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Abstract In this paper a method is presented that can be used for both the Lagrangian and the Eulerian solution of the Navier–Stokes equations in a domain of arbitrary shape, bounded by boundaries which move in any prescribed time‐varying fashion. The method uses the integral form of the governing equations for an arbitrary moving control volume, with pressure and Cartesian velocity components as dependent variables. Care is taken to also satisfy the space conservation law, which ensures a fully conservative computational procedure. Fully implicit temporal differencing makes the method stable for any time step. A detailed description is provided for the discretization in two dimensions, with a collocated arrangement of variables. Central differences are used to evaluate both the convection and diffusion fluxes. The well known SIMPLE algorithm is employed for pressure–velocity coupling. The resulting algebraic equation systems are solved iteratively in a sequential manner. Results are presented for a flow in a channel with a moving indentation; they show favourable agreement with experimental observations.
Demirdžić et al. (Tue,) studied this question.