Splitting schemes for a Lagrange multiplier formulation of FSI with immersed thin walled structure: stability and convergence analysis
The numerical approximation of incompressible fluid structure interaction problems with Lagrange mul tiplier is generally based on strongly coupled schemes. This delivers unconditional stability but at the expense of solving a computationally demanding coupled system at each time step. For the case of the coupling with immersed thin walled solids, we introduce a class of semi implicit coupling schemes which avoids strongly coupling without compromising stability and accuracy. A priori energy and error estimates are derived. The theoretical results are illustrated through numerical experiments in an academic benchmark.
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