期刊
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS
卷 85, 期 7, 页码 430-446出版社
WILEY
DOI: 10.1002/fld.4388
关键词
characteristics-Galerkin; energy stable; Eulerian formulation; finite element; fluid structure; monolithic scheme
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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