SUMMARYThe paper presents a semi-implicit algorithm for solving an unsteady fluid-structure interaction problem. The algorithm for solving numerically the fluid-structure interaction problems was obtained by combining the backward Euler scheme with a semi-implicit treatment of the convection term for the Navier-Stokes equations and an implicit centered scheme for the structure equations. The structure is governed either by the linear elasticity or by the non-linear St Venant-Kirchhoff elasticity models. At each time step, the position of the interface is predicted in an explicit way. Then, an optimization problem must be solved, such that the continuity of the velocity as well as the continuity of the stress hold at the interface. During the Broyden, Fletcher, Goldforb, Shano (BFGS) iterations for solving the optimization problem, the fluid mesh does not move, which reduces the computational effort. The term 'semi-implicit' used for the fully algorithm means that the interface position is computed explicitly, while the displacement of the structure, velocity and the pressure of the fluid are computed implicitly. Numerical results are presented.

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Summary We propose a numerical method for a fluid–structure interaction problem. The material of the structure is homogeneous, isotropic, and it can be described by the compressible neo‐Hookean constitutive equation, while the fluid is governed by the Navier–Stokes equations. Our study does not use turbulence model. Updated Lagrangian method is used for the structure and fluid equations are written in Arbitrary Lagrangian–Eulerian coordinates. One global moving mesh is employed for the fluid–structure domain, where the fluid–structure interface is an ‘interior boundary’ of the global mesh. At each time step, we solve a monolithic system of unknown velocity and pressure defined on the global mesh. The continuity of velocity at the interface is automatically satisfied, while the continuity of stress does not appear explicitly in the monolithic fluid–structure system. This method is very fast because at each time step, we solve only one linear system. This linear system was obtained by the linearization of the structure around the previous position in the updated Lagrangian formulation and by the employment of a linear convection term for the fluid. Numerical results are presented. Copyright © 2016 John Wiley & Sons, Ltd.