A combined method consisting of the mixed finite element method for flow and the local discontinuous Galerkin method for transport is introduced for the one-dimensional coupled system of incompressible miscible displa...A combined method consisting of the mixed finite element method for flow and the local discontinuous Galerkin method for transport is introduced for the one-dimensional coupled system of incompressible miscible displacement problem. Optimal error estimates in L∞(0,T;L2) for concentration c,in L2(0,T;L2)for cxand L∞(0,T;L2) for velocity u are derived. The main technical difficulties in the analysis include the treatment of the inter-element jump terms which arise from the discontinuous nature of the numerical method,the nonlinearity,and the coupling of the models. Numerical experiments are performed to verify the theoretical results. Finally,we apply this method to the one-dimensional compressible miscible displacement problem and give the numerical experiments to confirm the efficiency of the scheme.展开更多
A nonlinear parabolic system is derived to describe compressible miscible displacement in a porous medium.The concentration equation is treated by a mixed finite element method with characteristics(CMFEM)and the press...A nonlinear parabolic system is derived to describe compressible miscible displacement in a porous medium.The concentration equation is treated by a mixed finite element method with characteristics(CMFEM)and the pressure equation is treated by a parabolic mixed finite element method(PMFEM).Two-grid algorithm is considered to linearize nonlinear coupled system of two parabolic partial differential equations.Moreover,the L q error estimates are conducted for the pressure,Darcy velocity and concentration variables in the two-grid solutions.Both theoretical analysis and numerical experiments are presented to show that the two-grid algorithm is very effective.展开更多
In this article,a new characteristic finite difference method is developed for solving miscible displacement problem in porous media.The new method combines the characteristic technique with mass-preserving interpolat...In this article,a new characteristic finite difference method is developed for solving miscible displacement problem in porous media.The new method combines the characteristic technique with mass-preserving interpolation,not only keeps mass balance but also is of second-order accuracy both in time and space.Numerical results are presented to confirm the convergence and the accuracy in time and space.展开更多
The incompressible miscible displacement problem in porous media is modeled by a coupled system of two nonlinear partial differential equations,the pressure–velocity equation and the concentration equation.In this pa...The incompressible miscible displacement problem in porous media is modeled by a coupled system of two nonlinear partial differential equations,the pressure–velocity equation and the concentration equation.In this paper,we present a mixed finite volume element method(FVEM)for the approximation of the pressure–velocity equation and a standard FVEM for the concentration equation.A priori error estimates in L^(∞)(L^(2))are derived for velocity,pressure and concentration.Numerical results are presented to substantiate the validity of the theoretical results.展开更多
基金supported by National Natural Science Foundation of China(Grant No.11101431)the Fundamental Research Funds for the Central Universities
文摘A combined method consisting of the mixed finite element method for flow and the local discontinuous Galerkin method for transport is introduced for the one-dimensional coupled system of incompressible miscible displacement problem. Optimal error estimates in L∞(0,T;L2) for concentration c,in L2(0,T;L2)for cxand L∞(0,T;L2) for velocity u are derived. The main technical difficulties in the analysis include the treatment of the inter-element jump terms which arise from the discontinuous nature of the numerical method,the nonlinearity,and the coupling of the models. Numerical experiments are performed to verify the theoretical results. Finally,we apply this method to the one-dimensional compressible miscible displacement problem and give the numerical experiments to confirm the efficiency of the scheme.
基金Natural Science Foundation of Guangdong province,China(2018A0303100016)Educational Commission of Guangdong Province,China(2019KTSCX174)+1 种基金The second author's work is supported by the State Key Program of National Natural Science Foundation of China(11931003)National Natural Science Foundation of China(41974133,11671157).
文摘A nonlinear parabolic system is derived to describe compressible miscible displacement in a porous medium.The concentration equation is treated by a mixed finite element method with characteristics(CMFEM)and the pressure equation is treated by a parabolic mixed finite element method(PMFEM).Two-grid algorithm is considered to linearize nonlinear coupled system of two parabolic partial differential equations.Moreover,the L q error estimates are conducted for the pressure,Darcy velocity and concentration variables in the two-grid solutions.Both theoretical analysis and numerical experiments are presented to show that the two-grid algorithm is very effective.
基金supported by the Fundamental Research Funds for the Central Universities(Grant No.22CX03020A).
文摘In this article,a new characteristic finite difference method is developed for solving miscible displacement problem in porous media.The new method combines the characteristic technique with mass-preserving interpolation,not only keeps mass balance but also is of second-order accuracy both in time and space.Numerical results are presented to confirm the convergence and the accuracy in time and space.
文摘The incompressible miscible displacement problem in porous media is modeled by a coupled system of two nonlinear partial differential equations,the pressure–velocity equation and the concentration equation.In this paper,we present a mixed finite volume element method(FVEM)for the approximation of the pressure–velocity equation and a standard FVEM for the concentration equation.A priori error estimates in L^(∞)(L^(2))are derived for velocity,pressure and concentration.Numerical results are presented to substantiate the validity of the theoretical results.
