Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: ,  develop a mass conservative multiscale method for coupled flow and transport in heterogeneous porous media.  consider a coupled system consisting of a convection-dominated transport equation and a flow equation.  construct a coarse grid solver based on the Generalized Multiscale Finite Element Method (GMsFEM) for a coupled system. In particular, multiscale basis functions are constructed based on some snapshot spaces for the pressure and the concentration equations and some local spectral decompositions in the snapshot spaces. The resulting approach uses a few multiscale basis functions in each coarse block (for both the pressure and the concentration) to solve the coupled system.  use the mixed framework, which allows mass conservation. Our main contributions are: (1) the development of a mass conservative GMsFEM for the coupled flow and transport; (2) the development of a robust multiscale method for convection-dominated transport problems by choosing appropriate test and trial spaces within Petrov-Galerkin mixed formulation.  present numerical results and consider several heterogeneous permeability fields. Our numerical results show that with only a few basis functions per coarse block,  can achieve a good approximation.
['Eric T. Chung', 'Yalchin Efendiev', 'Wing Tat Leung', 'Jun Ren']
I am writing a research paper on a idea Multiscale Simulations for Coupled Flow and Transport Using the Generalized Multiscale Finite Element Method
[{"from": "human", "value": "I am writing a research paper on a idea Multiscale Simulations for Coupled Flow and Transport Using the Generalized Multiscale Finite Element Method"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: ,  develop a mass conservative multiscale method for coupled flow and transport in heterogeneous porous media.  consider a coupled system consisting of a convection-dominated transport equation and a flow equation.  construct a coarse grid solver based on the Generalized Multiscale Finite Element Method (GMsFEM) for a coupled system. In particular, multiscale basis functions are constructed based on some snapshot spaces for the pressure and the concentration equations and some local spectral decompositions in the snapshot spaces. The resulting approach uses a few multiscale basis functions in each coarse block (for both the pressure and the concentration) to solve the coupled system.  use the mixed framework, which allows mass conservation. Our main contributions are: (1) the development of a mass conservative GMsFEM for the coupled flow and transport; (2) the development of a robust multiscale method for convection-dominated transport problems by choosing appropriate test and trial spaces within Petrov-Galerkin mixed formulation.  present numerical results and consider several heterogeneous permeability fields. Our numerical results show that with only a few basis functions per coarse block,  can achieve a good approximation."}]