The Experts below are selected from a list of 303 Experts worldwide ranked by ideXlab platform
Changfeng Li - One of the best experts on this subject based on the ideXlab platform.
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Mixed finite volume element-upwind mixed volume element of compressible two-phase displacement and its numerical analysis
Journal of Computational and Applied Mathematics, 2020Co-Authors: Yirang Yuan, Changfeng Li, Huailing SongAbstract:Abstract A fundamental topic in numerical simulation of two-phase displacement is discussed in this paper. The mathematical model for the compressible problem is defined mainly by two nonlinear partial differential equations: a parabolic equation for the pressure and a convection–diffusion equation for the saturation. The Darcy Velocity is determined by the pressure, and affects the whole physical process. The system is solved by a composite numerical scheme. The conservative mixed volume element is used for the first equation. The computational accuracy is improved for the Darcy Velocity. The second equation is solved by a conservative upwind mixed volume element, where the mixed volume element and upwind approximation treat the diffusion and convection, respectively. The upwind method preserves the high computational accuracy, and numerical dispersion and nonphysical oscillation are eliminated. The saturation and its adjoint vector function are obtained simultaneously. An important feature in numerical scheme, the conservation of mass, is proved. By the traditional theoretical work of numerical analysis such as a priori estimates of differential equations, the optimal order error estimate is obtained. Finally, numerical tests show the effectiveness and practicability, then the present method possibly solves the challenging problems as a powerful tool.
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The method of mixed volume element-characteristic mixed volume element and its numerical analysis for groundwater pollution in binary medium
Applied Mathematics and Computation, 2019Co-Authors: Yirang Yuan, Changfeng LiAbstract:Abstract Groundwater pollution is an important topic of environmental sciences. Since the geologic structure is usually of crack-hole binary medium, its mathematical model is formulated by a nonlinear initial-boundary value problem of partial differential equations. The pressure is defined by an elliptic flow equation. The concentration of pollution is defined by a convection-diffusion equation. The surface adsorption concentration is defined by a first-order ordinary differential equation. The transport pressure appears within the concentration, and Darcy Velocity controls the concentration. The flow equation is solved by the conservative mixed volume element and the computational accuracy of Darcy Velocity is improved by one order. The mixed volume element with the characteristics is applied to approximate the concentration, i.e., the diffusion and convection are discretized by the method of mixed volume element and the characteristics, respectively. Sharp fronts are resolved stably by the characteristic discretizations without numerical dispersion or nonphysical oscillation. Large and accurate timesteps are used while the scheme has much smaller time truncation errors than those of standard methods on coarse grids. The mixed volume element is applied to approximate the diffusion. The concentration and its adjoint vector function are computed simultaneously, and the locally conservative law of mass is ensured. Using the theory and technique of a priori estimates of differential equations, we derive an optimal second order error in l2 norm. Numerical examples are given to show the effectiveness and practicability and the method is testified as a powerful tool in solving some actual applications.
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A mixed volume element with upwind multistep mixed volume element and convergence analysis for numerical simulation of nuclear waste contaminant disposal
Journal of Computational and Applied Mathematics, 2019Co-Authors: Changfeng Li, Yirang Yuan, Huailing SongAbstract:Abstract In this paper the authors discuss a numerical simulation problem of three-dimensional contamination treatment from nuclear waste. The mathematical model is defined by a nonlinear system of an initial–boundary problem of four partial differential equations: an elliptic equation for the fluid pressure, three convection–diffusion equations for the brine, radionuclides and heat. The pressure appears within the concentration equations and heat conduction equation, and the Darcy Velocity controls the concentrations and the temperature. The pressure is solved by the conservative mixed volume element method, and the order of accuracy is improved by the Darcy Velocity. The concentrations and temperature are treated by a combination of a multistep method, the upwind approximation and a mixed volume element. The partial derivatives to time variable are approximated by a multistep method. A mixed volume element and an upwind scheme are used to discretize the diffusion and the convection, respectively. The composite method can solve the convection-dominated diffusion problems well because it eliminates numerical dispersion and nonphysical oscillation and has high order computational accuracy. The mixed volume element has the local conservation of mass and energy, and it can obtain the concentrations and temperature and their adjoint vector functions simultaneously. The conservation nature plays an important role in numerical simulation of underground fluid. By the technique of a priori estimates of differential equations, we derive an optimal second order result in L 2 norm. Numerical examples are given to show the effectiveness and practicability of our approach and the composite method is testified as a powerful tool for solving the challenging benchmark problem.
