| The theory of poroelasticity is about the intersection between solid mechanics and fluid flow in porous media.It consists of a.mass conservation equation and a momentum conservation equation.The classical poroelastic model i.e.Biot model has been applied in various area,such as reservoir engineering.environmental engineering.In this case the fluid flow is described by Darcy’s law,the permeability and porosity is low,the fluid velocity is low.As the fluid velocity gradually increases.the relationship between flow velocity and pressure gradient changes into nonlinear.Darcy’s law no longer applies in this case,the Darcy-Forchheimer law is needed.In this thesis,the 3-field poroelastic model is considered.in which the fluid flow is described by Darcy-Forchheimer law.The model is nonlinear,the unknown variables are the displacement of solid phase u,the fluid velocity q and the fluid pressure p.The governing equations are defined as follows:(?).In this thesis,the linear finite element method is applied for the solid displacement,the RT mixed finite element method is applied for the fluid velocity and pressure.We analyze the error estimates of this method.And then we apply the BR finite element in place of the linear finite element to approximate the displacement.This method is Stokes-Biot stable,so this is stable about the Lamé constant λ and the constrained specific storage coefficient c0.Numerical experiments confirm the convergence rates of the two methods which are in consistent with the theoretical analysis. |
