Mesh shape preservation for flow-induced vibration problems

This paper describes a numerical technique that can prevent the mesh from severe distortion in flow-induced vibration calculations. An orthogonal transformed space that is related to the physical space through a Laplacian equation is introduced. At each time step, the mesh may deform significantly in the physical space due to structural vibration, but the mesh nodal value in the transformed space remains constant. As long as the coordinates in the physical space can be adjusted to render the transformed space independent of time, the mesh shape in the physical space is preserved, even though the mesh area may enlarge or reduce significantly. For simplicity, a two-dimensional flow-induced vibration problem is used to illustrate this method. Two side-by-side elastic cylinders in a cross flow are considered. The Reynolds number is fixed at 200, corresponding to a laminar wake. The mass ratio is chosen to be small so that large displacements of the cylinders can be realized. Predictions with and without mesh preservation are compared. The difference between the two results could be as large as 25% in the prediction of the mean transverse displacements of the cylinders. The method could be extended to three-dimensional flow-induced vibration problems without much difficulty.