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This paper describes thee different numerical methods for the computation of flows with moving immersed elastic boundaries. A two-dimensional incompressible fluid and a boundary in the form of a simple closed curve are considered. The inertia is assumed to be negligible and the Stokes equations are solved. The three methods are explicit, approximate-implicit, and implicit. The first two have been used before, but the implicit method is new in the context of flows with moving immersed boundaries. They differ only with respect to the computation of the boundary force. The results of the above methods at various values of the time-step size are compared in order to explore the numerical stability of the computation.
Tu et al. (Sun,) studied this question.