Research On Improved Groundwater Darcy Velocity Methods And Numerical Simulation Based On Multiscale Finite Element Method

The Darcy velocity field is of great significance for research in water environment assessment and groundwater pollution prevention.The continuous,stable,and accurate groundwater Darcy velocity field can accurately describe the convection term and improve the simulation accuracy of the convection-dispersion equation,and is also the key to establishing an accurate groundwater solute transport model.However,traditional methods such as finite element method obtain nodal Darcy velocity by directly solving the first-order derivative of the head.The first-order derivative values obtained by these methods are discontinuous at the node of the element,which cannot guarantee the continuity of Darcy velocity and may lead to the inflow and outflow at cross section unequal,which does not conform to the actual physical law.On the other hand,when dealing with heterogeneous problems,the traditional finite element method requires that the internal permeability coefficient of each element is constant,and often requires fine enough division to obtain a more accurate solution,which consumes a lot of computational cost and the solution efficiency is low.Therefore,it is of great significance to research accurate and efficient groundwater Darcy velocity method.In this paper,by combining the professional knowledge of hydrogeology and mathematics,a precise and efficient numerical calculation method of groundwater is carried out.By combining finite element dual-mesh method and multiscale finite element method,a dual-mesh multiscale finite element method is proposed to solve Darcy velocity efficiently.Finite element dual-mesh method can ensure the continuity of the Darcy velocity.It constructs double grids by translating the original grid for a very small distance and only needs to solve the water flow equation to obtain continuous nodal Darcy velocity.It has simple principles and easy operation.On the other hand,the multiscale finite element method can significantly reduce the computational cost of simulate heterogeneous groundwater problems by increasing scale.This method constructs base functions by solving simplified elliptic equations on the element.The multiscale base functions can accurately reflect the heterogeneity of the media,and then use the finite element format to assemble the total stiffness matrix on the coarse grid.So that small-scale information can be reflected into large-scale without solving at each small-scale.The multiscale finite element method does not require the internal permeability of each element to be constant,which can greatly improves the calculation efficiency and accuracy.Combining the advantages of finite element dual-mesh method and multiscale finite element method,the dual-mesh multiscale finite element method proposed in this paper can apply multiscale base functions to solve the head directly on the coarse grid,and apply finite element dual-mesh method to simulate nodal Darcy velocity.Therefore,it breaks through the limitations of the traditional finite element basic framework and improves the computational efficiency extremely in comparison to traditional nodal Darcy velocities methods.This paper also verifies the applicability and accuracy of dual-mesh multiscale finite element method in situation of two-dimensional stable flow with homogeneous permeability,two-dimensional stable flow with heterogeneous oscillating permeability,and two-dimensional transient flow with gradual permeability.Meanwhile the results are compared with Batu's finite element dual-mesh method and Yeh's Galerkin model and Finely divided Yeh's Galerkin model.It is found that dual-mesh multiscale finite element method can obtain the similar accuracy with Yeh's Galerkin model,the saves 90% of the calculation time.This method can also directly obtain the fine-scale nodal Darcy velocities by using the coarse-scale nodal Darcy velocities and the multiscale base functions,which can save a lot of computational cost.This study may provide a new approach to simulate nodal Darcy velocities in aquifers efficiently.