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Mixed volume element combined with characteristic mixed finite volume element method for oil–water two phase displacement problem
Journal of Computational and Applied Mathematics, 2018Co-Authors: Yirang Yuan, Changfeng Li, Qing YangAbstract:Abstract As the basic of numerical simulation of energy science, the displacement of three-dimensional oil–water two phase in porous media is discussed in this paper. For incompressible miscible displacement, the pressure is described by a flow equation in an elliptic mathematical formulation and the saturation is defined by a convection–diffusion equation. The pressure exists in the saturation equation by Darcy Velocity, and controls the whole flow. We develop and improve substantially the work of Arbogast and Wheeler, then put forward a mixed volume element combined with characteristic mixed finite volume element method for two-phase displacement problem. The flow equation is discretized by the conservative mixed volume element method, which could improve the accuracy of an order for computing Darcy Velocity. The saturation equation is solved by a characteristic mixed volume element method, where mixed volume element method is used to compute the diffusion term and the method of characteristics is adopted to discretize the convection term. The method of characteristics can confirm high stability of numerical simulation at the fronts, avoid numerical dispersion and nonphysical oscillation, and can adopt large time steps, obtain smaller time truncation error and improve the computation accuracy. Mixed volume element can solve the convection term, confirm conservation of mass at each element and approximate the saturation and the adjoint vector meanwhile. It is most important in numerical computation of seepage mechanics. Optimal second order estimates in L 2 norm are derived by theory and special techniques of priori estimates. Finally, numerical experiments are shown to illustrate the efficiency and practicability and to solve the international problem successfully.
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The method of mixed volume element‐characteristic mixed volume element and its numerical analysis for three‐dimensional slightly compressible two‐phase displacement
Numerical Methods for Partial Differential Equations, 2017Co-Authors: Yirang Yuan, Changfeng Li, Qing YangAbstract:Numerical simulation of oil-water two-phase displacement is a fundamental problem in energy mathematics. The mathematical model for the compressible case is defined by a nonlinear system of two partial differential equations: (1) a parabolic equation for pressure and (2) a convection-diffusion equation for saturation. The pressure appears within the saturation equation, and the Darcy Velocity controls the saturation. The flow equation is solved by the conservative mixed volume element method. The order of the accuracy is improved by the Darcy Velocity. The conservative mixed volume element with characteristics is applied to compute the saturation, that is, the diffusion is discretized by the mixed volume element and convection is computed by the method of characteristics. The method of characteristics has strong computational stability at sharp fronts and avoids numerical dispersion and nonphysical oscillation. Small time truncation error and accuracy are obtained through this method. The mixed volume element simulates diffusion, saturation, and the adjoint vector function simultaneously. By using the theory and technique of a priori estimates of differential equations, convergence of the optimal second order in l 2 norm is obtained. Numerical examples are provided to show the effectiveness and viability of this method. This method provides a powerful tool for solving challenging benchmark problems.
Yirang Yuan - One of the best experts on this subject based on the ideXlab platform.
