非匹配网格的三维流固耦合问题
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摘要
为研究流固耦合问题中的非匹配网格问题的准确可靠的数值计算方法,本文提出了一种基于非匹配网格的三维Common-Refinement方法,将其应用于离散后不可压缩流体与非线性超弹性体的非重叠子区域之间的接触面。采用Petrov-Galerkin有限元法离散不可压缩流体,并对大变形弹性结构体使用连续Galerkin有限元法进行离散。同时使用任意的Lagrangian-Eulerian(ALE)方法处理流固网格的大幅变形,并且采用全解耦的隐式分区方法去分别求解流固两相。为了满足两者之间液体和弹性耦合界面间牵引力的平衡条件,研究了共同细化方法的空间插值的准确性和可靠性。根据一系列的网格划分方案,通过改流体和固体网格之间的网格匹配系数系统地评估Common-Refinement方法的准确性和精度。将本方法应用于三维标准的圆柱体-弹性板问题,并与文献中标准解进行了对比。求解结果表明了这种方法在流固耦合问题中具有足够的准确性和可靠性。
To investigate an accurate and reliable numerical calculation method to solve the non-matching mesh problem in fluid-structure coupling,this paper presents a 3 D common-refinement method for non-matching meshes between discrete non-overlapping sub-domains of incompressible fluid and nonlinear elastic structure. The incompressible fluid flow was discretized by using a stabilized Petrov-Galerkin finite element method( FEM),and the large deformation structural formulation was discretized by using a continuous Galerkin FEM. An arbitrary Lagrangian-Eulerian formulation was used to process large deformation of fluid-structure mesh,and the fully decoupled implicit partition procedure was applied to solutions of the fluid and solid phases. To satisfy traction equilibrium condition along the fluid-elastic interface with non-matching meshes,this study investigates the accuracy and reliability of the spatial interpolation in the common refinement method( CRM). According to a series of mesh division schemes,this study systematically assessed the accuracy and precision of CRM by varying grid mismatch between the fluid and solid meshes,thereby demonstrating the second-order accuracy of CRM data transmission through uniform refinements of fluid and solid meshes along the interface. This method was further applied to a 3 D benchmark problem of cylinder-elastic plate and compared with the standard solution in the literature. Results show that this method is accurate and reliable in solving the fluid-structure coupling problem.
To investigate an accurate and reliable numerical calculation method to solve the non-matching mesh problem in fluid-structure coupling,this paper presents a 3 D common-refinement method for non-matching meshes between discrete non-overlapping sub-domains of incompressible fluid and nonlinear elastic structure. The incompressible fluid flow was discretized by using a stabilized Petrov-Galerkin finite element method( FEM),and the large deformation structural formulation was discretized by using a continuous Galerkin FEM. An arbitrary Lagrangian-Eulerian formulation was used to process large deformation of fluid-structure mesh,and the fully decoupled implicit partition procedure was applied to solutions of the fluid and solid phases. To satisfy traction equilibrium condition along the fluid-elastic interface with non-matching meshes,this study investigates the accuracy and reliability of the spatial interpolation in the common refinement method( CRM). According to a series of mesh division schemes,this study systematically assessed the accuracy and precision of CRM by varying grid mismatch between the fluid and solid meshes,thereby demonstrating the second-order accuracy of CRM data transmission through uniform refinements of fluid and solid meshes along the interface. This method was further applied to a 3 D benchmark problem of cylinder-elastic plate and compared with the standard solution in the literature. Results show that this method is accurate and reliable in solving the fluid-structure coupling problem.
引文
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[13]TUREK S,HRON J.Proposal for numerical benchmarking of fluid-structure interaction between an elastic object and laminar incompressible flow[M]//BUNGARTZ H J,SCHFER M.Fluid-Structure Interaction.Berlin,Heidelberg:Springer,2006:371-385.
[2]FELIPPA C,PARK K.Staggered transient analysis procedures for coupled mechanical systems:formulation[J].Computer methods in applied mechanics and engineering,1980,24(1):61-111.
[3]GURUGUBELLI P,JAIMAN R K.Self-induced flapping dynamics of a flexible inverted foil in a uniform flow[J].Journal of fluid mechanics,2015,781:657-694.
[4]JAIMAN R K,SEN S,GURUGUBELLI P S.A fully implicit combined field scheme for freely vibrating square cylinders with sharp and rounded corners[J].Computers&fluids,2015,112:1-18.
[5]JAIMAN R,GEUBELLE P,LOTH E,et al.Combined interface boundary condition method for unsteady fluid-structure interaction[J].Computer methods in applied mechanics and engineering,2011,200(1/2/3/4):27-39.
[6]De BOER A,VAN ZUIJLEN A H,BIJL H.Review of coupling methods for non-matching meshes[J].Computer methods in applied mechanics and engineering,2007,196(8):1515-1525.
[7]DE BOER A,VAN ZUIJLEN A H,BIJL H.Comparison of conservative and consistent approaches for the coupling of non-matching meshes[J].Computer methods in applied mechanics and engineering,2008,197(49/50):4284-4297.
[8]JAIMAN R K,JIAO X,GEUBELLE P H,et al.Conservative load transfer along curved fluid-solid interface with non-matching meshes[J].Journal of computational physics,2006,218(1):372-397.
[9]JAIMAN R,JIAO X,GEUBELLE P H,et al.Assessment of conservative load transfer for fluid-solid interface with non-matching meshes[J].International journal for numerical methods in engineering,2005,65(15):2014-2038.
[10]JANSEN K E,WHITING C,HULBERT G.A generalized-αmethod for integrating the filtered Navier-Stokes equations with a stabilized finite element method[J].Computer methods in applied mechanics and engineering,2000,190(3/4):305-319.
[11]JANDRON M A,HURD R,BELDEN J,et al.Modeling of hyperelastic water-skipping spheres using abaqus/explicit[C]//Proceedings of the 2014 SIMULIA Community Conference.2014.
[12]ZEMERLI C,LATZ A,ANDRH.Constitutive models for static granular systems and focus to the Jiang-Liu hyperelastic law[R].Fraunhofer(ITWM):Fraunhofer-Institut für Techno-und Wirtschaftsmathematik,2012.
[13]TUREK S,HRON J.Proposal for numerical benchmarking of fluid-structure interaction between an elastic object and laminar incompressible flow[M]//BUNGARTZ H J,SCHFER M.Fluid-Structure Interaction.Berlin,Heidelberg:Springer,2006:371-385.