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A method of a floating frame of reference that performs splitting of a deformable solid into rigid and deforming parts is presented within the context of non-smooth contact dynamics. The decomposition is made in such a way that the deforming part of the velocity field does not contribute either to the motion of the center of mass or the rotational motion. The corresponding numerical method that computes both rigid and deforming motions is presented and extended to multi-body dynamics simulation allowing non-smooth contact interactions, such as impacts and friction. Numerical experiments, where the method is compared with a more traditionally used Total Lagrangian method, justify its preference as a more efficient tool for the simulation of assemblies of stiff and massive objects.

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The paper introduces a finite element method for the Navier-Stokes equations of incompressible viscous fluid in a time-dependent domain. The method is based on a quasi-Lagrangian formulation of the problem and handling the geometry in a time-explicit way. We prove that numerical solution satisfies a discrete analogue of the fundamental energy estimate. This stability estimate does not require a CFL time-step restriction. The method is further applied to simulation of a flow in a model of the left ventricle of a human heart, where the ventricle wall dynamics is reconstructed from a sequence of contrast enhanced Computed Tomography images.