This article discusses the enhanced oil recovery numerical simulation of the chemical flooding(such as surfactants, alcohol, polymers) composed of two-dimensional multicomponent, ultiphase and incompressible mixed flu...This article discusses the enhanced oil recovery numerical simulation of the chemical flooding(such as surfactants, alcohol, polymers) composed of two-dimensional multicomponent, ultiphase and incompressible mixed fluids. After the oil field is waterflooded, there is still a large amount of crude oil left in the oil deposit. By adding certain chemical substances to the fluid injected, its driving capacity can be greatly increased. The mathematical model of two-dimensional enhanced oil recovery simulation can be described展开更多
We’ll study the FEM for a model for compressible miscible displacement in porous media which includes molecular diffusion and mechanical dispersion in one-dimensional space.A class of vertices-edges-elements interpol...We’ll study the FEM for a model for compressible miscible displacement in porous media which includes molecular diffusion and mechanical dispersion in one-dimensional space.A class of vertices-edges-elements interpolation operator ink is introduced.With the help of ink(not elliptic projection),the optimal error estimate in L∞(J;L2(Ω)) norm of FEM is proved.展开更多
In this note we announce the sharp error estimate of BDF2 scheme for linear diffusion reaction problem with variable time steps.Our analysis shows that the optimal second-order convergence does not require the high-or...In this note we announce the sharp error estimate of BDF2 scheme for linear diffusion reaction problem with variable time steps.Our analysis shows that the optimal second-order convergence does not require the high-order methods or the very small time stepsτ1=O(τ2)for the first level solution u1.This is,the first-order consistence of the first level solution u1 like BDF1(i.e.Euler scheme)as a starting point does not cause the loss of global temporal accuracy,and the ratios are updated to rk≤4.8645.展开更多
Presents the abstract L...-norm error estimate of nonconforming finite element method. Use of the Aubin Nitsche Lemma in estimating nonconforming finite element methods; Details on the equations.
A 2-dimensional, multicomponent, multiphase, and incompressible compositional reservoir simulator has been developed and applied to chemical flooding (surfactants, alcohol and polymers) and convergence analysis. The c...A 2-dimensional, multicomponent, multiphase, and incompressible compositional reservoir simulator has been developed and applied to chemical flooding (surfactants, alcohol and polymers) and convergence analysis. The characteristic finite difference methods for 2-dimensional enhanced oil recovery can be described as a coupled system of nonlinear partial differential equations. For a generic case of the cross interference and bounded region, we put forward a kind of characteristic finite difference schemes and make use of thick and thin grids to form a complete set, and of calculus of variations, the theory of prior estimates and techniques. Optimal order estimates in L^2 norm are derived for the error in the approximate solutions. Thus we have thoroughly solved the well-known theoretical problem proposed by a famous scientist, J. Douglas, Jr.展开更多
In the paper, we analyze the L2 norm error estimate of lower order finite element methods for the fourth order problem. We prove that the best error estimate in the L2 norm of the finite element solution is of second ...In the paper, we analyze the L2 norm error estimate of lower order finite element methods for the fourth order problem. We prove that the best error estimate in the L2 norm of the finite element solution is of second order, which can not be improved generally. The main ingredients are the saturation condition established for these elements and an identity for the error in the energy norm of the finite element solution. The result holds for most of the popular lower order finite element methods in the literature including： the Powell-Sabin C1 -P2 macro element, the nonconforming Morley element, the C1 -Q2 macro element, the nonconforming rectangle Morley element, and the nonconforming incomplete biquadratic element. In addition, the result actually applies to the nonconforming Adini element, the nonconforming Fraeijs de Veubeke elements, and the nonconforming Wang- Xu element and the Wang-Shi-Xu element provided that the saturation condition holds for them. This result solves one long standing problem in the literature： can the L2 norm error estimate of lower order finite element methods of the fourth order problem be two order higher than the error estimate in the energy norm？展开更多
We develop a family of characteristic discontinuous Galerkin methods for transient advection-diffusion equations,including the characteristic NIPG,OBB,IIPG,and SIPG schemes.The derived schemes possess combined advanta...We develop a family of characteristic discontinuous Galerkin methods for transient advection-diffusion equations,including the characteristic NIPG,OBB,IIPG,and SIPG schemes.The derived schemes possess combined advantages of EulerianLagrangian methods and discontinuous Galerkin methods.An optimal-order error estimate in the L2 norm and a superconvergence estimate in a weighted energy norm are proved for the characteristic NIPG,IIPG,and SIPG scheme.Numerical experiments are presented to confirm the optimal-order spatial and temporal convergence rates of these schemes as proved in the theorems and to show that these schemes compare favorably to the standard NIPG,OBB,IIPG,and SIPG schemes in the context of advection-diffusion equations.展开更多
A family of piecewise rational quintic interpolation is presented. Each interpolation of the family, which is identified uniquely by the value of a parameter ai, is of C^2 continuity without solving a system of consis...A family of piecewise rational quintic interpolation is presented. Each interpolation of the family, which is identified uniquely by the value of a parameter ai, is of C^2 continuity without solving a system of consistency equations for the derivative values at the knots, and can be expressed by the basis functions. Interpolant is of O（h^r） accuracy when f（x）∈C^r[a,b], and the errors have only a small floating for a big change of the parameter ai, it means the interpolation is stable for the parameter. The interpolation can preserve the shape properties of the given data, such as monotonicity and convexity, and a proper choice of parameter ai is given.展开更多
基金This project is sponsored by the National Scaling Programthe National Eighth-Five-Year Tackling Key Problems Program
文摘This article discusses the enhanced oil recovery numerical simulation of the chemical flooding(such as surfactants, alcohol, polymers) composed of two-dimensional multicomponent, ultiphase and incompressible mixed fluids. After the oil field is waterflooded, there is still a large amount of crude oil left in the oil deposit. By adding certain chemical substances to the fluid injected, its driving capacity can be greatly increased. The mathematical model of two-dimensional enhanced oil recovery simulation can be described
基金This research is supported by the Foundation for Talents for Next Century of Shandong University
文摘We’ll study the FEM for a model for compressible miscible displacement in porous media which includes molecular diffusion and mechanical dispersion in one-dimensional space.A class of vertices-edges-elements interpolation operator ink is introduced.With the help of ink(not elliptic projection),the optimal error estimate in L∞(J;L2(Ω)) norm of FEM is proved.
