A Study Of Decoupling Methods For Non-steady Incompressible Navier-Stokes/Darcy Model

In the past two decades,the study of fluid-structure interaction has become a research hotspot in computational fluid dynamics,especially the coupling of free flow and porous media flow..there are great applications in practical industrial production,medicine and earth science research,such as,which simulates the flow process of the river bed and can also describe various industrial processes that are related to filtration.Thus,it is a very necessary research subject to search more effective numerical methods.In this paper,we propose and analyze a new decoupled characteristic stabilized finite element(DCSFE)method for time-dependent Navier-Stokes/Darcy model.The key idea lies in combining the characteristic method with stabilized finite element method to solve the decoupled model by using the lowest-order conforming finite element space.In this method,the original model is divided into two parts,one is the non-stationary Navier-Stokes equation,the other is the Darcy equation.To deal with the difficulty caused by trilinear term with nonzero boundary condition,the characteristic method is used.On the other hand,the lowest-order finite element pair don't satisfy LBB condition,therefore stabilized technique is provided to overcome this flaw.The stability and convergence analysis of the numerical method are established.The results of numerical examples illuminate that it can improve efficiency of the solution.In addition,in order to further improve the efficiency of the solution,characteristic stabilized finite element(DCSFE)method with different sub-domain time steps is also studied.the stability of the numerical method ia proved and the error estimates are estimated.Numerical examples show that the method further improves the efficiency of the solution.