amount of calculation shows that the FDA method is more accurate and stable than other numerical methods.展开更多
Ideal proportional navigation （IPN） is a natural choice for exoatmospheric interception for its mighty capture capability and ease of implementation. The closed-form solution of two- dimensional ideal proportional n...Ideal proportional navigation （IPN） is a natural choice for exoatmospheric interception for its mighty capture capability and ease of implementation. The closed-form solution of two- dimensional ideal proportional navigation was conducted in previous public literature, whereas the practical interception happens in the three-dimensional space. A novel set of relative dynamic equations is adopted in this paper, which is with the advantage of decoupling relative motion in the instantaneous rotation plane of the line of sight from the rotation of this plane. The dimension-reduced IPN is constructed in this instantaneous plane, which functions as a three-dimensional guidance law. The trajectory features of dimension-reduced IPN are explored, and the capture regions of dimension-reduced IPN with limited acceleration against nonmaneuvering and maneuvering targets are analyzed by using phase plane method. It is proved that the capture capability of IPN is much stronger than true proportional navigation （TPN）, no matter the target maneuvers or not. Finally, simulation results indicate that IPN is more effective than TPN in exoatmospheric interception scenarios.展开更多
文摘Convection-dispersion of fluids flowing through porous media is an important phenomenon in immiscible and miscible displacement in hydrocarbon reservoirs. Exact calculation of this problem leads to perform more robust reservoir simulation and reliable prediction. There are various techniques that have been proposed to solve convection-dispersion equation. To check the validity of these techniques, the convection-dispersion equation was solved numerically using a series of well known numerical techniques. Such techniques that employed in this study include method of line, explicit, implicit, Crank-Nicolson and Barakat-Clark. Several cases were considered as input, and convection-dispersion equation was solved using the aforementioned techniques. Moreover the error analysis was also carried out based on the comparison of numerical and analytical results. Finally it was observed that method of line and explicit methods are not capable of simulating the convection-dispersion equation for wide range of input parameters. The Barakat-Clark method was also failed to predict accurate results and in some cases it had large deviation from analytical solution. On the other hand, the simulation results of implicit and Crank-Nicolson have more qualitative and quantitative agreement with those obtained by the analytical solutions.
基金This work was supported by a joint grant from the National Natural Science Foundation of China (Grant No. 60131160743) and Hong Kong (Grant No. N CityU102/01) .
文摘Mathematically, the Black-Scholes model of American option pricing is a free boundary problem of partial differential equation. It is well known that this model is a nonlinear problem, and it has no closed form solution. We can only obtain an approximate solution by numerical method, but the precision and stability are hard to control, because the singularity at the exercise boundary near expiration date has a great effect on precision and stability for numerical method. We propose a new numerical method, FDA method, to solve the American option pricing problem, which combines advantages the Semi-Analytical Method and the Front-Fixed Difference Method. Using the FDA method overcomes the difficulty resulting from the singularity at the terminal of optimal exercise boundary. A large amount of calculation shows that the FDA method is more accurate and stable than other numerical methods.
基金co-supported by the National Science Foundation of China(No.11222215)the National Basic Research Program of China(No.2013CB733100)
文摘Ideal proportional navigation （IPN） is a natural choice for exoatmospheric interception for its mighty capture capability and ease of implementation. The closed-form solution of two- dimensional ideal proportional navigation was conducted in previous public literature, whereas the practical interception happens in the three-dimensional space. A novel set of relative dynamic equations is adopted in this paper, which is with the advantage of decoupling relative motion in the instantaneous rotation plane of the line of sight from the rotation of this plane. The dimension-reduced IPN is constructed in this instantaneous plane, which functions as a three-dimensional guidance law. The trajectory features of dimension-reduced IPN are explored, and the capture regions of dimension-reduced IPN with limited acceleration against nonmaneuvering and maneuvering targets are analyzed by using phase plane method. It is proved that the capture capability of IPN is much stronger than true proportional navigation （TPN）, no matter the target maneuvers or not. Finally, simulation results indicate that IPN is more effective than TPN in exoatmospheric interception scenarios.
