Two-grid Algorithm For The Coupled Stokes-Darcy System Based On Domain Decomposition Method

Stokes-Darcy coupling model is widely used in the simulation of groundwater flow and blood diffusion in blood vessels.For the Stokes-Darcy coupling system with Beavers-Joseph-Saffman(BJS)interface conditions,this paper proposes a two-grid algorithm based on domain decomposition(TGDDM).The main purpose is to com-bine the advantages of the domain decomposition method and the two-grid method to save computational resources and time on the premise that the algorithm has good convergenceFirst of all,we establish the Stokes-Darcy coupling model by using the mass inter-face,force balance,and BJS conditions as the interface conditions of the model,then give the weak form of the decoupling problem,after then use the existing Robin do-main decomposition algorithm to obtain the approximate solution of the coarse mesh problem.The coarse mesh approximation is used to replace some interface terms of the fine mesh problem.Instead of iterating,the solution of the fine mesh problem is obtained directly.In addition,we perform an error analysis on the TGDDM algorithm.and the results show that there is an optimal error order O(h2)when the coarse mesh size H and the fine mesh size h satisfy H=h4/5.When H=h2/3,due to the limited technology,the error order is O(h5/3),which does not achieve the purpose of the op-timal error order.At the same time,we extend the error analysis of the algorithm to a finite element space of high-order approximation O(hm)and propose corresponding conjecturesThree numerical experiments were performed at the end of the article.Experiment 1 is a problem,and its exact solution is known.We use the TGDDM algorithm to calculate coarse and fine grids of different sizes.The results show that the optimal error order when H=h2/3 should be O(h2),which indicates that the error order O(h5/3)obtained by the analysis is not optimal.Experiments 2 and 3 are a general model and a simplified petroleum extraction problem,respectively.These two problems are simulated with TGDDM and finite element DDM,and the results show that both methods are stable.In all three experiments,we compared the CPU time of TGDDM with finite element DDM,and concluded that TGDDM can save much CPU time.