Behaviour of Lagrangian triangular mixed fluid finite elements

The behaviour of mixed fluid finite elements, formulated based on the Lagra ngian frame of reference, is investigated to understand the effects of lock ing due to incompressibility and irrotational constraints. For this purpose , both linear and quadratic mixed triangular fluid elements are formulated. It is found that there exists a close relationship between the penalty fin ite element approach that uses reduced/selective numerical integration to a lleviate locking, and the mixed finite element approach. That is, performin g reduced/selective integration in the penalty approach amounts to reducing the order of pressure interpolation in the mixed finite element approach f or obtaining similar results. A number of numerical experiments are perform ed to determine the optimum degree of interpolation of both the mean pressu re and the rotational pressure in order that the twin constraints are satis fied exactly. For this purpose, the benchmark solution of the rigid rectang ular tank is used. It is found that, irrespective of the degree of mean and the rotational pressure interpolation, the linear triangle mesh, with or w ithout central bubble function (incompatible mode), locks when both the con straints are enforced simultaneously. However, for quadratic triangle, line ar interpolation of the mean pressure and constant rotational pressure ensu res exact satisfaction of the constraints and the mesh does not lock. Based on the results obtained from the numerical experiments, a number of import ant conclusions are arrived at.