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Mixed finite volume element-upwind mixed volume element of compressible two-phase displacement and its numerical analysis
Journal of Computational and Applied Mathematics, 2020Co-Authors: Yirang Yuan, Changfeng Li, Huailing SongAbstract:Abstract A fundamental topic in numerical simulation of two-phase displacement is discussed in this paper. The mathematical model for the compressible problem is defined mainly by two nonlinear partial differential equations: a parabolic equation for the pressure and a convection–diffusion equation for the saturation. The Darcy Velocity is determined by the pressure, and affects the whole physical process. The system is solved by a composite numerical scheme. The conservative mixed volume element is used for the first equation. The computational accuracy is improved for the Darcy Velocity. The second equation is solved by a conservative upwind mixed volume element, where the mixed volume element and upwind approximation treat the diffusion and convection, respectively. The upwind method preserves the high computational accuracy, and numerical dispersion and nonphysical oscillation are eliminated. The saturation and its adjoint vector function are obtained simultaneously. An important feature in numerical scheme, the conservation of mass, is proved. By the traditional theoretical work of numerical analysis such as a priori estimates of differential equations, the optimal order error estimate is obtained. Finally, numerical tests show the effectiveness and practicability, then the present method possibly solves the challenging problems as a powerful tool.
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The method of mixed volume element-characteristic mixed volume element and its numerical analysis for groundwater pollution in binary medium
Applied Mathematics and Computation, 2019Co-Authors: Yirang Yuan, Changfeng LiAbstract:Abstract Groundwater pollution is an important topic of environmental sciences. Since the geologic structure is usually of crack-hole binary medium, its mathematical model is formulated by a nonlinear initial-boundary value problem of partial differential equations. The pressure is defined by an elliptic flow equation. The concentration of pollution is defined by a convection-diffusion equation. The surface adsorption concentration is defined by a first-order ordinary differential equation. The transport pressure appears within the concentration, and Darcy Velocity controls the concentration. The flow equation is solved by the conservative mixed volume element and the computational accuracy of Darcy Velocity is improved by one order. The mixed volume element with the characteristics is applied to approximate the concentration, i.e., the diffusion and convection are discretized by the method of mixed volume element and the characteristics, respectively. Sharp fronts are resolved stably by the characteristic discretizations without numerical dispersion or nonphysical oscillation. Large and accurate timesteps are used while the scheme has much smaller time truncation errors than those of standard methods on coarse grids. The mixed volume element is applied to approximate the diffusion. The concentration and its adjoint vector function are computed simultaneously, and the locally conservative law of mass is ensured. Using the theory and technique of a priori estimates of differential equations, we derive an optimal second order error in l2 norm. Numerical examples are given to show the effectiveness and practicability and the method is testified as a powerful tool in solving some actual applications.
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A mixed volume element with upwind multistep mixed volume element and convergence analysis for numerical simulation of nuclear waste contaminant disposal
Journal of Computational and Applied Mathematics, 2019Co-Authors: Changfeng Li, Yirang Yuan, Huailing SongAbstract:Abstract In this paper the authors discuss a numerical simulation problem of three-dimensional contamination treatment from nuclear waste. The mathematical model is defined by a nonlinear system of an initial–boundary problem of four partial differential equations: an elliptic equation for the fluid pressure, three convection–diffusion equations for the brine, radionuclides and heat. The pressure appears within the concentration equations and heat conduction equation, and the Darcy Velocity controls the concentrations and the temperature. The pressure is solved by the conservative mixed volume element method, and the order of accuracy is improved by the Darcy Velocity. The concentrations and temperature are treated by a combination of a multistep method, the upwind approximation and a mixed volume element. The partial derivatives to time variable are approximated by a multistep method. A mixed volume element and an upwind scheme are used to discretize the diffusion and the convection, respectively. The composite method can solve the convection-dominated diffusion problems well because it eliminates numerical dispersion and nonphysical oscillation and has high order computational accuracy. The mixed volume element has the local conservation of mass and energy, and it can obtain the concentrations and temperature and their adjoint vector functions simultaneously. The conservation nature plays an important role in numerical simulation of underground fluid. By the technique of a priori estimates of differential equations, we derive an optimal second order result in L 2 norm. Numerical examples are given to show the effectiveness and practicability of our approach and the composite method is testified as a powerful tool for solving the challenging benchmark problem.
