Refactorization of Cauchy’s Method: A Second-Order Partitioned Method for Fluid–Thick Structure Interaction Problems

This work focuses on the derivation and analysis of a novel, strongly-coupled partitioned method for fluid–structure interaction problems. The flow is assumed to be viscous incompressible, structure modeled using linear elastodynamics equations. We assume that thick, i.e., same number spatial dimensions as fluid. Our newly developed numerical based Robin boundary conditions, well refactorization Cauchy’s one-legged ‘ $$\theta $$ -like’ method, written sequence Backward Euler–Forward Euler steps used discretize problem in time. family methods, parametrized by , B-stable any \in [\frac{1}{2} 1]$$ second-order accurate = \frac{1}{2} + {\mathcal {O}}(\tau )$$ where $$\tau time step. In proposed algorithm, fluid sub-problems, discretized scheme, are first solved iteratively until convergence. Then, variables linearly extrapolated, equivalent solving Forward prove iterative procedure convergent, stable provided [\frac{1}{2},1]$$ . Numerical examples, finite element discretization space, explore convergence rates different values parameters problem, compare our other schemes from literature. also both monolithic non-iterative solver benchmark with within physiological range blood flow, obtaining an excellent agreement scheme.