A Finite Element numerical method has been developed to simulate the fluid flow over two dimensional and time dependent domains with rigid moving objects or boundaries. This method falls under the general category of Arbitrary Lagrangian Eulerian methods. In this method the global mesh is fixed and adaptations are made locally in both space and time to describe interface movement. Therefore, the global mesh is independent of interface movement, and the possibility of mesh entanglement is eliminated. During the simulations, very small elements or elements with very large aspect ratios as compared with the elements of the fixed mesh may be generated to correctly describe the position and shape of the interfaces, these elements are then combined with the adjacent mesh elements which are much larger and used together in the calculations. The question of how these large abrupt changes in the mesh affect the accuracy of the calculations is examined through local truncation error analysis and numerical experiments. The two-dimensional flow between two plates separating at a prescribed speed, which admits an analytical solution, is used to verify and illustrate the results. It is determined that the accuracy of the calculations is not adversely affected by the large and abrupt changes in the size of the elements and that the convergence rate of the method is of second order. The behavior of the local error next to the interfaces is shown to be of the same order as in the rest of the computational domain.
FEM, ALE, Error Assessment, Moving Boundary
Level of Degree
First Committee Member (Chair)
Second Committee Member
Hatamipourdehnow, Vahid. "Error Assessment in FEM Calculations of Flows with Moving Boundaries." (2015). https://digitalrepository.unm.edu/me_etds/88