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Mixed volume element combined with characteristic mixed finite volume element method for oil–water two phase displacement problem
Journal of Computational and Applied Mathematics, 2018Co-Authors: Yirang Yuan, Changfeng Li, Qing YangAbstract:Abstract As the basic of numerical simulation of energy science, the displacement of three-dimensional oil–water two phase in porous media is discussed in this paper. For incompressible miscible displacement, the pressure is described by a flow equation in an elliptic mathematical formulation and the saturation is defined by a convection–diffusion equation. The pressure exists in the saturation equation by Darcy Velocity, and controls the whole flow. We develop and improve substantially the work of Arbogast and Wheeler, then put forward a mixed volume element combined with characteristic mixed finite volume element method for two-phase displacement problem. The flow equation is discretized by the conservative mixed volume element method, which could improve the accuracy of an order for computing Darcy Velocity. The saturation equation is solved by a characteristic mixed volume element method, where mixed volume element method is used to compute the diffusion term and the method of characteristics is adopted to discretize the convection term. The method of characteristics can confirm high stability of numerical simulation at the fronts, avoid numerical dispersion and nonphysical oscillation, and can adopt large time steps, obtain smaller time truncation error and improve the computation accuracy. Mixed volume element can solve the convection term, confirm conservation of mass at each element and approximate the saturation and the adjoint vector meanwhile. It is most important in numerical computation of seepage mechanics. Optimal second order estimates in L 2 norm are derived by theory and special techniques of priori estimates. Finally, numerical experiments are shown to illustrate the efficiency and practicability and to solve the international problem successfully.
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The method of mixed volume element‐characteristic mixed volume element and its numerical analysis for three‐dimensional slightly compressible two‐phase displacement
Numerical Methods for Partial Differential Equations, 2017Co-Authors: Yirang Yuan, Changfeng Li, Qing YangAbstract:Numerical simulation of oil-water two-phase displacement is a fundamental problem in energy mathematics. The mathematical model for the compressible case is defined by a nonlinear system of two partial differential equations: (1) a parabolic equation for pressure and (2) a convection-diffusion equation for saturation. The pressure appears within the saturation equation, and the Darcy Velocity controls the saturation. The flow equation is solved by the conservative mixed volume element method. The order of the accuracy is improved by the Darcy Velocity. The conservative mixed volume element with characteristics is applied to compute the saturation, that is, the diffusion is discretized by the mixed volume element and convection is computed by the method of characteristics. The method of characteristics has strong computational stability at sharp fronts and avoids numerical dispersion and nonphysical oscillation. Small time truncation error and accuracy are obtained through this method. The mixed volume element simulates diffusion, saturation, and the adjoint vector function simultaneously. By using the theory and technique of a priori estimates of differential equations, convergence of the optimal second order in l 2 norm is obtained. Numerical examples are provided to show the effectiveness and viability of this method. This method provides a powerful tool for solving challenging benchmark problems.
Zhimin Du - One of the best experts on this subject based on the ideXlab platform.
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interface condition for the Darcy Velocity at the water oil flood front in the porous medium
PLOS ONE, 2017Co-Authors: Xiaolong Peng, Baosheng Liang, Zhimin DuAbstract:Flood front is the jump interface where fluids distribute discontinuously, whose interface condition is the theoretical basis of a mathematical model of the multiphase flow in porous medium. The conventional interface condition at the jump interface is expressed as the continuous Darcy Velocity and fluid pressure (named CVCM). Our study has inspected this conclusion. First, it is revealed that the principle of mass conservation has no direct relation to the Velocity conservation, and the former is not the true foundation of the later, because the former only reflects the kinetic characteristic of the fluid particles at one position(the interface), but not the different two parts of fluid on the different side of the interface which required by the interface conditions. Then the reasonableness of CVCM is queried from the following three aspects:(1)Using Mukat's two phase seepage equation and the mathematical method of apagoge, we have disproved the continuity of each fluid Velocity;(2)Since the analytical solution of the equation of Buckley-Leveret equations is acquirable, its Velocity jumps at the flood front presents an appropriate example to disprove the CVCM;(3) The numerical simulation model gives impractical result that flood front would stop moving if CVCM were used to calculate the velocities at the interface between two gridcells. Subsequently, a new one, termed as Jump Velocity Condition Model (JVCM), is deduced from Muskat's two phase seepage equations and Darcy's law without taking account of the capillary force and compressibility of rocks and fluids. Finally, several cases are presented. And the comparisons of the Velocity, pressure difference and the front position, which are given by JVCM, CVCM and SPU, have shown that the result of JVCM is the closest to the exact solution.
