Eddy Viscosity-FV Methods For The Linear Time-Dependent Convection Dominated Diffusion Problem

The problem of convection dominated diffusion has been the research hotspot at present. Due to the hyperbolic character of this problem and the effect of the term of diffusion, conventional solution of Garlerkin finite element often appears false numeric surge. After 1970s, a good many non-standard finite element methods are discu- ssed. Although they have different configurations, they have a comm- on starting point:trying to deal with the term of convection, numeric computation to some extent can image the character of convection dominated and avoid numeric surge. There are comparatively impor- tant methods: finite volume method and subgrid scale eddy viscosity method. finite volume method can keep the character of original physical problem, especially for conservation, and also its calculation scheme is relatively easy; the stability of the solution which is get by subgrid scale eddy viscosity method is higher and the accuracy is improved. In order to utilize the advantages of finite volume method and subgrid scale eddy viscosity method and overcome some lack of each method, a kind of method which is combined finite volume method and subgrid scale eddy viscosity method to deal with the linear time-dependent convection dominated convection diffusion problem is proposed. It is showed by the theoretical analysis on this format that the method which is proposed in this paper can enhance the stability of the solution and overcome the phenomenon of false numeric surge. Meanwhile, the accuracy of the solution by subgrid scale eddy visco- sity method is gained.