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SUMMARYThis paper describes the application of the Taylor-Galerkin method to the calculation of incompressible viscous flows. A finite element fractional-step method for the Navier-Stokes equations is combined with the Taylor-Galerkin method to achieve an accurate treatment of the convection part of the problem. A scheme of second-order accuracy in time for the non-linear convection written in non-conservative form is presented. Numerical results are provided to illustrate the quality of the computed transient solutions in two dimensions.

The difficulties encountered in the use of standard, Galerkin‐type, parabolic isoparametric elements for explicit transient analysis are illustrated. These are associated with the mass lumping procedure as well as with incoherencies in the nodal loads induced by the element local field. To overcome these difficulties, it is suggested that the parabolic element equations be formulated by a weighted residual method in which the weighting functions are the usual serendipity functions modified by an appropriate bubble‐shape function. It is shown that such a formulation enables all the shortcomings of the Galerkin approach to be overcome. An example problem indicates the extent of improvement in results that can be obtained by the proposed method.

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