An energy stable monolithic Eulerian fluid‐structure finite element method |
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Authors: | Frédéric Hecht Olivier Pironneau |
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Institution: | 1. Laboratoire Jacques‐Louis Lions, Sorbonne Universités, Paris, France;2. UPMC (Paris VI), Paris, France |
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Abstract: | When written in an Eulerian frame, the conservation laws of continuum mechanics are similar for fluids and solids leading to a single set of variables for a monolithic formulation. Such formulations are well adapted to large displacement fluid‐structure configurations, but stability is a challenging problem because of moving geometries. In this article, the method is presented; time implicit discretizations are proposed with iterative algorithms well posed at each step, at least for small displacements; stability is discussed for an implicit in time finite element method in space by showing that energy decreases with time. The key numerical ingredient is the Characterics‐Galerkin method coupled with a powerful mesh generator. A numerical section discusses implementation issues and presents a few simple tests. It is also shown that contacts are easily handled by extending the method to variational inequalities. This paper deals only with incompressible neo‐Hookean Mooney‐Rivlin hyperelastic material in 2 dimensions in a Newtonian fluid, but the method is not limited to these; compressible and 3D cases will be presented later. |
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Keywords: | characteristics‐Galerkin energy stable Eulerian formulation finite element fluid structure monolithic scheme |
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