Transient finite element method for calculating steady state three‐dimensional free surfaces

In order to reduce the cost of large three‐dimensional calculations of steady state free surfaces, we have combined a time‐dependent approach, a decoupling algorithm and a conjugate gradient solver along the lines introduced earlier by Gresho and Chan. The free surface is calculated separately by applying the kinematic condition to a number of faces defined on the undeformed surface. For the pseudo‐time‐marching technique we show that it is economical to adopt different time steps for the free surface calculation and the other fields. The accuracy of the method is tested on the well‐known circular die problem; the method is then used to reveal the effects of inertia and shear thinning on square and rectangular dies.