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| An Energy Stable Monolithic Eulerian Fluid-Structure Numerical Scheme |
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Citation： |
Olivier PIRONNEAU.An Energy Stable Monolithic Eulerian Fluid-Structure Numerical Scheme[J].Chinese Annals of Mathematics B,2018,39(2):213~232 |
| Page view： 1222
Net amount： 862 |
Authors： |
Olivier PIRONNEAU; |
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| Abstract： |
The conservation laws of continuum mechanics, written in an
Eulerian frame, do not distinguish fluids and solids, except in the
expression of the stress tensors, usually with Newton's hypothesis
for the fluids and Helmholtz potentials of energy for hyperelastic
solids. By taking the velocities as unknown monolithic methods for
fluid structure interactions (FSI for short) are built. In this
paper such a formulation is analysed when the solid is compressible
and the fluid is incompressible. The idea is not new but the
progress of mesh generators and numerical schemes like the
Characteristics-Galerkin method render this approach feasible and
reasonably robust. In this paper the method and its discretisation
are presented, stability is discussed through an energy estimate. A
numerical section discusses implementation issues and presents a few
simple tests. |
Keywords： |
Fluid-Structure interactions, Numerical method, Energy stability, Finite element method |
Classification： |
65M60, 74F10, 74S30, 76D05, 76M25 |
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