Parallel Three-domain Domain Decomposition Method Of Stokes-Darcy Coupled Model

There are a large number of multi-physics and multi-domain problems in engineering nature,such as the Stokes-Darcy model,which describes the coupling phenomenon of free flow and porous media flow,and can be used to simulate processes such as oil extraction and groundwater pollution.In this thesis,two domain decomposition methods(DDM)are proposed for the Stokes-Darcy coupled problem with the BeaversJoseph-Saffman(BJS)interface condition:a superimposed parallel three-domain DDM and a non-superimposed parallel three-domain DDM.Based on the multi-physics and multi-domain characteristics of the Stokes-Darcy model,this thesis uses the domain decomposition idea to decompose the global domain of the model into two subdomains,Stokes and Darcy,and then performs secondary domain decomposition on the Darcy subdomain,and the three domains are solved in parallel,thereby saving computing time and cost.Specifically,this thesis first expresses the interface conditions to divide the Stokes-Darcy problem into a free flow domain and a porous media domain,and then divides the porous media domain into two superimposed or non-superimposed subdomains for the first time.Because of the interaction between the free flow domain and the porous media domain,we can't simply combine the domain decomposition method of the Stokes-Darcy model and the classical elliptic model to solve the Stokes-Darcy problem.In this thesis,by constructing Robin-type interface conditions,the decoupling weak form of domain decomposition is deduced,and two parallel three-domain DDMs are constructed by combining compatibility conditions to realize parallel computing.In this thesis,the convergence of two parallel three-domain DDMs is theoretically analyzed,and numerical examples verify the accuracy and effectiveness of the algorithm.