基金Natural Science Foundation of Hubei Province(2019CFA007)Supported by NSFC(11771035).
文摘In this note we announce the sharp error estimate of BDF2 scheme for linear diffusion reaction problem with variable time steps.Our analysis shows that the optimal second-order convergence does not require the high-order methods or the very small time stepsτ1=O(τ2)for the first level solution u1.This is,the first-order consistence of the first level solution u1 like BDF1(i.e.Euler scheme)as a starting point does not cause the loss of global temporal accuracy,and the ratios are updated to rk≤4.8645.
文摘Presents the abstract L...-norm error estimate of nonconforming finite element method. Use of the Aubin Nitsche Lemma in estimating nonconforming finite element methods; Details on the equations.
基金Project supported by the National Scaling Program and the National Eighth-Five-Year Tackling Key Problems Program
文摘A 2-dimensional, multicomponent, multiphase, and incompressible compositional reservoir simulator has been developed and applied to chemical flooding (surfactants, alcohol and polymers) and convergence analysis. The characteristic finite difference methods for 2-dimensional enhanced oil recovery can be described as a coupled system of nonlinear partial differential equations. For a generic case of the cross interference and bounded region, we put forward a kind of characteristic finite difference schemes and make use of thick and thin grids to form a complete set, and of calculus of variations, the theory of prior estimates and techniques. Optimal order estimates in L^2 norm are derived for the error in the approximate solutions. Thus we have thoroughly solved the well-known theoretical problem proposed by a famous scientist, J. Douglas, Jr.
文摘In the paper, we analyze the L2 norm error estimate of lower order finite element methods for the fourth order problem. We prove that the best error estimate in the L2 norm of the finite element solution is of second order, which can not be improved generally. The main ingredients are the saturation condition established for these elements and an identity for the error in the energy norm of the finite element solution. The result holds for most of the popular lower order finite element methods in the literature including： the Powell-Sabin C1 -P2 macro element, the nonconforming Morley element, the C1 -Q2 macro element, the nonconforming rectangle Morley element, and the nonconforming incomplete biquadratic element. In addition, the result actually applies to the nonconforming Adini element, the nonconforming Fraeijs de Veubeke elements, and the nonconforming Wang- Xu element and the Wang-Shi-Xu element provided that the saturation condition holds for them. This result solves one long standing problem in the literature： can the L2 norm error estimate of lower order finite element methods of the fourth order problem be two order higher than the error estimate in the energy norm？
文摘We develop a family of characteristic discontinuous Galerkin methods for transient advection-diffusion equations,including the characteristic NIPG,OBB,IIPG,and SIPG schemes.The derived schemes possess combined advantages of EulerianLagrangian methods and discontinuous Galerkin methods.An optimal-order error estimate in the L2 norm and a superconvergence estimate in a weighted energy norm are proved for the characteristic NIPG,IIPG,and SIPG scheme.Numerical experiments are presented to confirm the optimal-order spatial and temporal convergence rates of these schemes as proved in the theorems and to show that these schemes compare favorably to the standard NIPG,OBB,IIPG,and SIPG schemes in the context of advection-diffusion equations.
基金Supported by National Nature Science Foundation of China(No.61070096)the Natural Science Foundation of Shandong Province(No.ZR2012FL05,No.2015ZRE27056)
文摘A family of piecewise rational quintic interpolation is presented. Each interpolation of the family, which is identified uniquely by the value of a parameter ai, is of C^2 continuity without solving a system of consistency equations for the derivative values at the knots, and can be expressed by the basis functions. Interpolant is of O（h^r） accuracy when f（x）∈C^r[a,b], and the errors have only a small floating for a big change of the parameter ai, it means the interpolation is stable for the parameter. The interpolation can preserve the shape properties of the given data, such as monotonicity and convexity, and a proper choice of parameter ai is given.