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The Interface Conditions for Pressures at Oil-water Flood Front in the Porous Media Considering Capillary Pressure
arXiv: Fluid Dynamics, 2016Co-Authors: Xiaolong Peng, Zhimin Du, Fei MoAbstract:Flood front is the jump interface where fluids distribute discontinuously, whose interface condition is the theoretical basis of a mathematical model of the multiphase flow in porous medium. The conventional interface condition at the jump interface is expressed as the continuous Darcy Velocity and fluid pressure (named CPVCM). This paper has inspected it via the studying the water-oil displacement in one dimensional reservoir with considering capillary pressure but ignoring the compressibility and gravity. It is proved theoretically that the total Darcy Velocity and total pressure (defined by Antoncev etc.), instead of the Darcy velocities and pressures of water and oil, are continuous at the flood front without considering the compressibility of fluid and porous media. After that, new interface conditions for the pressures and Darcy Velocity of each fluid are established, which are collectively named as Jump Pressures and Velocities Conditions Model (JPVCM) because the model has shown the jump pressures and jump Darcy velocities at the flood front. Finally, three application-examples are proposed and the results show JPVCM is more reasonable than CPVCM. Keywords: Flood front; Jump Condition; Two phase; numerical flux; mathematical model
Xiaolong Peng - One of the best experts on this subject based on the ideXlab platform.
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interface condition for the Darcy Velocity at the water oil flood front in the porous medium
PLOS ONE, 2017Co-Authors: Xiaolong Peng, Baosheng Liang, Zhimin DuAbstract:Flood front is the jump interface where fluids distribute discontinuously, whose interface condition is the theoretical basis of a mathematical model of the multiphase flow in porous medium. The conventional interface condition at the jump interface is expressed as the continuous Darcy Velocity and fluid pressure (named CVCM). Our study has inspected this conclusion. First, it is revealed that the principle of mass conservation has no direct relation to the Velocity conservation, and the former is not the true foundation of the later, because the former only reflects the kinetic characteristic of the fluid particles at one position(the interface), but not the different two parts of fluid on the different side of the interface which required by the interface conditions. Then the reasonableness of CVCM is queried from the following three aspects:(1)Using Mukat's two phase seepage equation and the mathematical method of apagoge, we have disproved the continuity of each fluid Velocity;(2)Since the analytical solution of the equation of Buckley-Leveret equations is acquirable, its Velocity jumps at the flood front presents an appropriate example to disprove the CVCM;(3) The numerical simulation model gives impractical result that flood front would stop moving if CVCM were used to calculate the velocities at the interface between two gridcells. Subsequently, a new one, termed as Jump Velocity Condition Model (JVCM), is deduced from Muskat's two phase seepage equations and Darcy's law without taking account of the capillary force and compressibility of rocks and fluids. Finally, several cases are presented. And the comparisons of the Velocity, pressure difference and the front position, which are given by JVCM, CVCM and SPU, have shown that the result of JVCM is the closest to the exact solution.
