Mixed Volume Element Method For Two-Dimensional Darcy-Forchheimer Model

Fluid in porous media flows at a low speed, small pores, permeable condi-tions, Darcy velocity and pressure gradients meet a simple linear relationship, i.e. Darcy’s law. When the flow rate of the fluid continued to increase, Darcy velocity and pressure gradient meet a non-linear relationship, then we must use the Darcy-Forchheimer Equation to describe it.In this paper, we firstly consider mixed finite volume method on rectangular grids for the Two-dimensional Darcy-Forchheimer model We take the lowest order Raviart-Thomas finite element space and piecewise con-stant function space as the solution function space, we introduce the migration op-erator γh, the lowest order Raviart-Thomas finite element space is mapped into the trial function space. which makes it easy to construct the space. And the method also has the advantages of a high order of accuracy, high parallelizability and so on.secondly,it proves the existence and uniqueness of solutions for mixed finite volume method, introduces some lemma. By making the numerical analysis,we obtain the optimal error estimates of L2-norm and Hdiv-norm about the unknown function solutions. Finally, we consider the numerical simulation for linear equations and nonlinearequations, so we prove the validity of the conclusions.