A velocity approach for the ALE-method applied to 2D and 3D problems

An improved, gradient based ALE-method, is introduced and investigated for both the 2D and the 3D case. A new method for the mesh velocity computation is applied. The method is based on discretising the Laplace equation with finite elements. An upwind transport algorithm using the finite element data structure is introduced. After the ALE-method is introduced, it is tested with the Molenkamp test. The material velocity and the mesh velocity are prescribed in this case, therefore only the transport part of the ALE formulation is tested. The transport algorithm is stable, and shows acceptable results in this severe test case. In the 3D case the algorithm is less accurate and it does not show oscillations. In the 2D case the algorithm is more accurate, but there are oscillations. Subsequently, a 2D forging simulation is carried out, for which the ALE method gives better results than the Updated Lagrangian method.