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The Interface Conditions for Pressures at Oil-water Flood Front in the Porous Media Considering Capillary Pressure
arXiv: Fluid Dynamics, 2016Co-Authors: Xiaolong Peng, Zhimin Du, Fei MoAbstract:Flood front is the jump interface where fluids distribute discontinuously, whose interface condition is the theoretical basis of a mathematical model of the multiphase flow in porous medium. The conventional interface condition at the jump interface is expressed as the continuous Darcy Velocity and fluid pressure (named CPVCM). This paper has inspected it via the studying the water-oil displacement in one dimensional reservoir with considering capillary pressure but ignoring the compressibility and gravity. It is proved theoretically that the total Darcy Velocity and total pressure (defined by Antoncev etc.), instead of the Darcy velocities and pressures of water and oil, are continuous at the flood front without considering the compressibility of fluid and porous media. After that, new interface conditions for the pressures and Darcy Velocity of each fluid are established, which are collectively named as Jump Pressures and Velocities Conditions Model (JPVCM) because the model has shown the jump pressures and jump Darcy velocities at the flood front. Finally, three application-examples are proposed and the results show JPVCM is more reasonable than CPVCM. Keywords: Flood front; Jump Condition; Two phase; numerical flux; mathematical model
Qing Yang - One of the best experts on this subject based on the ideXlab platform.
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Mixed volume element combined with characteristic mixed finite volume element method for oil–water two phase displacement problem
Journal of Computational and Applied Mathematics, 2018Co-Authors: Yirang Yuan, Changfeng Li, Qing YangAbstract:Abstract As the basic of numerical simulation of energy science, the displacement of three-dimensional oil–water two phase in porous media is discussed in this paper. For incompressible miscible displacement, the pressure is described by a flow equation in an elliptic mathematical formulation and the saturation is defined by a convection–diffusion equation. The pressure exists in the saturation equation by Darcy Velocity, and controls the whole flow. We develop and improve substantially the work of Arbogast and Wheeler, then put forward a mixed volume element combined with characteristic mixed finite volume element method for two-phase displacement problem. The flow equation is discretized by the conservative mixed volume element method, which could improve the accuracy of an order for computing Darcy Velocity. The saturation equation is solved by a characteristic mixed volume element method, where mixed volume element method is used to compute the diffusion term and the method of characteristics is adopted to discretize the convection term. The method of characteristics can confirm high stability of numerical simulation at the fronts, avoid numerical dispersion and nonphysical oscillation, and can adopt large time steps, obtain smaller time truncation error and improve the computation accuracy. Mixed volume element can solve the convection term, confirm conservation of mass at each element and approximate the saturation and the adjoint vector meanwhile. It is most important in numerical computation of seepage mechanics. Optimal second order estimates in L 2 norm are derived by theory and special techniques of priori estimates. Finally, numerical experiments are shown to illustrate the efficiency and practicability and to solve the international problem successfully.
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The method of mixed volume element‐characteristic mixed volume element and its numerical analysis for three‐dimensional slightly compressible two‐phase displacement
Numerical Methods for Partial Differential Equations, 2017Co-Authors: Yirang Yuan, Changfeng Li, Qing YangAbstract:Numerical simulation of oil-water two-phase displacement is a fundamental problem in energy mathematics. The mathematical model for the compressible case is defined by a nonlinear system of two partial differential equations: (1) a parabolic equation for pressure and (2) a convection-diffusion equation for saturation. The pressure appears within the saturation equation, and the Darcy Velocity controls the saturation. The flow equation is solved by the conservative mixed volume element method. The order of the accuracy is improved by the Darcy Velocity. The conservative mixed volume element with characteristics is applied to compute the saturation, that is, the diffusion is discretized by the mixed volume element and convection is computed by the method of characteristics. The method of characteristics has strong computational stability at sharp fronts and avoids numerical dispersion and nonphysical oscillation. Small time truncation error and accuracy are obtained through this method. The mixed volume element simulates diffusion, saturation, and the adjoint vector function simultaneously. By using the theory and technique of a priori estimates of differential equations, convergence of the optimal second order in l 2 norm is obtained. Numerical examples are provided to show the effectiveness and viability of this method. This method provides a powerful tool for solving challenging benchmark problems.
