Investigation of the Arbitrary Lagrangian Eulerian Formulation to Simulate Shock Tube Problems

A critical step in modeling complex problems using numerical simulations is validating the numerical approach using simplified problems. The current study investigates application of the Arbitrary Lagrangian Eulerian (ALE) formulation, as implemented in LS-DYNA, to simulate a pseudo 1-D shock tube problem. The shock tube problem was selected since analytical results can be directly determined from the initial conditions. A shock tube is modeled as two regions of fluid at two different pressures separated by a thin membrane. The two regions are usually, but not necessarily, comprised of the same fluid. One region, know as the driver, is at a higher pressure than the other. Ideally, the thin membrane is completely destroyed to initiate flow, allowing the high pressure region to interact with the low pressure region. If the difference in pressures between the two regions is sufficient, a shock wave will propagate into the low pressure region and an expansion wave will propagate into the high pressure region. The current study is conducted to test the ability of the ALE formulation in LS-DYNA to correctly predict the shock and expansion wave propagation seen in a shock tube test. The results of this study are dependent on a number of factors such as the size and orientation of the mesh. A convergence study to determine the minimum mesh density to correctly simulate the shock phenomena was also conducted. This is of special importance when the ALE formulation is used in real world problems where the required mesh size can become quite large, and therefore computationally prohibitive.