Physics – Fluid Dynamics
Scientific paper
1999-04-27
Computer Methods in Applied Mechanics and Engineering, 180:219-238, 1999
Physics
Fluid Dynamics
26 pages, 2 figures, lemma 2 proof corrected
Scientific paper
In this work the issue of whether key energetic properties (nonlinear, exponential-type dissipation in the abscence of forcing and long-term stability under conditions of time dependent loading) are automatically inherited by deforming reference descriptions is resolved. These properties are intrinsic to real flows and the conventional Navier-Stokes equations. A completely general reference description of an incompressible, Newtonian fluid, which reconciles the differences between opposing schools of thought in the literature is derived for the purposes of this investigation. The work subsequently focusses on establishing a class of time discretisations which inherit these self-same energetic properties, irrespective of the time increment employed. The findings of this analysis have profound consequences for the use of certain classes of finite difference schemes in the context of deforming references. It is significant that many algorithms presently in use do not automatically inherit the fundamental qualitative features of the dynamics. An `updated' approach as a means of avoiding ever burgeoning deformation gradients and a still further simplified implementation are further topics explored.
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