In this paper, we study the global existence of classical solutions for the convective-diffusive Cahn-Hilliard equation with concentration dependent mobility. Based on the Schauder type estimates, we establish the glo...In this paper, we study the global existence of classical solutions for the convective-diffusive Cahn-Hilliard equation with concentration dependent mobility. Based on the Schauder type estimates, we establish the global existence of classicalsolutions.展开更多
A perturbation finite volume(PFV)method for the convective-diffusion integral equa- tion is developed in this paper.The PFV scheme is an upwind and mixed scheme using any higher-order interpolation and second-order in...A perturbation finite volume(PFV)method for the convective-diffusion integral equa- tion is developed in this paper.The PFV scheme is an upwind and mixed scheme using any higher-order interpolation and second-order integration approximations,with the least nodes similar to the standard three-point schemes,that is,the number of the nodes needed is equal to unity plus the face-number of the control volume.For instance,in the two-dimensional(2-D)case,only four nodes for the triangle grids and five nodes for the Cartesian grids are utilized,respectively.The PFV scheme is applied on a number of 1-D linear and nonlinear problems,2-D and 3-D flow model equations.Comparing with other standard three-point schemes,the PFV scheme has much smaller numerical diffusion than the first-order upwind scheme(UDS).Its numerical accuracies are also higher than the second-order central scheme(CDS),the power-law scheme(PLS)and QUICK scheme.展开更多
A streamline upwind finite element method using 6-node triangular element is presented. The method is applied to the convection term of the governing transport equation directly along local streamlines. Several convec...A streamline upwind finite element method using 6-node triangular element is presented. The method is applied to the convection term of the governing transport equation directly along local streamlines. Several convective-diffusion examples are used to evaluate efficiency of the method. Results show that the method is monotonic and does not produce any oscillation. In addition, an adaptive meshing technique is combined with the method to further increase accuracy of the solution, and at the same time, to minimize computational time and computer memory requirement.展开更多
The convective-diffusion equations are very common in applied mechanics.One-dimensional convective-diffusion equation can be given aswhere φ is the unknown function to be solved, such as conceniration, temperature, e...The convective-diffusion equations are very common in applied mechanics.One-dimensional convective-diffusion equation can be given aswhere φ is the unknown function to be solved, such as conceniration, temperature, etc.,t, the time; x, the coordinate; D, the diffusive constant, and V is the velocity of fluidflow.展开更多
基金This work is partially supported by the grant for the project of the MOST of China,and partially supported by NNSF(10125107)of China.
文摘In this paper, we study the global existence of classical solutions for the convective-diffusive Cahn-Hilliard equation with concentration dependent mobility. Based on the Schauder type estimates, we establish the global existence of classicalsolutions.
基金The project supported by the National Natural Science Foundation of China(10272106,10372106)
文摘A perturbation finite volume(PFV)method for the convective-diffusion integral equa- tion is developed in this paper.The PFV scheme is an upwind and mixed scheme using any higher-order interpolation and second-order integration approximations,with the least nodes similar to the standard three-point schemes,that is,the number of the nodes needed is equal to unity plus the face-number of the control volume.For instance,in the two-dimensional(2-D)case,only four nodes for the triangle grids and five nodes for the Cartesian grids are utilized,respectively.The PFV scheme is applied on a number of 1-D linear and nonlinear problems,2-D and 3-D flow model equations.Comparing with other standard three-point schemes,the PFV scheme has much smaller numerical diffusion than the first-order upwind scheme(UDS).Its numerical accuracies are also higher than the second-order central scheme(CDS),the power-law scheme(PLS)and QUICK scheme.
文摘A streamline upwind finite element method using 6-node triangular element is presented. The method is applied to the convection term of the governing transport equation directly along local streamlines. Several convective-diffusion examples are used to evaluate efficiency of the method. Results show that the method is monotonic and does not produce any oscillation. In addition, an adaptive meshing technique is combined with the method to further increase accuracy of the solution, and at the same time, to minimize computational time and computer memory requirement.
基金Project partially supported by the National Natural Science Foundation of China and the Doctoral Foundation of the Educational Commission.
文摘The convective-diffusion equations are very common in applied mechanics.One-dimensional convective-diffusion equation can be given aswhere φ is the unknown function to be solved, such as conceniration, temperature, etc.,t, the time; x, the coordinate; D, the diffusive constant, and V is the velocity of fluidflow.
