1. The Lagrange-Galerkin method for fluid-structure interaction problems
- Author
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Jean-François Scheid, Jorge San Martín, Loredana Smaranda, Departamento de Ingeniería Matemática, Facultad de Ciencias Fisicas y Matemáticas, Institut Élie Cartan de Lorraine (IECL), Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS), Department of Mathematics and Computer Science, Faculty of Mathematics and Computer Science, CORIDA, ECOS-CONICYT, and BMC, Ed.
- Subjects
Backward differentiation formula ,fish swimming ,Algebra and Number Theory ,Finite elements for Navier-Stokes equations ,Mathematical analysis ,010103 numerical & computational mathematics ,Exponential integrator ,01 natural sciences ,Euler equations ,characteristics method ,010101 applied mathematics ,Physics::Fluid Dynamics ,symbols.namesake ,Multigrid method ,Collocation method ,symbols ,[MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP] ,0101 mathematics ,[MATH.MATH-AP] Mathematics [math]/Analysis of PDEs [math.AP] ,Galerkin method ,Differential algebraic equation ,Analysis ,Mathematics ,Numerical partial differential equations - Abstract
In this paper, we consider a Lagrange-Galerkin scheme to approximate a two-dimensional fluid-structure interaction problem. The equations of the system are the Navier-Stokes equations in the fluid part, coupled with ordinary differential equations for the dynamics of the solid. We are interested in studying numerical schemes based on the use of the characteristics method for rigid and deformable solids. The schemes are based on a global weak formulation involving only terms defined on the whole fluid-solid domain. Convergence results are stated for both semi and fully discrete schemes. This article reviews known results for rigid solid along with some new results on deformable structure yet to be published.
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