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Acceleration of a fixed point algorithm for fluid-structure interaction using transpiration conditions. (English) Zbl 1118.74315
Summary: We address the numerical solution of fluid-structure interaction problems. This issue is particularly difficulty to tackle when the fluid and the solid densities are of the same order, for instance as it happens in hemodynamic applications, since fully implicit coupling schemes are required to ensure stability of the resulting method. Thus, at each time step, we have to solve a highly non-linear coupled system, since the fluid domain depends on the unknown displacement of the structure. Standard strategies for solving this non-linear problems, are fixed point based methods such as Block-Gauss-Seidel (BGS) iterations. Unfortunately, these methods are very CPU time consuming and usually show slow convergence. We propose a modified fixed-point algorithm which combines the standard BGS iterations with a transpiration formulation. Numerical experiments show the great improvement in computing time with respect to the standard BGS method.

MSC:
74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
65M99 Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems
76D05 Navier-Stokes equations for incompressible viscous fluids
76M25 Other numerical methods (fluid mechanics) (MSC2010)
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