A Combined Mixed Finite Element And Discontinuous Galerkin Method For Simulating Wormhole Propagation

In recent years,the flow simulation of porous media has been a topic of great concern to scholars.Due to the expansion of oil production in the project and the need for new oilfield production,the acid dissolution matrix model has attracted people s attention,but it may be caused by acid dissolu-tion.Problems such as subsequent contamination make numerical predictions and experiments for such models.This special model of acid-soluble matrix is called the wormhole propagation model.This paper revolves around the analysis and simulation of the numerical format of the wormhole propagation simulation.The wormhole model is mainly composed of the reaction mass transfer equation,the Darcy or non-Darcy equation and the estimation of porosity.The model is as follows:(?)In this paper,a coupling method combined mixed finite element and discontin-uous Galerkin method has stability for the above problems.The velocity and pressure is approximated by Raviart-Thomas hybrid finite element method,and the reaction mass transfer equation is approximated by using internal penalty discontinuous Galerkin method.Then a priori error estimates of the flow equation are obtained by using the stability condition,and the optimal order estimates for all kind of internal penalty discontinuous Galerkin methods are obtained by the properties of hp interpolation.And the analytical solution is constructed to verify the convergence order of the error estimate.This paper mainly discusses the stability and convergence of the coupling algorithm for the above model.The full text is divided into four chapters:The first chapter introduces the background of the Combined mixed el-ement method and discontinuous Galerkin method coupling method,the re-search status at homeland and abroad and the knowledge of wormhole propa-gation model.The second chapter gives the semi-discrete format of the mixed element method and discontinuous Galerkin method of wormhole propagation simula-tion,and gives the stability analysis of the format.The third chapter gives the convergence analysis of the mixed element discontinuous element coupling scheme of wormhole propagation simulation,and validates the theoretical results with numerical examples.The forth chapter gives the summary of the content of this article.